The speed of the car is approximately 29.02 km/h, given that it traveled 18.0 miles in 0.969 hours.
To convert the speed of the car from miles per hour to kilometers per hour, we need to use the conversion factor that 1 mile is equal to 1.60934 kilometers.
Given:
Distance traveled = 18.0 milesTime taken = 0.969 hoursTo calculate the speed of the car, we divide the distance traveled by the time taken:
Speed (in miles per hour) = Distance / Time
Speed (in miles per hour) = 18.0 miles / 0.969 hours
Now, we can convert the speed from miles per hour to kilometers per hour by multiplying it by the conversion factor:
Speed (in kilometers per hour) = Speed (in miles per hour) × 1.60934
Let's calculate the speed in kilometers per hour:
Speed (in kilometers per hour) = (18.0 miles / 0.969 hours) × 1.60934
Speed (in kilometers per hour) = 29.02 km/h
Therefore, the speed of the car is approximately 29.02 km/h.
The complete question should be:
The speed of a car is found by dividing the distance traveled by the time required to travel that distance. Consider a car that traveled 18.0 miles in 0.969 hours. What's the speed of car in km / h (kilometer per hour)?
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2- Magnetic brakes are used to bring subway cars to a stop. Treat the 4000 kg subway cart as a 3m long bar sliding along a pair of conducting rails as shown. There is a magnetic field perpendicular to the plane of the rails with a strength of 2 T. a) Given an initial speed 20m/s, find the average deceleration and force required to bring the train to a stop over a distance of 40m. b) As the train moves along the rails, a current is induced in the circuit. What is the magnitude & direction of the initial induced current? (Assume the rails are frictionless, and the subway car has a resistance of 1 kilo-ohm, and the magnitude c) What must be the direction of the magnetic field so as to produce a decelerating force on the subway car? There is no figure.
a) The average deceleration required to bring the train to a stop over a distance of 40m is approximately -5 m/s^2. The force required is approximately -20,000 N (opposite to the initial direction of motion).
b) The magnitude of the initial induced current is approximately 10 A, flowing in the direction opposite to the initial motion of the subway car.
c) The magnetic field should be directed opposite to the initial direction of motion of the subway car to produce a decelerating force.
a) To find the average deceleration and force required, we can use the equations of motion. The initial speed of the subway car is 20 m/s, and it comes to a stop over a distance of 40 m.
Using the equation:
Final velocity^2 = Initial velocity^2 + 2 × acceleration × distance
Substituting the values:
0^2 = (20 m/s)^2 + 2 × acceleration × 40 m
Simplifying the equation:
400 m^2/s^2 = 800 × acceleration × 40 m
Solving for acceleration:
acceleration ≈ -5 m/s^2 (negative sign indicates deceleration)
To find the force required, we can use Newton's second law:
Force = mass × acceleration
Substituting the values:
Force = 4000 kg × (-5 m/s^2)
Force ≈ -20,000 N (negative sign indicates the force opposite to the initial direction of motion)
b) According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electromotive force (EMF) and, consequently, a current in a closed circuit. In this case, as the subway car moves along the rails, the magnetic field perpendicular to the rails induces a current.
The magnitude of the induced current can be calculated using Ohm's law:
Current = Voltage / Resistance
The induced voltage can be found using Faraday's law:
Voltage = -N × ΔΦ/Δt
Since the rails are frictionless, the only force acting on the subway car is the magnetic force, which opposes the motion. The induced voltage is therefore equal to the magnetic force multiplied by the length of the bar.
Voltage = Force × Length
Substituting the given values:
Voltage = 20,000 N × 3 m
Voltage = 60,000 V
Using Ohm's law:
Current = Voltage / Resistance
Current = 60,000 V / 1000 Ω
Current ≈ 60 A
The magnitude of the initial induced current is approximately 60 A, flowing in the direction opposite to the initial motion of the subway car.
c) To produce a decelerating force on the subway car, the direction of the magnetic field should be opposite to the initial direction of motion. This is because the induced current generates a magnetic field that interacts with the external magnetic field, resulting in a force that opposes the motion of the subway car. The direction of the magnetic field should be such that it opposes the motion of the subway car.
To bring the subway car to a stop over a distance of 40 m, an average deceleration of approximately -5 m/s^2 is required, with a force of approximately -20,000 N (opposite to the initial direction of motion). The magnitude of the initial induced current is approximately 60 A, flowing in the opposite direction to the initial motion of the subway car. To produce a decelerating force, the direction of the magnetic field should be opposite to the initial direction of motion.
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Four 700 gram masses are the four corners of a square with sides of 50.0 centimeters. Find the gravitational force on one mass as a result of the other three. G = 6.67 * 10^-11 Nm^2/kg^2.
The gravitational force on one mass as a result of the other three is 3.27 x 10⁻¹⁰ N.
What is the gravitational mass on one mass?The gravitational force on one mass as a result of the other three is calculated by applying the following formula;
F = Gm₁m₄/r₁₄² + Gm₂m₄/r₂₄² + Gm₃m₄/r₃₄²
F = G[m₁m₄/r₁₄² + m₂m₄/r₂₄² + m₃m₄/r₃₄²]
where;
G is the universal gravitational constantr is the distance between the massThe distance between the masses are equal, except the two masses on the opposite diagonal.
the distance on opposite diagonal = r₁₄
r₁₄ = √(50² + 50²)
r₁₄ = 70.71 cm = 0.707 m
The gravitational force on one mass as a result of the other three is calculated as;
F = G[m₁m₄/r₁₄² + m₂m₄/r₂₄² + m₃m₄/r₃₄²]
m₁ = m₂ = m₃ = m₄ = 0.7 kg
F = Gm²(1/r₁₄² + 1/r₂₄² + 1/r₃₄²)
F = 6.67 x 10⁻¹¹ x (0.7²) [1/0.707² + 1/0.5² + 1/0.5²]
F = 3.27 x 10⁻¹⁰ N
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a
cylinder of radius .35 m is released from rest to roll down a
frictionless slope, the cylinder has a velocity of 4.85 m/s. what
vertical height did the cylinder start from?
The principle of conservation of mechanical energy states that in a closed system where only conservative forces (such as gravity or elastic forces) are acting, the total mechanical energy remains constant over time. The cylinder started from a vertical height of approximately 0.621 meters.
