To solve this problem, let's define the coordinate axis as follows:
The x-axis will be horizontal, pointing towards the right.
The y-axis will be vertical, pointing upwards.
(a) To find the horizontal distance covered by the block before hitting the ground, we need to calculate the time it takes for the block to fall.
We can use the equation for vertical displacement:
[tex]y = 0.5 * g * t^2[/tex]
where y is the vertical distance, g is the acceleration due to gravity, and t is the time.
Vertical distance (y) = 0.782 m
Acceleration due to gravity (g) = 9.8 m/s^2
Rearranging the equation, we get:
[tex]t = sqrt((2 * y) / g)[/tex]
Substituting the values:
t = sqrt((2 * 0.782 m) / 9.8 m/s^2)
Now we have the time taken by the block to fall. To find the horizontal distance covered, we can use the formula:
x = v * t
where v is the horizontal velocity.
Mass of the block (m) = 1.35 kg
Mass of the bullet (m_bullet) = 0.0105 kg
Initial horizontal velocity (v_bullet) = 715 m/s
The horizontal velocity of the block and bullet combined will be the same as the initial velocity of the bullet.
Substituting the values:
x = (v_bullet) * t
Calculating this expression will give us the horizontal distance covered by the block before hitting the ground.
(b) To find the horizontal and vertical components of the block's velocity when it hits the ground, we can use the following equations:
For the horizontal component:
v_x = v_bullet
For the vertical component:
v_y = g * t
Acceleration due to gravity (g) = 9.8 m/s^2
Time taken (t) = the value calculated in part (a)
Substituting the values, we can calculate the horizontal and vertical components of the velocity.
(c) To find the magnitude of the velocity vector and its direction, we can use the Pythagorean theorem and trigonometry.
The magnitude of the velocity vector (v) can be calculated as:
[tex]v = sqrt(v_x^2 + v_y^2)[/tex]
The direction of the velocity vector (θ) can be calculated as:
[tex]θ = atan(v_y / v_x)[/tex]
Using the values of v_x and v_y calculated in part (b), we can determine the magnitude and direction of the velocity vector when the block hits the ground.
(d) To draw the velocity vectors and the resultant velocity vector, you can create a coordinate axis with the x and y axes as defined earlier. Draw the horizontal velocity vector v_x pointing to the right with a magnitude of v_bullet. Draw the vertical velocity vector v_y pointing upwards with a magnitude of g * t. Then, draw the resultant velocity vector v with the magnitude and direction calculated in part (c) originating from the starting point of the block. Label the vectors and the angles accordingly.
Remember to use appropriate scales and angles based on the calculated values.
Learn more about horizontal distance from the given link
https://brainly.com/question/24784992
#SPJ11
2. A well-mixed vessel of volume, V = 50 m³, is half-filled with acetic acid solution at a concentration of Co (20 kg/m³). Pure water is fed at a steady flow rate of Qo (5.0 m³/h) into the vessel and the well-mixed solution is pumped from the vessel at the same rate. The concentration of salt in the exit fluid C(t) kg/m³, is monitored. Derive the unsteady state differential material balance for the concentration of salt in the exit stream flowing from the vessel and show that it follows the following exponential relationship: open st C(t) = Coexp (20) V/2 [25%] artolizsup b. Determine the concentration of acetic acid present in the fluid in the intent vessel after a period of 10 hours. [10% ] A noitesup A relationship mots on [30%] nepobyl [30%] c. If the inlet flow rate had been 7.5 m³/h and the exit flow was maintained at 5 m³/h, derive the unsteady state mass balance for this case. d. Determine the volume of solution in the vessel after 10 hours and the concentration of the acetic acid in the stream leaving the vessel. [5%] e. What would you need to do after the 10 hour mark has been reached in d?
The problem involves analyzing the concentration dynamics in a well-mixed vessel, deriving the material balance, determining the exponential relationship, calculating the concentration of acetic acid after 10 hours, exploring the effects of flow rate changes, and addressing the actions to be taken after the 10-hour mark.
What does the given problem involve and what are the key objectives?The given problem involves a well-mixed vessel containing acetic acid solution and water. The goal is to derive the unsteady state differential material balance for the concentration of salt in the exit stream and determine its exponential relationship.
The concentration of acetic acid in the vessel after 10 hours is also requested. Additionally, the impact of changing the inlet and exit flow rates is considered, and the corresponding unsteady state mass balance is derived.
The volume of the solution in the vessel and the concentration of acetic acid in the exit stream after 10 hours are determined. Finally, the question asks for suggestions on what should be done after the 10-hour mark is reached.
The problem involves analyzing the dynamics of concentration changes, applying material balance principles, and understanding the effects of flow rates and time on the system's behavior.
Learn more about acetic acid
brainly.com/question/15202177
#SPJ11
to your 1. [0/1 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 3.4.P.043. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A particle moves in a straight line at a constant velocity of 39 m/s. What is its displacement (in m) between t=0 and t-7.2 s? (Assume the particle's direction of travel to be the positive direction. Indicate the direction with the sign of your answer.) xm Additional Materials Reading MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 2. [0/1 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 3.4.P.044. A particle moves in a straight line with an initial velocity of 27 m/s and a constant acceleration of 32 m/s². If at t-0, x=0, what is the particle's position (in m) att s x m + Additional Materials Reading ENOTEC ASK YOUR TEACHER PRACTICE ANOTHER
The displacement (in m) of a particle moving in a straight line at a constant velocity of 39 m/s between t=0 and t=7.2 s is 280.8 m in the positive direction.