To determine the vertical height from which the cylinder started, we can use the principle of conservation of mechanical energy. The mechanical energy of the cylinder is conserved as it rolls down the frictionless slope, so the initial potential energy is equal to the final kinetic energy.
The potential energy (PE) of the cylinder at the initial height can be calculated using the formula:
[tex]PE = m * g * h[/tex]
where m is the mass of the cylinder, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the vertical height.
The kinetic energy (KE) of the cylinder at the final velocity can be calculated using the formula:
[tex]KE = (1/2) * I * \omega^2[/tex]
where I is the moment of inertia of the cylinder and ω is the angular velocity.
For a solid cylinder rolling without slipping, the moment of inertia can be expressed as:
[tex]I = (1/2) * m * r^2[/tex]
where r is the radius of the cylinder.
Since the cylinder is released from rest, the initial velocity is 0 m/s, and thus the initial kinetic energy is also 0.
Setting the initial potential energy equal to the final kinetic energy, we have:
[tex]m * g * h = (1/2) * I * \omega^2[/tex]
Substituting the expressions for I and ω, we get:
[tex]m * g * h = (1/2) * (1/2) * m * r^2 * (v/r)^2[/tex]
Simplifying the equation, we have:
[tex]g * h = (1/4) * v^2[/tex]
Solving for h, we find:
[tex]h = (1/4) * v^2 / g[/tex]
Substituting the given values, we can calculate the vertical height:
[tex]h = (1/4) * (4.85 m/s)^2 / 9.8 m/s^2[/tex]
[tex]h = 0.621 m[/tex]
Therefore, the cylinder started from a vertical height of approximately 0.621 meters.
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In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression x = 9.8 cos (14.5 t + 1.6) where x is in centimeters and t is in seconds. What is the Amplitude? What is the Angular Frequency? What is the Period?Find the initial position of the piston (t = 0). Find the initial velocity of the piston (t = 0). Find the initial acceleration of the piston (t = 0).
The amplitude of the piston's oscillation is 9.8 centimeters. The angular frequency is 14.5 radians per second. The period of the motion is approximately 0.436 seconds.
The given expression for the position of the piston, x = 9.8 cos (14.5 t + 1.6), represents simple harmonic motion. In this expression, the coefficient of the cosine function, 9.8, represents the amplitude of the oscillation. Therefore, the amplitude of the piston's motion is 9.8 centimeters.
The angular frequency of the oscillation can be determined by comparing the argument of the cosine function, 14.5 t + 1.6, with the general form of simple harmonic motion, ωt + φ, where ω is the angular frequency. In this case, the angular frequency is 14.5 radians per second. The angular frequency determines how quickly the oscillation repeats itself.
The period of the motion can be calculated using the formula T = 2π/ω, where T represents the period and ω is the angular frequency. Plugging in the value of ω = 14.5, we find that the period is approximately 0.436 seconds. The period represents the time taken for one complete cycle of the oscillation.
To find the initial position of the piston at t = 0, we substitute t = 0 into the given expression for x. Doing so gives us x = 9.8 cos (1.6). Evaluating this expression, we can find the specific value of the initial position.
The initial velocity of the piston at t = 0 can be found by taking the derivative of the position function with respect to time, dx/dt. By differentiating x = 9.8 cos (14.5 t + 1.6) with respect to t, we can determine the initial velocity.
Similarly, the initial acceleration of the piston at t = 0 can be found by taking the second derivative of the position function with respect to time, d²x/dt². Differentiating the position function twice will yield the initial acceleration of the piston.
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A parallel-plate capacitor with empty space between its plates is fully charged by a battery. If a dielectric (with dielectric constant equal to 2) is then placed between the plates after the battery is disconnected, which one of the following statements will be true? The capacitance will increase, and the stored electrical potential energy will increase. The capacitance will decrease, and the stored electrical potential energy will increase. The capacitance will increase, and the stored electrical potential energy will decrease. The capacitance will decrease, and the stored electrical potential energy will decrease.
When a dielectric (with a dielectric constant equal to 2) is placed between the plates of a parallel-plate capacitor with empty space between its plates after the battery is disconnected, the capacitance will increase, and the stored electrical potential energy will decrease. The correct option is - The capacitance will increase, and the stored electrical potential energy will decrease.
The capacitance of the parallel-plate capacitor with the empty space between its plates is given by;
C = ε0A/d
where C is the capacitance, ε0 is the permittivity of free space (8.85 x 10⁻¹² F/m), A is the surface area of the plates of the capacitor, and d is the distance between the plates.
When a dielectric is placed between the plates of the capacitor, the permittivity of the dielectric will replace the permittivity of free space in the equation.
Since the permittivity of the dielectric is greater than the permittivity of free space, the capacitance of the capacitor will increase by a factor equal to the dielectric constant (K) of the dielectric (C = Kε0A/d).
Thus, the capacitance will increase, and the stored electrical potential energy will decrease.
An increase in the capacitance means that more charge can be stored on the capacitor, but since the battery has already been disconnected, the voltage across the capacitor remains constant.
The stored electrical potential energy is given by;
U = 1/2 QV
where U is the stored electrical potential energy, Q is the charge stored on the capacitor, and V is the voltage across the capacitor.
Since the voltage across the capacitor remains constant, the stored electrical potential energy will decrease since the capacitance has increased.
Therefore, the correct option is- The capacitance will increase, and the stored electrical potential energy will decrease.
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D Question 31 20 pts Identical charges q- +5.00 u C are placed at opposite corners of a square that has sides of length 8.00 cm. Point A is at one of the empty corners, and point B is at the center of the square. A charge qo -3.00 u C of mass 5 10 kg is placed at point A and moves along the diagonal of the square to point B. a. What is the electric potential at point A due to q: and q₂? [Select] b. What is the electric potential at point B due to as and q? [Select] c. How much work does the electric force do on go during its motion from A to B? [Select] d. If qo starts from rest and moves in a straight line from A to B, what is its speed at point B? [Select]
The formula for work done by the electric force is given by,W = qΔVwhere W is the work done by the electric force, q is the charge, and ΔV is the potential difference between the initial and final positions of the charge.
a. To calculate the electric potential at point A due to charges q₁ and q₂, we can use the formula for electric potential:
V = k * (q₁ / r₁) + k * (q₂ / r₂)
where V is the electric potential, k is the Coulomb constant (9 x 10⁹ N m²/C²), q₁ and q₂ are the charges, and r₁ and r₂ are the distances between the charges and point A, respectively.
Since the charges q₁ and q₂ are located at opposite corners of the square, the distances r₁ and r₂ are equal to the length of the square's side, which is 8.00 cm or 0.08 m.
Plugging in the values, we get:
V = (9 x 10⁹ N m²/C²) * (5.00 x 10⁻⁶ C / 0.08 m) + (9 x 10⁹ N m²/C²) * (5.00 x 10⁻⁶ C / 0.08 m)
Simplifying the expression, we find that the electric potential at point A due to q₁ and q₂ is 1.125 x 10⁶ V.
b. To calculate the electric potential at point B due to charges q₁ and q₂, we use the same formula as in part a, but substitute the distances r₁ and r₂ with the distance between point B and the charges. Since point B is at the center of the square, the distance from the center to any charge is half the length of the square's side, which is 0.04 m.
Plugging in the values, we get:
V = (9 x 10⁹ N m²/C²) * (5.00 x 10⁻⁶ C / 0.04 m) + (9 x 10⁹ N m²/C²) * (5.00 x 10⁻⁶ C / 0.04 m)
Simplifying the expression, we find that the electric potential at point B due to q₁ and q₂ is 2.25 x 10⁶ V.
c. The work done by the electric force on qo during its motion from A to B can be calculated using the formula:
W = qo * (V_B - V_A)
where W is the work done, qo is the charge, V_B is the electric potential at point B, and V_A is the electric potential at point A.
Plugging in the values, we get:
W = (3.00 x 10⁻⁶ C) * (2.25 x 10⁶ V - 1.125 x 10⁶ V)
Simplifying the expression, we find that the work done by the electric force on qo during its motion from A to B is 2.25 J.
d. If qo starts from rest and moves in a straight line from A to B, its speed at point B can be calculated using the principle of conservation of mechanical energy. The work done by the electric force (found in part c) is equal to the change in mechanical energy, given by:
ΔE = (1/2) * m * v_B²
where ΔE is the change in mechanical energy, m is the mass of qo, and v_B is the speed of qo at point B.
Rearranging the equation, we can solve for v_B:
v_B = sqrt((2 * ΔE) / m)
Plugging in the values, we get:
v_B = sqrt((2 * 2.25 J) / (5.00 kg))
Simplifying the expression, we find that the speed of qo at point B is approximately 0.67 m/s.
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A physics student wishes to measure the voltage change and current across a resistor in a circuit using a voltmeter and an ammeter respectively. How should the student connect the voltmeter and ammeter to the circuit? O a. The voltmeter should be connected in series with the resistor, and the ammeter should be connected in parallel with the resistor. O b. The voltmeter should be connected in series with the resistor, and the ammeter should be connected in series with the resistor. O c. The voltmeter and ammeter should be connected in a series combination that is, in turn, connected in parallel with the resistor d. The voltmeter should be connected in parallel with the resistor, and the ammeter should be connected in parallel with the resistor. Oe. The voltmeter should be connected in parallel with the resistor, and the ammeter should be connected in series with the resistor. QUESTION 17 A conducting, multi-turn circular loop of radius 12.0 cm carries a current of 15.0 A and has a magnetic field strength of 0.0250 T at the center of the loop. How many turns are in the loop? O a. 160 turns O b.583 turns O c. 274 turns O d. 515 turns O e. 318 turns QUESTION 18 3.0 moles of helium gas, that initially occupies a volume of 30 L at a temperature of 280 K, isothermally expands to 40 L. How much work does the gas perform on its environment? O a. 2.00 kcal O b.5.00 kcal O c. 6.00 kcal O d. 3.00 kcal O e. 4.00 kcal
Answer: While measuring voltage change and current across a resistor in a circuit, a physics student should connect the voltmeter in parallel to the resistor, and the ammeter in series with the resistor.
The number of turns in a conducting, multi-turn circular loop of radius 12.0 cm that carries a current of 15.0 A and has a magnetic field strength of 0.0250 T at the center of the loop can be calculated using the formula:N = B_0A/i,where N is the number of turns, B_0 is the magnetic field strength, A is the area of the loop and i is the current flowing through the loop.
Area of the circular loop, [tex]A = πr² = π(0.12 m)² = 0.045 m[/tex]
The moles of helium gas that initially occupies a volume of 30 L at a temperature of 280 K and isothermally expands to 40 L can be calculated using the ideal gas law formula, PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant and T is the temperature.
Rearranging the formula to get the number of moles of gas:[tex]n = PV/RT[/tex]
The work done by the gas can be calculated using the formula, [tex]W = nRT ln(V_f/V_i), where V_f[/tex] is the final volume and V_i is the initial volume.
The work done is given by:[tex]W = 3.0 mol x (8.314 J/mol K) x 280 K ln(40/30)W = 2.01 kJ = 2.01/4.18 = 0.481 kcal[/tex]
Therefore, the work done by the gas on its environment is 0.481 kcal.
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A uniform magnetic field B has a strength of 5.5 T and a direction of 25.0° with respect to the +x-axis. A proton (1.602e-19)is traveling through the field at an angle of -15° with respect to the +x-axis at a velocity of 1.00 ×107 m/s. What is the magnitude of the magnetic force on the proton?
The magnitude of the magnetic force on the proton is 4.31 × 10⁻¹¹ N.
Given values: B = 5.5 Tθ = 25°q = 1.602 × 10⁻¹⁹ VC = 1.00 × 10⁷ m/s Formula: The formula to calculate the magnetic force is given as;
F = qvBsinθ
Where ;F is the magnetic force on the particle q is the charge on the particle v is the velocity of the particle B is the magnetic field strengthθ is the angle between the velocity of the particle and the magnetic field strength Firstly, we need to determine the angle between the velocity vector and the magnetic field vector.
From the given data, The angle between velocity vector and x-axis;α = -15°The angle between magnetic field vector and x-axis;β = 25°The angle between the velocity vector and magnetic field vectorθ = 180° - β + αθ = 180° - 25° - 15°θ = 140° = 2.44346 rad Now, we can substitute all given values in the formula;
F = qvBsinθF
= (1.602 × 10⁻¹⁹ C) (1.00 × 10⁷ m/s) (5.5 T) sin (2.44346 rad)F
= 4.31 × 10⁻¹¹ N
Therefore, the magnitude of the magnetic force on the proton is 4.31 × 10⁻¹¹ N.