Velocity is defined as the rate of change of displacement with respect to time. When a body moves with a constant velocity, its displacement is calculated using the formula; d = vt where, d is the displacement, v is the velocity, and t is the time taken.
Therefore, the displacement of the particle is calculated as;
d = vt
= 39 × 7.2
= 280.8 m
The direction of the particle is given as positive direction, hence the displacement is 280.8 m in the positive direction. An acceleration is said to be constant when there is uniform change in velocity over a period of time. The acceleration of the particle is given as 32 m/s² and initial velocity is given as 27 m/s.
The position of the particle at time t is calculated using the formula;
X = xo + vot + 1/2 at²
where, X is the position of the particle, xo is the initial position, vo is the initial velocity, t is the time taken, and a is the acceleration.
Here, xo is given as 0, vo is given as 27 m/s, a is given as 32 m/s², and
t is given as 0.X = 0 + 27(0) + 1/2(32)(0)X
= 0
The particle's position at t=0 is 0 m.
To know velocity visit :
https://brainly.com/question/30559316
#SPJ11
18. (4 pts) If you have a conduction loop in a constant Magnetic field (as shown) and the magnetic field suddenly doubles, what direction is the resulting induced magnetic field? (Draw the induced field) 19. Bonus (2pts) What direction is the induced current in problem 18 ? (Draw it on the figure)
The resulting induced magnetic field in the conduction loop will be in the opposite direction to the original magnetic field.
When a magnetic field passing through a conduction loop changes, it induces an electric current in the loop according to Faraday's law of electromagnetic induction. In this scenario, the magnetic field suddenly doubles. To determine the direction of the resulting induced magnetic field, we can apply Lenz's law, which states that the induced magnetic field opposes the change that caused it.
Initially, let's assume the original magnetic field is pointing into the page. According to Lenz's law, the induced magnetic field in the conduction loop will try to oppose this increase in the magnetic field. Therefore, the resulting induced magnetic field will be in the opposite direction to the original magnetic field, coming out of the page.
As for the direction of the induced current in problem 18, it can be determined using the right-hand rule. If we place our right hand with the thumb pointing in the direction of the induced magnetic field (out of the page), the direction of the induced current in the loop will be in the counterclockwise direction.
To learn more about magnetic -
brainly.com/question/15260355
#SPJ11
Please help! Due very soon! I will upvote!
Question 24 Review Session 3 In Problem II, we knew the image was virtual because O it was 120 cm from the lens. O it was on the same side as the object. O it was upright O the lens was diverging. Que
In the case of lenses, the image will always be reversed if it is real. Additionally, in the case of lenses, the picture is inverted if the image distance is positive. On the opposite side of the lens, these images will develop.
In the case of mirrors, a virtual picture will always be upright. When light rays from a source do not intersect to form an image, an optical system (a set of lenses and/or mirrors) creates a virtual picture (as opposed to a real image). Instead, they can be 'traced back' to a point behind the lens or mirror.
To learn more about lenses, click here.
https://brainly.com/question/32156996
#SPJ4
The image was virtual because it was on the same side as the object.
In Problem II, we determine whether the image is virtual or not. From the given options, "it was on the same side as the object" indicates that the image is virtual. When an object is placed in front of a lens, the lens produces an image of the object on the other side of the lens. However, in this case, since the image is on the same side as the object, it is virtual.
A virtual image is an image that cannot be projected onto a screen. It appears to be behind the lens and is seen through the lens by an observer. Virtual images are always erect and located on the same side of the lens as the object.
Learn more about virtual images:
https://brainly.com/question/13197137
#SPJ11
The average temperature on Titan is 105 K, compared to Earth's 15°C. For 1 m' of air on both worlds and knowing that the pressure on the surface of Titan is 50% greater than the air pressure here, how many more molecules are there in the volume of Titan air compared to the volume of Earth air?
The number of molecules in a gas is directly proportional to the pressure, volume, and temperature according to the ideal gas law
In this case, we are comparing the number of molecules in the same volume of air on Titan and Earth. Given that the pressure on the surface of Titan is 50% greater than the air pressure on Earth, we can conclude that the number of molecules in the volume of Titan air is greater. This is because an increase in pressure leads to a higher density of molecules in the same volume. Additionally, it's important to note that the average temperature on Titan is 105 K, which is significantly colder compared to Earth's 15°C (288 K). Lower temperatures result in decreased molecular kinetic energy, causing the molecules to be less energetic and move more slowly. Despite the lower temperature, the higher pressure compensates for the reduced molecular motion, resulting in a greater number of molecules in the same volume of Titan air compared to Earth air. In summary, due to the higher pressure and lower temperature on Titan, the number of molecules in the volume of Titan air is significantly higher compared to the volume of Earth air.
To learn more about Titan , click here : https://brainly.com/question/12526162
#SPJ11
What is the wave speed if a wave with a wavelength of 8.30 cm
has a period of 2.44 s? Answer to the hundredths place or two
decimal places.
The wave speed is approximately 3.40 cm/s.The wave speed is determined by dividing the wavelength by the period of the wave.
The wave speed represents the rate at which a wave travels through a medium. It is determined by dividing the wavelength of the wave by its period. In this scenario, the wavelength is given as 8.30 cm and the period as 2.44 s.
To calculate the wave speed, we divide the wavelength by the period: wave speed = wavelength/period. Substituting the given values, we have wave speed = 8.30 cm / 2.44 s. By performing the division and rounding the answer to two decimal places, we can determine the wave speed.