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Turn the Helmholtz-coil current to zero. What do you observe
happens to the electron beam? Why?
The Helmholtz-coil current is turned to zero, the electron beam shifts upwards due to the Lorentz force.
When the Helmholtz-coil current is turned to zero, the electron beam shifts upwards due to the Lorentz force.
Let's dive into it below:
The Helmholtz coil creates a uniform magnetic field that causes the electron beam to travel in a straight line.
The force acting on a charged particle traveling through a magnetic field is the Lorentz force, which is perpendicular to both the magnetic field and the velocity of the particle.
This force is the one that causes the electron beam to be deflected into a circular path.
However, when the Helmholtz-coil current is turned to zero, the magnetic field vanishes.
As a result, the Lorentz force disappears.
The only force that still acts on the beam of electrons is gravity, which pulls them downwards.
The electrons, therefore, travel in a straight line, shifting upwards due to the Lorentz force of the coil.
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16) a) How do you separate diffusion current (id) from kinetic current (ik) in a polarographic measurements? b) Explain the difference between charging current and faradaic current c) What is the purpose of measuring the current at discrete intervals in differential pulse polarography (DPP)? d) Why is stripping the most sensitive polarographic technique?
Charging current is related to the electrical double layer, while faradaic current involves electrochemical reactions.
How can diffusion current be separated from kinetic current in polarographic measurements?Separating diffusion current (id) from kinetic current (ik) in polarographic measurements can be achieved by applying a high-frequency potential modulation. This modulation causes the diffusion current to oscillate while the kinetic current remains relatively steady.
By analyzing the current response at different modulation frequencies, it is possible to isolate and determine the diffusion current contribution.
Charging current and faradaic current are two types of currents in electrochemical reactions. Charging current refers to the current associated with the charging or discharging of the electrical double layer at the electrode-electrolyte interface. It is typically a capacitive current that occurs rapidly at the beginning of an electrochemical process.
Faradaic current, on the other hand, is the current associated with the electrochemical reactions happening at the electrode. It involves the transfer of electrons between the electrode and the species in the electrolyte, following Faraday's law of electrolysis.
In differential pulse polarography (DPP), measuring the current at discrete intervals allows for the detection of changes in current over time
. By measuring the current at specific intervals, typically at regular time intervals, it is possible to observe the differential current response associated with the electrochemical processes occurring in the system. This helps in identifying and characterizing various analytes present in the sample.
Stripping is considered the most sensitive polarographic technique because it involves the preconcentrating of analytes onto the electrode surface before measuring the current.
The preconcentrating step allows for the accumulation of analytes at the electrode, resulting in increased sensitivity.
During the stripping step, a voltage is applied to remove the accumulated analytes from the electrode, and the resulting current is measured. This technique enhances the detection limit and improves the sensitivity of the measurement compared to other polarographic methods.
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A cylindrical copper cable carries a current of 1200 A. There is a potential difference of 0.016 V between two points on the cable that are 0.24 m apart. What is the diameter the cable? The resistivity of copper is 1.7 x 10^-8 Ωm.
A cylindrical copper cable carries a current of 1200 A. There is a potential difference of 0.016 V between two points on the cable that are 0.24 m apart.
The resistivity of copper is 1.7 x 10^-8 Ωm.
The formula for resistance is:
R = (ρl)/AR is resistanceρ is resistivity l is the length of the wireA is cross-sectional area of wire, the formula for cross-sectional area is:
[tex]A = (ρl)/RA = (ρl)/R= (1.7 x 10^-8 Ωm * 0.24 m)/((0.016 V)/1200 A))A = 5.1 x 10^-6 m^2[/tex]
Now, using the formula for cross-sectional area of a cylinder:
[tex]A = πd²/4We can write: πd²/4 = 5.1 x 10^-6 m^2d² = (4 * 5.1 x 10^-6 m^2)/πd² = 1.63 x 10^-6 m²d = √(1.63 x 10^-6 m²)d = 1.28 x 10^-3 m = 1.28 mm,[/tex]
the diameter of the copper cable is 1.28 mm.
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A solution consisting of 30% MgSO4 and 70% H2O is cooled to 60°F. During cooling, 5% of the water evaporates.
whole system. How many kilograms of crystals will be obtained from 1000 kg of original mixture?
The amount of MgSO4 crystals obtained from the 1000 kg of original mixture is 85.5 kg given that a solution consisting of 30% MgSO4 and 70% H2O is cooled to 60°F.
The total amount of the mixture is 1000 kg. The solution consists of 30% MgSO4 and 70% H2O.The weight of MgSO4 in the initial solution = 30% of 1000 kg = 300 kg
The weight of water in the initial solution = 70% of 1000 kg = 700 kg
The mass of the solution (mixture) = 1000 kg
During cooling, 5% of water evaporates => The mass of water in the final mixture = 0.95 × 700 kg = 665 kg
The mass of MgSO4 in the final mixture = 300 kg
Remaining mixture (H2O) after evaporation = 665 kg
The amount of MgSO4 crystals obtained = Final MgSO4 weight – Initial MgSO4 weight = 300 – (1000 – 665) × 0.3 = 85.5 kg
Therefore, the amount of MgSO4 crystals obtained from the 1000 kg of original mixture is 85.5 kg.
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Q|C A Carnot heat engine operates between temperatures Th and Tc . (d) Does the answer to part (c) depend on Tc ? Explain.
Yes, the answer to part (c) does depend on Tc. In a Carnot heat engine, the efficiency of the engine is given by the equation: Efficiency = 1 - (Tc / Th).
Where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir. The efficiency of the engine is directly affected by the temperature of the cold reservoir.
As Tc increases, the efficiency of the engine decreases. Therefore, the answer to part (c) does depend on Tc. The efficiency of the engine is directly affected by the temperature of the cold reservoir.
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An impulse internal to the system will not change the momentum of
that system ( True or False)
False. An impulse internal to the system can change the momentum of that system.
According to Newton's third law of motion, every action has an equal and opposite reaction. When an impulse occurs within a system, it involves the application of an internal force for a certain period of time, resulting in a change in momentum. The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. Therefore, an impulse internal to the system can indeed cause a change in the momentum of the system.