To learn more about speed click here:
brainly.com/question/28224010
#SPJ11
If it takes a ball dropped from rest 2.417 s to fall to the ground, from what height h was it released?
To find the height from which the ball was released, we can use the formula for the distance fallen by an object under free fall: d = 0.5 g t 2. In this formula, d represents the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s 2), and t is the time taken to fall.
Given that the time taken to fall is 2.417 s, we can plug in these values into the formula:
d = 0.5 * 9.8 * (2.417)^2
Simplifying this equation, we get:
d = 0.5 9.8 5.855489
d ≈ 28.672 m
Therefore, the ball was released from a height of approximately 28.672 meters. This is the main answer.
The formula used to calculate the distance fallen by an object under free fall is derived from the equations of motion. In this case, we assumed that the ball was dropped from rest, which means it started with an initial velocity of zero. If the ball had an initial velocity, we would need to use a different formula, such as d = where v_0 represents the initial velocity. However, since the question states that the ball was dropped from rest, we can use the simplified formula.
In conclusion, the ball was released from a height of approximately 28.672 meters.
To know more about velocity visit:
brainly.com/question/30559316
#SPJ11
The coefficient of kinetic friction between the block and the ramp is 0.20. The pulley is frictionless. a. What is the acceleration of the system? Ans: a = 4.12 m/s2 b. What is the Tension
Substitute the given values to find the tension.T = (5.0 kg * 4.12 m/s²) + (5.0 kg * 9.81 m/s²) * (1 - 0.20)T = 20.6 N + 39.24 NT = 59.84 N Therefore, the acceleration of the system is 4.12 m/s2 and the tension is 59.84 N.
Given: The coefficient of kinetic friction between the block and the ramp is 0.20. The pulley is frictionless.A. The acceleration of the system The tension T can be determined as follows:Determine the acceleration of the system by utilizing the formula for force of friction.The formula for force of friction is shown below:f
= μFnf
= friction forceμ
= coefficient of friction Fn
= Normal force The formula for the force acting downwards is shown below:F
= m * gF
= force acting downward sm
= mass of the system g
= acceleration due to gravity Determine the net force acting downwards by utilizing the following formula:Net force downwards
= F - f Net force downwards
= m * g - μFnNet force downwards
= m * g - μ * m * gNet force downwards
= (m * g) * (1 - μ)
The net force acting on the system is given by:T - (m * a)
= (m * g) * (1 - μ)
Substitute the given values to find the acceleration of the system.a
= 4.12 m/s2B.
The tension Substitute the calculated value of acceleration into the equation given above:T - (m * a)
= (m * g) * (1 - μ)T
= (m * a) + (m * g) * (1 - μ).
Substitute the given values to find the tension.T
= (5.0 kg * 4.12 m/s²) + (5.0 kg * 9.81 m/s²) * (1 - 0.20)T
= 20.6 N + 39.24 NT
= 59.84 N
Therefore, the acceleration of the system is 4.12 m/s2 and the tension is 59.84 N.
To know more about acceleration visit:
https://brainly.com/question/2303856
#SPJ11
15.1
Part A
An ideal gas expands isothermally, performing 2.70×103 J of work in the process.
Subpart 1
Calculate the change in internal energy of the gas.
Express your answer with the appropriate units.
ΔU =
Subpart 2
Calculate the heat absorbed during this expansion.
Express your answer with the appropriate units.
Q =
Part B
A gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric pressure. When 254 kcal of heat is added to the gas, the volume is observed to increase slowly from 12.0 m3 to 16.2 m3
Subpart 1
Calculate the work done by the gas.
Express your answer with the appropriate units.
W =
Subpart 2
Calculate the change in internal energy of the gas.
Express your answer with the appropriate units.
ΔU =
Part A Subpart 1: For an isothermal process, the change in internal energy (ΔU) is zero. This is because the internal energy of an ideal gas only depends on its temperature, and in an isothermal process, the temperature remains constant. Therefore:
ΔU = 0
Subpart 2:
The heat absorbed during an isothermal process can be calculated using the equation:
Q = W
Where Q is the heat absorbed and W is the work done. In this case, the work done is given as 2.70×[tex]10^3[/tex] J. Therefore:
Q = 2.70×[tex]10^3[/tex] J
Part B
Subpart 1:
The work done by the gas can be calculated using the formula:
W = PΔV
Where P is the pressure and ΔV is the change in volume. In this case, the pressure is maintained at atmospheric pressure, which is typically around 101.3 kPa. The change in volume is given as:
ΔV = Vf - Vi = 16.2 m³ - 12.0 m³ = 4.2 m³
Converting atmospheric pressure to SI units
P = 101.3 kPa = 101.3 × [tex]10^3[/tex] Pa
Calculating the work done:
W = (101.3 × [tex]10^3[/tex] Pa) * (4.2 m³)
= 425.46 × [tex]10^3[/tex] J
≈ 4.25 × [tex]10^5[/tex] J
Subpart 2:
The change in internal energy (ΔU) can be calculated using the first law of thermodynamics:
ΔU = Q - W
In this case, the heat added (Q) is given as 254 kcal. Converting kcal to joules:
Q = 254 kcal * 4.184 kJ/kcal [tex]* 10^3[/tex]J/kJ
= 1.06 × [tex]10^6[/tex] J
Calculating the change in internal energy:
ΔU = 1.06 × 1[tex]0^6[/tex] J - 4.25 ×[tex]10^5[/tex] J
6.33 × [tex]10^5[/tex] J
To know more about isothermal process refer to-
https://brainly.com/question/30159786
#SPJ11
special relativity question. please give a detailed explanation An atom is at rest in the laboratory frame, but in an excited state with rest mass Moi. At t=0, it emits a photon with energy E, and de-excites into its ground state with rest mass Mof. a) What is the final momentum of the recoil atom in terms of E,? b) What is E, in terms of Mo, and Mo.?