For example, in a collision between two objects, such as billiard balls on a pool table, the impulses exerted between the balls during the collision will cause their momenta to change. The change in momentum is a result of the internal forces between the objects during the collision. This demonstrates that an impulse internal to the system can alter the momentum of the system as a whole.
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A car comes to a stop six seconds after the driver applies the brakes. While the brakes are on, the following velocities are recorded:
The car has a negative acceleration of 4.17 m/s². It comes to a stop after six seconds as the velocity is decreasing at a constant rate of 4.17 m/s every second.
A car comes to a stop six seconds after the driver applies the brakes.
While the brakes are on, the following velocities are recorded:
Initial velocity, u = 25 m/sFinal velocity, v = 0 m/sTime, t = 6 s
Average acceleration, a can be calculated by the equation: a = (v - u) / t.
Therefore, substituting the values gives us:a = (0 - 25) / 6 = -4.17 m/s².
Here, the minus sign indicates that the acceleration is in the opposite direction to that of the initial velocity (deceleration).
The negative acceleration means that the velocity of the car decreases.
Therefore, the car's velocity is decreasing by 4.17 m/s every second. Hence, the car will come to a stop after six seconds as given in the problem statement.
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When you are looking at a rainbow the Sun is located: Right in front of you The location of the Sun could be anywhere Right behind you At a 90 degree angle relative to your location
when you look at a rainbow, the sun is located right behind you, at a 42-degree angle relative to your location. The sun's position is critical in creating the rainbow, and it is a fascinating meteorological phenomenon that never ceases to amaze us.
When you look at a rainbow, the sun is located at a 42-degree angle relative to your location. Rainbows are a meteorological phenomenon that occurs when sunlight enters water droplets and then refracts, reflects, and disperses within the droplets.
A primary rainbow is caused by a single reflection of sunlight within the water droplets, whereas a secondary rainbow is caused by two internal reflections of light within the droplets.
To locate the sun's position concerning a rainbow, consider the following. When you see a rainbow, the sunlight enters the water droplets from behind your back and then disperses into the spectrum of colors.
Therefore, the sun is always behind you when you face a rainbow, as the sun's rays are reflected off the raindrops and into your eyes.
However, the sun's angle relative to the observer is crucial in creating a rainbow.
The sun's position can be determined using the following formula:
The light enters the droplets at a 42-degree angle from the observer's shadow and then leaves the droplets at a 42-degree angle, creating the arc shape that you see.
In conclusion, when you look at a rainbow, the sun is located right behind you, at a 42-degree angle relative to your location.
The sun's position is critical in creating the rainbow, and it is a fascinating meteorological phenomenon that never ceases to amaze us.
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An infinite line charge of uniform linear charge density λ = -2.1 µC/m lies parallel to the y axis at x = -1 m. A point charge of 1.1 µC is located at x = 2.5 m, y = 3.5 m. Find the x component of the electric field at x = 3.5 m, y = 3.0 m. kN/C Enter 0 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0.5 up to 10 attempts]
In the figure shown above, a butterfly net is in a uniform electric field of magnitude E = 120 N/C. The rim, a circle of radius a = 14.3 cm, is aligned perpendicular to the field.
Find the electric flux through the netting. The normal vector of the area enclosed by the rim is in the direction of the netting.
The electric flux is:
The electric flux is 7.709091380790923. The electric field due to an infinite line charge of uniform linear charge density λ is given by:
E = k * λ / x
The electric field due to an infinite line charge of uniform linear charge density λ is given by:
E = k * λ / x
where k is the Coulomb constant and x is the distance from the line charge.
The x component of the electric field at x = 3.5 m, y = 3.0 m is:
E_x = k * λ / (3.5) = -2.86 kN/C
The electric field due to the point charge is given by:
E = k * q / r^2
where q is the charge of the point charge and r is the distance from the point charge.
The x component of the electric field due to the point charge is:
E_x = k * 1.1 * 10^-6 / ((3.5)^2 - (2.5)^2) = -0.12 kN/C
The total x component of the electric field is:
E_x = -2.86 - 0.12 = -2.98 kN/C
The electric flux through the netting is:
Φ = E * A = 120 * (math.pi * (14.3 / 100)^2) = 7.709091380790923
Therefore, the electric flux is 7.709091380790923.
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Person A and B both lift an object of 50 kg to a height of 2 m. It takes person A10 seconds to lift up the object but it only takes person B 1 second to do the same. (a) How much work do A and B perform? (b) Who is more powerful? Prove
(a) Person A and Person B both perform 1000 Joules of work.
(b) Person B is more powerful.
When calculating work, we use the formula: Work = Force × Distance × cos(θ), where Force is the force applied, Distance is the distance traveled, and θ is the angle between the force and the direction of motion.
In this scenario, both Person A and Person B lift the same object to the same height, so the distance traveled is the same for both individuals. The force applied is equal to the weight of the object, which is given as 50 kg.
For Person A, it took 10 seconds to lift the object, while Person B accomplished the task in just 1 second. Since work is defined as the product of force and distance, and distance is the same for both individuals, we can conclude that the person who accomplishes the task in less time performs more work.
Therefore, Person B, who lifted the object in 1 second, is more powerful than Person A.
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Under what condition is ∣ A + B ∣=∣ A ∣ + ∣ B ∣ ? The statement is never true. Vectors A and B are in opposite directions. Vectors A and B are in the same direction. The statement is always true. Vectors A and B are in perpendicular directions.
Under the condition that vectors A and B are in the same direction, the equation ∣ A + B ∣=∣ A ∣ + ∣ B ∣ holds. Vectors A and B are in the same direction.
Let A and B be any two vectors. The magnitude of vector A is represented as ∣ A ∣ .
When we add vectors A and B, the resultant vector is given by A + B.
The magnitude of the resultant vector A + B is represented as ∣ A + B ∣ .
According to the triangle inequality, the magnitude of the resultant vector A + B should be less than or equal to the sum of the magnitudes of the vectors A and B individually. That is,∣ A + B ∣ ≤ ∣ A ∣ + ∣ B ∣
But, this inequality becomes equality when vectors A and B are in the same direction.
In other words, when vectors A and B are in the same direction, the magnitude of their resultant vector is equal to the sum of their individual magnitudes. Thus, the equation ∣ A + B ∣=∣ A ∣ + ∣ B ∣ holds for vectors A and B in the same direction.
Therefore, the answer is vectors A and B are in the same direction.
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The following three questions relate to the information here: Ripples radiate out from vibrating source in water. After 6.00 s, 42 ripples have been generated with the first ripple covering a distance of 3.00 m from the source (each ripple constitutes a wave).
What is the wavelength of the ripples? (a) 0.048 m (b) 0.071 m (c) 0.43 m (d) 3.0 m
What is the frequency of the ripples? (a) 14 Hz (b) 7.0 Hz (c) 0.33 Hz (d) 0.17 Hz
What is the speed of the ripples? (a) 0.1 m s−1 (b) 0.2 m s−1 (c) 0.4 m s−1 (d) 0.5 m s
The correct answers to the given questions are as follows:
a) The wavelength of the ripples is (d) 3.0 m.
b) The frequency of the ripples is (b) 7.0 Hz.
c) The speed of the ripples is not provided in the given options. It is 21.0 m/s.
To solve these questions, we can use the formula:
v = λf,
where
v is the speed of the ripples,
λ is the wavelength, and
f is the frequency.
Wavelength of the ripplesGiven that the first ripple covers a distance of 3.00 m from the source, we can assume this is equal to the wavelength of the ripples:
λ = 3.00 m.
Therefore, the answer is (d) 3.0 m.
Frequency of the ripplesWe are given that after 6.00 seconds, 42 ripples have been generated. The frequency (f) can be calculated by dividing the number of ripples by the time:
f = number of ripples/time.
f = 42 ripples / 6.00 s.
f = 7.0 Hz.
Therefore, the answer is (b) 7.0 Hz.
Speed of the ripplesUsing the formula v = λf, we can substitute the known values:
v = (3.00 m) × (7.0 Hz).
v = 21.0 m/s.
Therefore, the answer is none of the provided options. The speed of the ripples is 21.0 m/s.
Therefore,
a) The wavelength of the ripples is (d) 3.0 m.
b) The frequency of the ripples is (b) 7.0 Hz.
c) The speed of the ripples is not provided in the given options. It is 21.0 m/s.
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The wavelength of the ripples is 0.071 m. The answer is (b) 0.071 m. The frequency of the ripples is 7.0 Hz. The answer is (b) 7.0 Hz. The speed of the ripples is approximately 0.497 m/s. The answer is (d).
After 6.00 s, 42 ripples have been generated, with the first ripple covering a distance of 3.00 m from the source.
Each ripple constitutes a wave.
(a) To find the wavelength of the ripples:
Wavelength = Total Distance / Number of Ripples
Wavelength = 3.00 / 42
Wavelength = 0.071 m
Therefore, the wavelength of the ripples is 0.071 m. The answer is (b) 0.071 m.
(b) To find the frequency of the ripples:
Frequency = Number of Ripples / Total Time
Frequency = 42 / 6.00
Frequency = 7.0 Hz
Therefore, the frequency of the ripples is 7.0 Hz. The answer is (b) 7.0 Hz.
(c) To find the speed of the ripples:
Speed = 7.0 × 0.071
Speed = 0.497 m/s
Therefore, the speed of the ripples is approximately 0.497 m/s. The answer is (d).
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Using Gauss' law, obtain in every universe (o Spsco): the profile of the electric field density vector D(p), determine electric flux v(), the resulting electric field vector E(p) for a charge distributed on a spherical shell of inner radius p=a
р and outer radius q=d. whose distribution is =
pvQI(41p (b-a)) [C/m3] at the origin of the coordinates. Draw the Gaussians correctly to obtain the solution for each part of the problem space. Draw the profile of the flux, and the electric field for all environments.
To solve this problem using Gauss' law, let's consider the charge distribution on the spherical shell between inner radius p=a and outer radius q=d. The charge density distribution is given by ρ = pvQI(4πp(b-a)) [C/m³] at the origin of the coordinates.
First, we'll determine the electric field density vector D(p) using Gauss' law. Gauss' law states that the electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of the medium.
Since we have a spherical symmetry in this problem, we'll consider a Gaussian surface in the form of a sphere with radius r. We'll calculate the electric flux through this Gaussian surface and equate it to the total charge enclosed.
The resulting electric field vector E(p) is related to D(p) by the equation E = εD, where ε is the permittivity of the medium.
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a 0.6 kg drawbar A hanging from a 2.8 kg spool G with a radius of gyration of kg = 33.6 mm and a diameter d = 28 mm. how fast is the drawbar falling when it has descended 0.5 m?
The drawbar falls at a speed of approximately 2.70 m/s when it has descended 0.5 m.
To find the speed at which the drawbar is falling, we need to consider the conservation of energy. Initially, the drawbar has potential energy due to its height, and as it falls, this potential energy is converted into kinetic energy.
The potential energy (PE) of the drawbar at a height h is given by:
PE = mgh,
where:
m = mass of the drawbar (0.6 kg),g = acceleration due to gravity (9.8 m/s²),h = height of descent (0.5 m).The kinetic energy (KE) of the drawbar is given by:
KE = (1/2)mv²,
where:
m = mass of the drawbar (0.6 kg),v = speed of the drawbar.By equating the initial potential energy to the final kinetic energy, we can solve for the speed of the drawbar.
mgh = (1/2)mv².
Simplifying the equation, we get:
v = √(2gh).
Now, we need to determine the height h using the information given about the spool. The radius of gyration [tex]k_{G}[/tex] is related to the diameter d as follows:
[tex]k_{G}[/tex] = d/2.
Given the diameter d = 28 mm, we can calculate the radius of gyration [tex]k_{G}[/tex] as:
[tex]k_{G}[/tex] = 28 mm / 2 = 14 mm = 0.014 m.
The height h can be determined by subtracting the radius of gyration from the descent distance:
h = 0.5 m - 0.014 m = 0.486 m.
Now we can calculate the speed v using the derived height h:
v = √(2 * g * h)
= √(2 * 9.8 m/s² * 0.486 m)
≈ 2.70 m/s.
Therefore, when the drawbar has descended 0.5 m, it is falling at a speed of approximately 2.70 m/s.
The complete question should be:
A 0.6 kg drawbar A hanging from a 2.8 kg spool G with a radius of gyration of k[tex]_{G}[/tex] = 33.6 mm and a diameter d = 28 mm. How fast is the drawbar falling when it has descended 0.5 m?
The drawbar falls at ________ m/s.
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A system receives energy of 150 J by heat from surrounding and performs work of 60 J. Find the change in its internal energy. 120J 150 J 90 J 60 J
The change in internal energy of the system is 90 J. The correct option is - 90 J.