According to the conservation of energy principle, the energy of the photon must be equal to the energy difference between the excited and the ground state of the atom. E = Moi - Mof c². The energy E in terms of Moi and Mof is given by the equation E = (Moi - Mof) c².
(a) Calculation of the final momentum of the recoil atom:
Let's consider an excited atom with a rest mass of Moi, initially at rest in the laboratory frame. The atom de-excites into its ground state by emitting a photon with an energy of E, and a final rest mass of Mof.
The final momentum of the atom can be determined from the conservation of momentum principle. When the photon is emitted in one direction, the atom recoils in the opposite direction. The momentum before the photon emission is zero, thus, the total momentum of the system is zero. The momentum of the atom after the photon emission is p. According to the conservation of momentum principle, the total momentum of the system is zero, so the momentum of the photon and atom must balance each other.
Hence the momentum of the photon is also p. Therefore, the momentum of the atom can be calculated as p = E/c.where c is the speed of light.
(b) Calculation of the energy E in terms of Moi and Mof:
According to the conservation of energy principle, the energy of the photon must be equal to the energy difference between the excited and the ground state of the atom.E = Moi - Mof c².The energy E in terms of Moi and Mof is given by the equation E = (Moi - Mof) c².
To learn more about energy visit;
https://brainly.com/question/1932868
#SPJ11
please help!
An uncharged 10-µF capacitor is being charged in series with a 720-22 resistor across a 100-V battery. From the given equation, at the end of one time constant: q = % (1 - e-t/RC) the charge on the c
At the end of one time constant, the charge on the capacitor is approximately 6.32 µC. This can be calculated using the equation q = C (1 - e^(-t/RC)), where C is the capacitance and RC is the time constant.
To find the charge on the capacitor at the end of one time constant, we can use the equation q = C (1 - e^(-t/RC)), where q is the charge, C is the capacitance, t is the time, R is the resistance, and RC is the time constant. In this case, the capacitance is given as 10 µF and the time constant can be calculated as RC = 720 Ω * 10 µF = 7200 µs.
At the end of one time constant, the time is equal to the time constant, which means t/RC = 1. Substituting these values into the equation, we get q = 10 µF (1 - e^(-1)) ≈ 6.32 µC. Therefore, the charge on the capacitor is approximately 6.32 µC at the end of one time constant.
To learn more about capacitor click here:
brainly.com/question/31627158
#SPJ11
4. Find the work done by the force component along the displacement in the interval from 0 to 1.0 m and 2.0 to 4.0 m.
The work done by the force component along the displacement in the interval from 0 to 1.0 m is positive, and in the interval from 2.0 to 4.0 m, it is zero.
Work is defined as the product of the component of a force in the direction of displacement and the magnitude of displacement. If the force and displacement are in the same direction, the work is positive. If they are perpendicular or in opposite directions, the work is zero or negative, respectively.
In the given intervals, we have two scenarios:
Interval from 0 to 1.0 m: The work done by the force component along the displacement is positive. This implies that the force and displacement are in the same direction, resulting in positive work.
Interval from 2.0 to 4.0 m: The work done by the force component along the displacement is zero. This indicates that either the force is perpendicular to the displacement or there is no force acting in that interval. In both cases, the work done is zero.
Therefore, in the interval from 0 to 1.0 m, the work done is positive, and in the interval from 2.0 to 4.0 m, the work done is zero.
To know more about work done, refer here:
https://brainly.com/question/2750803#
#SPJ11
5. (-/2 points) DETAILS SERCP11 2.4.P.050. MY NOTES A small mailbag is released from a helicopter that is descending steadily at 1.57 m/s. (a) After 3.00 s, what is the speed of the mailbag? V= m/s (b) How far is it below the helicopter? d = m (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.57 m/s? m/s d = m Need Help? Read It 6. (-/1.5 Points) DETAILS SERCP11 3.2.P.015. MY NOTES A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 23.09 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.67 m/s2 for a distance of 30.0 m to the edge of the cliff, which is 20.0 m above the ocean. (a) Find the car's position relative to the base of the cliff when the car lands in the ocean. m (b) Find the length of time the car is in the air. Need Help? Read It
(a) The speed of the mailbag after 3.00 seconds is 4.71 m/s (b) The mailbag is 4.71 meters below the helicopter at this time. (c) If the helicopter is rising steadily at 1.57 m/s, the answers to parts (a) and (b) would be the same
(a) To find the speed of the mailbag after 3.00 seconds when the helicopter is descending steadily at 1.57 m/s, we can simply subtract the descending speed of the helicopter from the mailbag's speed. The descending speed of the mailbag is 1.57 m/s since it is released from a descending helicopter. Thus, the speed of the mailbag after 3.00 seconds is 1.57 m/s + 3.00 s = 4.71 m/s.
(b) The distance below the helicopter after 3.00 seconds can be calculated by multiplying the speed of the mailbag (4.71 m/s) by the time (3.00 seconds). This gives us 4.71 m/s × 3.00 s = 14.13 meters. Therefore, the mailbag is 14.13 meters below the helicopter after 3.00 seconds.