To find the change in internal energy, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
Heat added to the system = 150 J
Work done by the system = 60 J
Change in internal energy = Heat added - Work done
Change in internal energy = 150 J - 60 J
Change in internal energy = 90 J
Therefore, the change in the internal energy of the system is 90 J.
So, the correct option is 90 J.
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1. The human eye detects (b) a) longitudinal waves b) transverse waves 2. The type of lens used to correct for being nearsighted. (a) a) concave lens b) convex lens 3. The primary colors of light are 4. Briefly explain why the sky appears blue during the day. 5. Matching: Place the following scientists - Newton, Young, Einstein, Maxwell, Huygens a) particle theory for light b) wave theory of light
The human eye detects transverse waves, The type of lens used to correct for being nearsighted concave lens, The primary colours of light are blue, green and red.
Briefly explain why the sky appears blue during the day: At sunset, the sky often turns a warm orange or red hue because of the way that the atmosphere scatters sunlight. The blue colour of the sky is due to Rayleigh's scattering. As white light hits the Earth's atmosphere, blue light scatters more easily than red light due to its shorter wavelength. As a result, the blue light is scattered in all directions and makes the sky appear blue.
Matching: Particle theory of light- Newton, Wave theory of light- Young and Huygens
The human eye detects transverse waves. A concave lens is used to correct for being nearsighted. The primary colours of light are blue, green and red. The blue colour of the sky is due to Rayleigh's scattering. The particle theory of light was proposed by Newton while the wave theory of light was proposed by Young and Huygens.
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A car company claims that one of its vehicles could go up a hill with a slope of 39.1 degrees. What must be the minimum coefficient of static friction between the road and tires
The minimum coefficient of static friction between the road and tires of the vehicle must be at least 0.810 for the car to go up a hill with a slope of 39.1 degrees.
To determine the minimum coefficient of static friction required for the car to go up a hill with a slope of 39.1 degrees, we can use the following formula:
μ ≥ tan(θ)
where μ is the coefficient of static friction and θ is the angle of the slope.
Substituting the given values:
μ ≥ tan(39.1 degrees)
Using a calculator, we find:
μ ≥ 0.810
Therefore, the minimum coefficient of static friction required between the road and tires of the vehicle must be at least 0.810.
The complete question should be:
A car company claims that one of its vehicles could go up a hill with a slope of 39.1 degrees. What must be the minimum coefficient of static friction between the road and tires of the vehicle?
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Question 43 1 pts An aluminum calorimeter of mass 52 g, has 172 g water, both at a temperature of 20.9°C. A 159-g piece of Copper originally kept in boiling water (T= 100°C) is transferred to the calorimeter. Calculate the final equilibrium temperature of the mixture in °C. Specific Heats: Al = 900 J/kg, water =4186 J/g, Cu = 387 J/kg.
The final equilibrium temperature of the mixture is approximately 22.8°C when the copper piece is transferred to the aluminum calorimeter containing water.
To determine the final equilibrium temperature of the mixture, we can use the principle of energy conservation. The heat gained by the cooler objects (water and aluminum calorimeter) should be equal to the heat lost by the hotter object (copper piece).
First, let's calculate the heat gained by the water and calorimeter. The specific heat capacity of water is 4186 J/kg°C, and the mass of water is 172 g. The specific heat capacity of aluminum is 900 J/kg°C, and the mass of the calorimeter is 52 g. The initial temperature of both the water and calorimeter is 20.9°C. We can calculate the heat gained as follows:
Heat gained by water and calorimeter = (mass of water × specific heat capacity of water + mass of calorimeter × specific heat capacity of aluminum) × (final temperature - initial temperature)
Next, let's calculate the heat lost by the copper piece. The specific heat capacity of copper is 387 J/kg°C. The mass of the copper piece is 159 g, and its initial temperature is 100°C. We can calculate the heat lost as follows:
Heat lost by copper = mass of copper × specific heat capacity of copper × (initial temperature - final temperature)
Since the heat gained and heat lost should be equal, we can set up the following equation:
(mass of water × specific heat capacity of water + mass of calorimeter × specific heat capacity of aluminum) × (final temperature - initial temperature) = mass of copper × specific heat capacity of copper × (initial temperature - final temperature)
By solving this equation, we can find the final equilibrium temperature of the mixture. After performing the calculations, we find that the final equilibrium temperature is approximately 22.8°C.
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Consider two objects of masses mi 8 kg and m2 = 4 kg. m1 is travelling along the negative y-axis at 52 km/hr and strikes the second stationary mass m2, locking the two masses together. (a) What is the velocity of the first mass before the collision? Vmı =<?,?,?> (b) What is the velocity of the second mass before the collision? Vm2 =<?,?,?> (c) The final velocity of the two masses can be calculated using the formula? (d) What is the final velocity of the two masses? Ve =<?,?,?> (e) Choose the correct answer (i) (ii) The final momentum of the system is less than the initial momentum of the system The final momentum of the system is greater than the initial momentum of the system The final momentum of the system is equal to the initial momentum of the system (iii) (f) What is the total initial kinetic energy of the two masses (Ki =?)? (g) What is the total final kinetic energy of the two masses(Kg =?)? = (h) How much of the mechanical energy is lost due to this collision (AEint =?)?
Answer:
a.) The velocity of the first mass before the collision is Vmi = <-52, 0, 0> m/s.
b.) The velocity of the second mass before the collision is Vm2 = <0, 0, 0> m/s.
c.) The final velocity of the two masses is Vf = <-36, 0, 0> m/s.
e.) The final momentum of the system is equal to the initial momentum of the system. This is because momentum is conserved in a collision.
f.) The total initial kinetic energy of the two masses is Ki =1440J.
g.) The total final kinetic energy of the two masses is Kg=2160J.
h.) 720 J of mechanical energy is lost due to this collision. This energy is likely converted into heat and sound during the collision.
Explanation:
(a) The velocity of the first mass before the collision is Vmi = <-52, 0, 0> m/s.
(b) The velocity of the second mass before the collision is Vm2 = <0, 0, 0> m/s.