(c) If the helicopter is rising steadily at 1.57 m/s, the answers to parts (a) and (b) remain the same. This is because the speed of the mailbag relative to the helicopter is the same, regardless of whether the helicopter is ascending or descending. The speed of the mailbag after 3.00 seconds would still be 4.71 m/s, and the distance below the helicopter would still be 4.71 meters.
To learn more about speed click here, brainly.com/question/17661499
#SPJ11
1. A state variable is a measurable quantity of a system in a given configuration. The value of the state variable only depends on the state of the system, not on how the system got to be that way. Categorize the quantities listed below as either a state variable or one that is process-dependent, that is, one that depends on the process used to transition the system from one state to another. Q, heat transferred to system p, pressure V, volume n, number of moles Eth, thermal energy T, temperature W, work done on system Process-dependent variables State Variables
State Variables: p (pressure), V (volume), n (number of moles), Eth (thermal energy), T (temperature)
Process-dependent variables: Q (heat transferred to system), W (work done on system)
State variables are measurable quantities that only depend on the state of the system, regardless of how the system reached that state. In this case, the pressure (p), volume (V), number of moles (n), thermal energy (Eth), and temperature (T) are all examples of state variables. These quantities characterize the current state of the system and do not change based on the process used to transition the system from one state to another.
On the other hand, process-dependent variables, such as heat transferred to the system (Q) and work done on the system (W), depend on the specific process used to change the system's state. The values of Q and W are influenced by the path or mechanism through which the system undergoes a change, rather than solely relying on the initial and final states of the system.
Learn more about thermal energy here:
brainly.com/question/31631845
#SPJ11
Does Archimedes’ principle tell us that if an immersed object
displaces 5 N of fluid, the buoyant force on the object is 5 N?.
Explain why.
Archimedes' principle tells us that if an immersed object displaces more than 100N of fluid, the buoyant force on the object is equal to the weight of the fluid displaced.
Therefore, if an object displaces 5 N of fluid, the buoyant force on the object will be less than 5 N.The reason for this is because the buoyant force is equal to the weight of the fluid displaced by the object. In other words, the weight of the fluid that is displaced by the object determines the buoyant force on the object. If the object is only displacing 5 N of fluid, then the buoyant force will be less than 5 N because the weight of the fluid displaced is less than 5 N.Archimedes' principle is important for understanding the behavior of objects in fluids.
It helps us to understand why objects float or sink and how the buoyant force on an object is related to the weight of the fluid displaced.
To know more about force visit:
https://brainly.com/question/30507236
#SPJ11
A concave mirror produces a real image that is 5 times as large as the object. The object is located 8.4 cm in front of the mirror. Is the image upright or inverted?
Upright
Inverted
What is the focal length of this mirror? in cm
The image is inverted and the focal length is 7cm
What is image formed by a concave mirror?A concave mirror is a curved mirror where the reflecting surface is on the inner side of the curved shape.
Images formed by concave mirror are :
Real , Inverted and the size depends on the position of the object.
We should also take note that concave mirror can produce virtual image at a circumstance.
Since the image is real, the image will be inverted. All real images are inverted.
Using lens formula
1/f = 1/u + 1/v
1/f = 1/8.4 + 1/42
1/f = 42+8.4 )/352.8
1/f = 50.4 / 352.8
f = 352.8/50.4
f = 7 cm
Therefore the focal length of the mirror is 7cm
learn more about image of concave mirror from
https://brainly.com/question/27841226
#SPJ4
The positron is the antiparticle to the electron. It has the same mass and a positive electric charge of the same magnitude as that of the electron. Positronium is a hydrogenlike atom consisting of a positron and an electron revolving around each other. Using the Bohr model, find (a) the allowed distances between the two particles.
The allowed distances between the two particles in positronium can be determined using the Bohr model by calculating the distance using the formula r = n² * (0.529 Å) / Z, where n is the principal quantum number and Z is the atomic number,
In the Bohr model, the allowed distances between the two particles in positronium can be determined using the principles of quantum mechanics. The Bohr model states that the electron and positron orbit each other in circular paths with certain allowed distances, known as orbits or energy levels. The distance between the particles is given by the formula:
r = n² * (0.529 Å) / Z
Where r is the distance between the particles, n is the principal quantum number, and Z is the atomic number. In the case of positronium, Z is 1, as it is hydrogen-like
For example, if we take n = 1, the distance between the particles would be:
r = 1² * (0.529 Å) / 1 = 0.529 Å
Similarly, for n = 2, the distance would be:
r = 2² * (0.529 Å) / 1 = 2.116 Å
So, the allowed distances between the two particles in positronium, according to the Bohr model, depend on the principal quantum number n. As n increases, the distance between the particles increases as well.
For more such questions on Bohr model visit:
https://brainly.com/question/4138548
#SPJ8
In an engine, a piston oscillates with simple harmonic motion so that its position varies
according to the expression, x = 4.00 cos (4t + ϖ/4) where x is in centimeters and t is in
seconds.
(a) At t = 0, find the position of the piston.
(b) At t = 0, find velocity of the piston.
(c) At t = 0, find acceleration of the piston.
(d) Find the period and amplitude of the motion.
The amplitude of the motion is the maximum displacement of the piston from its equilibrium position. The amplitude of the motion is 4cm.
The position of a piston in an engine is given by the equation, x = 4.00cos(4t + ω/4), where x is in centimeters and t is in seconds.
(a) At t = 0, find the position of the piston.
Substituting t = 0 into the equation for x, we get:
x = 4.00cos(ω/4)
At t = 0, the cosine term simplifies to cos(ω/4) = +√2/2, since cos(0) = 1.
Therefore, the position of the piston at t = 0 is:
x = 4.00 * √2/2 = 2.828 cm
(b) At t = 0, find velocity of the piston.
The velocity of the piston is given by the derivative of the position function with respect to time. Taking the derivative of x with respect to t, we get:
v = dx/dt = -16.00sin(4t + ω/4)
Substituting t = 0 and using the same value of cosine as before, we get:
v = -16.00sin(ω/4)
Since sin(ω/4) = 1/√2, the velocity at t = 0 is:
v = -16.00/√2 = -11.31 cm/s
(c) At t = 0, find acceleration of the piston.
The acceleration of the piston is given by the second derivative of the position function with respect to time. Taking the second derivative of x with respect to t, we get:
a = d^2x/dt^2 = -64.00cos(4t + ω/4)
Substituting t = 0 and using the same value of cosine as before, we get:
a = -64.00cos(ω/4)
Since cos(ω/4) = √2/2, the acceleration at t = 0 is:
a = -64.00 * √2/2 = -45.25 cm/s^2
(d) Find the period and amplitude of the motion.
The period of the motion is the time it takes for the piston to complete one full cycle of motion. The period is given by the formula:
T = 2π/ω
where ω is the angular frequency of the motion. From the given equation, we can see that the angular frequency is 4.
Therefore, the period of the motion is:
T = 2π/4 = π/2 seconds
The amplitude of the motion is the maximum displacement of the piston from its equilibrium position. From the given equation, we can see that the amplitude is 4 cm.
Therefore, the amplitude of the motion is:
A = 4 cm
for more such questions on amplitude
https://brainly.com/question/3613222
#SPJ8
Sheena can row a boat at 3.00mi/h in still water. She needs to cross a river that is 1.20mi wide with a current flowing at 2.00mi/h. Not having her calculator ready, she guesses that to go straight across, she should head upstream at an angle of 25.0 ′′ from the direction straight across the river. How long does it take her to cross the river?
It takes her 1 hour and 5 minutes to cross the river.
We have to find the time it will take Sheena to cross the river.
Let's consider the given information. Sheena can row a boat at 3.00mi/h in still water and the river that is 1.20mi wide with a current flowing at 2.00mi/h.
She guesses that to go straight across, she should head upstream at an angle of 25.0 ′′ from the direction straight across the river.
As per the given information, Sheena's boat speed in still water is 3.00mi/h. The current speed is 2.00mi/h. This means, the total effective speed of the boat will be the vector sum of boat speed and current speed. effective speed
= 3.00mi/h - 2.00mi/hcos 25
°≈ 1.10 mi/h
Now we know that the river's width is 1.20 miles. The effective speed of the boat is 1.10 mi/h.
Hence, the time taken to cross the river is 1.20/1.10
≈ 1.09 hours
= 1 hour and 5 minutes.
To know more about minutes visit:
https://brainly.com/question/32674197
#SPJ11
Part A Challenge problem, do this one last: A newly developed transparent material, Hellerium, has an index of refraction for visible light that varies with wavelength as n = 30.0 nm/2/21/2, where is in nm A 275-nm-thick layer of Hellerium is placed on glass (n = 1.55). For what visible wavelengths will the reflected light have maximum constructive interference? Express your answer in nanometers. If there is more than one wavelength, enter each wavelength separated by a comma. VALO c = nm Submit Request Answer Provide Feedback
To determine the visible wavelengths at which the reflected light will have maximum constructive interference, we need to consider the interference conditions arising from the thickness of the Helerum layer.
By analyzing the interference equation and using the given refractive indices, we can calculate the wavelengths that satisfy the condition for constructive interference. Constructive interference occurs when the path difference between the reflected waves from the two interfaces (air-Hellerium and Hellerium-glass) is an integer multiple of the wavelength.
The interference condition can be expressed as:
2nt = mλ,where n is the refractive index of Hellerium, t is the thickness of the Hellerium layer, m is an integer representing the order of interference, and λ is the wavelength of light.Substituting the given values, we have:2(30.0 nm/2/21/2)(275 nm) = mλ.Simplifying the equation, we find:
8250 = mλ.
To find the values of λ that satisfy the equation, we need to determine the values of m that correspond to constructive interference. Since the question asks for visible wavelengths, we consider the range of visible light from approximately 400 nm to 700 nm.
For constructive interference, we calculate the corresponding values of m for each wavelength in the visible range:For λ = 400 nm, m = 8250/400 ≈ 20.63.
For λ = 410 nm, m = 8250/410 ≈ 20.12.
For λ = 420 nm, m = 8250/420 ≈ 19.64.We continue this process for each wavelength in the visible range.
The wavelengths that satisfy the condition for constructive interference will have an integer value for m. Based on the calculations, we find that the visible wavelengths for maximum constructive interference are approximately 400 nm, 410 nm, 420 nm, and so on, with a difference of approximately 10 nm between each wavelength.
Therefore, the reflected light will exhibit maximum constructive interference at these specific wavelengths.
Learn more about constructive interference click here: brainly.com/question/31857527
#SPJ11
The work done by a constant 50 V/m electric field on a +2.0 C
charge over along a displacement of 0.50 m parallel to the electric
field in question is:
The work done by a constant 50 V/m electric field on a +2.0 C charge over along a displacement of 0.50 m parallel to the electric field is 50 J.