(c) The final velocity of the two masses can be calculated using the following formula:
V_f = (m_1 * V_1 + m_2 * V_2) / (m_1 + m_2)
where:
V_f is the final velocity of the two masses
m_1 is the mass of the first object
V_1 is the velocity of the first object
m_2 is the mass of the second object
V_2 is the velocity of the second object
V_f = (8 kg * (-52 m/s) + 4 kg * (0 m/s)) / (8 kg + 4 kg)
V_f = -36 m/s
Therefore, the final velocity of the two masses is Vf = <-36, 0, 0> m/s.
(e) The final momentum of the system is equal to the initial momentum of the system. This is because momentum is conserved in a collision.
(f) The total initial kinetic energy of the two masses is Ki = 1/2 * m_1 * V_1^2 + 1/2 * m_2 * V_2^2
Ki = 1/2 * 8 kg * (-52 m/s)^2 + 1/2 * 4 kg * (0 m/s)^2
Ki = 1440 J
(g) The total final kinetic energy of the two masses is Kg = 1/2 * (m_1 + m_2) * V_f^2
Kg = 1/2 * (8 kg + 4 kg) * (-36 m/s)^2
Kg = 2160 J
(h) The amount of mechanical energy lost due to this collision is AEint = Ki - Kg = 2160 J - 1440 J = 720 J.
Therefore, 720 J of mechanical energy is lost due to this collision. This energy is likely converted into heat and sound during the collision.
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The lifting mechanism raises a box of mass 32 kg through a vertical distance of 2.5m in 5.4s. (i) Calculate the gravitational potential energy gained by the box.
The gravitational potential energy gained by the box is 784 J.
The mass of the box is 32 kg, the vertical distance through which the box is lifted is 2.5 m, and the time taken for the lifting is 5.4 s.
To determine the gravitational potential energy gained by the box, we can use the formula: P.E. = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical distance through which the object is lifted.
Substituting the given values, we have:
P.E. = (32 kg) × (9.8 m/s²) × (2.5 m)
P.E. = 784 J
Therefore, the gravitational potential energy gained by the box is 784 J.
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A house is heated by a 24.0-kW electric furnace. The local power company charges $0.0500 per kW.h and the heating bill for
January is $261. How much time At day must the furnace have been running on
an average January day?
On an average January day, the furnace must have been running for approximately 9.06 days.
To determine the amount of time the furnace must have been running on an average January day, we can use the formula:
Energy consumed = Power x Time
Given that the electric furnace has a power of 24.0 kW and the heating bill for January is $261, we can calculate the energy consumed:
Energy consumed = $261 / $0.0500 per kW.h = 5220 kW.h
Now, we can rearrange the formula to solve for time:
Time = Energy consumed / Power
Time = 5220 kW.h / 24.0 kW
Time = 217.5 hours
Since we're looking for the time in days, we divide by 24 to convert the hours to days:
Time = 217.5 hours / 24 hours/day
Time ≈ 9.06 days
Therefore, on an average January day, the furnace must have been running for approximately 9.06 days.
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8. A 5.00−kg bowling ball moving at 8.00 m/s collides with a 0.850−kg bowling pin, which is scattered at an angle to the initial direction of the bowling ball and with a speed of 15.0 m/s. a. Calculate the final velocity (magnitude and direction) of the bowling ball. Answer b. Is the collision elastic? Answer 9. A wheel rotates at a constant rate of 2.0×10 3 rev/min. (a) What is its angular velocity in radians per second? Answer (b) Through what angle does it turn in 10 s? Express the solution in radians and degrees. Answer Radians Answer Degrees. 10. A wheel has a constant angular acceleration of 7.0rad/s 2 . Starting from rest, it turns through 400rad. (a) What is its final angular velocity? Answer (b) How much time elapses while it turns through the 400 radians? Answer
The angular velocity of the wheel is 209.44 radians/s.the final velocity of the bowling ball is 36.67 m/s in the positive direction.
To solve the given problems, we'll use the principles of conservation of momentum and rotational motion.8a. Calculate the final velocity (magnitude and direction) of the bowling ball:
Let's assume the positive direction is the initial direction of the bowling ball. According to the law of conservation of momentum:
(mass of bowling ball) × (initial velocity of bowling ball) = (mass of bowling pin) × (final velocity of bowling ball) + (mass of bowling pin) × (final velocity of bowling pin)(5.00 kg) × (8.00 m/s) = (0.850 kg) × (final velocity of bowling ball) + (0.850 kg) × (15.0 m/s) 40.00 kg·m/s = 0.7225 kg·m/s + 12.75 kg·m/s + (0.7225 kg) × (final velocity of bowling ball)
Simplifying the equation:
40.00 kg·m/s - 13.4725 kg·m/s = (0.7225 kg) × (final velocity of bowling ball) 26.5275 kg·m/s = (0.7225 kg) × (final velocity of bowling ball)
final velocity of bowling ball = 26.5275 kg·m/s / 0.7225 kg
final velocity of bowling ball = 36.67 m/s
Therefore, the final velocity of the bowling ball is 36.67 m/s in the positive direction.
8b. To determine whether the collision is elastic or not, we need to compare the kinetic energy before and after the collision. If the kinetic energy is conserved, the collision is elastic. If not, it is inelastic.
Kinetic energy before the collision:
KE_initial = (1/2) × (mass of bowling ball) × (initial velocity of bowling ball)^2
= (1/2) × (5.00 kg) × (8.00 m/s)^2
= 160 J
Kinetic energy after the collision:
KE_final = (1/2) × (mass of bowling ball) × (final velocity of bowling ball)^2 + (1/2) × (mass of bowling pin) × (final velocity of bowling pin)^2
= (1/2) × (5.00 kg) × (36.67 m/s)^2 + (1/2) × (0.850 kg) × (15.0 m/s)^2
= 3368 J
Since KE_initial = 160 J and KE_final = 3368 J, the kinetic energy is not conserved, indicating an inelastic collision.
9a. Given:
Angular velocity = 2.0 × 10^3 rev/min
To convert rev/min to radians per second, we need to use conversion factors:
1 revolution (rev) = 2π radians
1 minute (min) = 60 seconds (s)
Angular velocity = (2.0 × 10^3 rev/min) × (2π radians/1 rev) × (1 min/60 s)
= (2.0 × 10^3) × (2π/60) radians/s
= 209.44 radians/s
Therefore, the angular velocity of the wheel is 209.44 radians/s.
Given:
Time = 10 s
Using the formula for angular displacement:
θ = ω_initial × t + (1/2) × α × t^2
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