Potential difference (V) = 50 V/mCharge (Q) = +2.0 CDisplacement (d) = 0.50 mWe have to calculate the work done by a constant 50 V/m electric field on a +2.0 C charge over a displacement of 0.50 m parallel to the electric field.Let's start with the formula that is used to find the work done by the electric field.Work Done (W) = Potential difference (V) * Charge (Q) * Displacement (d)W = V * Q * dPutting the values in the above formula, we get;W = 50 V/m × +2.0 C × 0.50 m= 50 × 2.0 × 0.50 J= 50 J. Hence, the work done by a constant 50 V/m electric field on a +2.0 C charge over along a displacement of 0.50 m parallel to the electric field is 50 J.
Learn more about electric field :
https://brainly.com/question/30544719
#SPJ11
A 30−μF capacitor is connected across a 60−Hz. AC source whose voltage amplitude is 50 V. (a) What is the maximum charge on the capacitor? (b) What is the maximum current into the capacitor? (c) What is the phase relationship between the capacitor charge and the current in the circuit?
(a) The maximum charge on a capacitor is given by the equation Q = C × V, where Q is the charge, C is the capacitance, and V is the voltage amplitude. Plugging in the values, we have Q = (30 × [tex]10^{(-6)}[/tex] F) × (50 V), which equals 1.5 × [tex]10^{(-3)}[/tex] C.
(b) The maximum current into the capacitor is given by the equation I = C × ω × V, where I is the current, C is the capacitance, ω is the angular frequency (2πf), and V is the voltage amplitude. Plugging in the values, we have I = (30 × [tex]10^{(-6)}[/tex] F) × (2π × 60 Hz) × (50 V), which simplifies to 0.056 A or 56 mA.
(c) In an AC circuit with a capacitor, the current leads the voltage by a phase angle of 90 degrees. Therefore, the phase relationship between the capacitor charge and the current is such that the charge on the capacitor reaches its maximum value when the current is at its peak. This means that the charge and current are out of phase by 90 degrees.
In conclusion, for the given circuit, the maximum charge on the capacitor is 1.5 × [tex]10^{(-3)}[/tex] C, the maximum current into the capacitor is 56 mA, and the phase relationship between the capacitor charge and the current is 90 degrees, with the charge leading the current.
To know more about Capacitance visit-
brainly.com/question/31871398
#SPJ11
1. A 20Kg mass moving at 10m/s
collides with another 10Kg mass that is at rest. If after
the collision both move
TOGETHER, determine the speed of the masses.
The masses move together with a final speed of 6.67 m/s due to conservation of momentum.
To calculate the final speed of the masses after the collision, we can apply the principle of conservation of momentum. The initial momentum before the collision is given by the sum of the individual momenta of the two masses: (20 kg * 10 m/s) + (10 kg * 0 m/s) = 200 kg·m/s. Since the masses move together after the collision, their final momentum is also equal to 200 kg·m/s.
We can then determine the final speed by dividing the total momentum by the combined mass of the masses: 200 kg·m/s / (20 kg + 10 kg) = 6.67 m/s. Therefore, the speed of the masses after the collision is 6.67 m/s.
To learn more about momentum click here:
brainly.com/question/30677308
#SPJ11
The quark model asserts that every baryon is composed of a. ΩΩΩ
b. ΩΩ
c. ΩΩΩ
d. ΩΩ
The correct option that represents the asserts that every baryon is composed of (a) ΩΩΩ, which indicates that according to the quark model, every baryon is composed of three quarks.
The quark model is a fundamental theory in particle physics that describes the structure of baryons, which are a type of subatomic particle. In the context of the quark model, baryons are particles that consist of three quarks.
(a) The answer "ΩΩΩ" represents a baryon composed of three Ω (Omega) quarks.
(b) The answer "ΩΩc" is not a valid option in the context of the quark model.
(c) The answer "ΩΩΩ" represents a baryon composed of three Ω (Omega) quarks.
(d) The answer "ΩΩ" represents a baryon composed of two Ω (Omega) quarks.
Therefore, the correct option is (a) ΩΩΩ, which indicates that according to the quark model, every baryon is composed of three quarks.
Learn more about quark model at: https://brainly.com/question/29617670
#SPJ11
a meteor lands in your bedroom at 8AM Monday morning and is
measured to be emitting at 1450 mCi. at 8PM Thursday it is only
emitting 1132uCi. calculate the half life.
The half-life of the meteor's radioactive decay is approximately 396.61 hours based on the given measurements.
To calculate the half-life of the meteor's radioactive decay, we can use the following formula:
N = N₀ * (1/2)^(t / T)
Where:
- N is the current activity (in this case, 1132 μCi).
- N₀ is the initial activity (1450 mCi = 1450000 μCi).
- t is the time elapsed (in this case, 84 hours).
- T is the half-life we want to determine.
Let's solve the equation for T:
1132 = 1450000 * (1/2)^(84 / T)
Dividing both sides of the equation by 1450000:
1132 / 1450000 = (1/2)^(84 / T)
To simplify the equation, let's express 1132 / 1450000 as a decimal:
0.0007793 = (1/2)^(84 / T)
Now, take the logarithm of both sides of the equation:
log(0.0007793) = log((1/2)^(84 / T))
Using logarithm properties, we can bring down the exponent:
log(0.0007793) = (84 / T) * log(1/2)
Rearranging the equation to solve for T:
T = (84 * log(1/2)) / log(0.0007793)
Using a calculator:
T ≈ 396.61 hours
Therefore, the half-life of the meteor's radioactive decay is approximately 396.61 hours.
To know more about decay, click here:
brainly.com/question/1770619?
#SPJ11
An ideal gas expands isothermally, performing 5.00×10 3
J of work in the process. Calculate the change in internal energy of the gas. Express your answer with the appropriate units. Calculate the heat absorbed during this expansion. Express your answer with the appropriate units.
For an isothermal expansion of an ideal gas, the change in internal energy is zero. In this case, the gas performs 5.00×10^3 J of work, and the heat absorbed during the expansion is also 5.00×10^3 J.
An isothermal process involves a change in a system while maintaining a constant temperature. In this case, an ideal gas is expanding isothermally and performing work. We need to calculate the change in internal energy of the gas and the heat absorbed during the expansion.
To calculate the change in internal energy (ΔU) of the gas, we can use the first law of thermodynamics, which states that the change in internal energy is equal to the heat (Q) absorbed or released by the system minus the work (W) done on or by the system. Mathematically, it can be represented as:
ΔU = Q - W
Since the process is isothermal, the temperature remains constant, and the change in internal energy is zero. Therefore, we can rewrite the equation as:
0 = Q - W
Given that the work done by the gas is 5.00×10^3 J, we can substitute this value into the equation:
0 = Q - 5.00×10^3 J
Solving for Q, we find that the heat absorbed during this expansion is 5.00×10^3 J.
To know more about the first law of thermodynamics, refer here:
https://brainly.com/question/32101564#
#SPJ11
A beaker contains 2 grams of ice at a temperature of -10°C. The mass of the beaker may be ignored. Heat is supplied to the beaker at a constant rate of 2200J/minute. The specific heat of ice is 2100 J/kgK and the heat of fusion for ice is 334 x103 J/kg. How much time passes
before the ice starts to melt?
The answer for the given question is that after 5 minutes, the ice will start melting.
Let the time taken for ice to melt be t minutes.
Therefore, heat supplied to ice = heat of fusion of ice + heat required to raise the temperature of ice from -10°C to 0°C
Heat required to raise the temperature of ice from -10°C to 0°C = mass of ice × specific heat of ice × temperature difference. i.e Q1 = 2 × 2100 × 10 = 42000 Joules.
Heat of fusion of ice = mass of ice × heat of fusion of ice, i.e Q2 = 2 × 334000 = 668000 Joules.
Heat supplied to ice = 2200 × t Joules. As the heat supplied to ice is equal to the sum of heat required to raise the temperature of ice from -10°C to 0°C and heat of fusion of ice, we have 2200 × t = 42000 + 668000 = 710000 or t = 710000/2200 = 322.73 sec ≈ 5 minutes.
Therefore, it takes about 5 minutes for the ice to start melting.
Learn more about heat of fusion: https://brainly.com/question/30403515
#SPJ11
The temperature of an ideal gas in a sealed rigid 0.60-m-container is reduced from 480K to 270 K. The final pressure of the gas is 90 KPA. The molar heat capacity at constant volume of the gas is 28.0 J/mol K. How much heat is absorbed by the gas during this process? (R = 3.31 J/mol К) -130kJ -170 kJ 130 kJ 170 kj 0 kJ
The amount of heat absorbed by the gas during the process is -130 kJ.
To calculate the heat absorbed, we can use the formula:
Q = nCΔT
Where Q is the heat absorbed, n is the number of moles of the gas, C is the molar heat capacity at constant volume, and ΔT is the change in temperature.
First, we need to determine the number of moles of the gas. This can be done using the ideal gas law equation:
PV = nRT
Rearranging the equation, we have:
n = PV/RT
Substituting the given values (P = 90 kPa, V = 0.60 m³, R = 3.31 J/mol K, T = 270 K), we can calculate n.
Next, we can substitute the values of n, C, and ΔT (ΔT = final temperature - initial temperature) into the formula Q = nCΔT to find the heat absorbed.
After performing the calculations, we find that the heat absorbed is approximately -130 kJ.
Therefore, the correct answer is -130 kJ.
To learn more about heat, click here: https://brainly.com/question/13892799
#SPJ11
An object is 2m away from a convex mirror in a store, its image
is 1 m behind the mirror. What is the focal length of the
mirror?
The focal length of the convex mirror is -2 m. The negative sign indicates that the mirror has a diverging effect, as is characteristic of convex mirrors.
To determine the focal length of a convex mirror, we can use the mirror equation:
1/f = 1/d_o + 1/d_i
Where f is the focal length, d_o is the object distance (distance of the object from the mirror), and d_i is the image distance (distance of the image from the mirror).
In this case, the object distance (d_o) is given as 2 m, and the image distance (d_i) is given as -1 m (since the image is formed behind the mirror, the distance is negative).
Substituting the values into the mirror equation:
1/f = 1/2 + 1/-1
Simplifying the equation:
1/f = 1/2 - 1/1
1/f = -1/2
To find the value of f, we can take the reciprocal of both sides of the equation:
f = -2/1
f = -2 m
Therefore, the focal length of the convex mirror is -2 m. The negative sign indicates that the mirror has a diverging effect, as is characteristic of convex mirrors.
Learn more about a convex mirror:
https://brainly.com/question/32811695
#SPJ11
A beach comber finds a corked bottle. The air in the bottle is at a pressure of 1 atm and 25C. If the bottle is heated the cork pops out at a temperature of 86C. a.) What is the pressure in the bottle just before the cork is popped. b.) What is the magnitude of the friction force holding the cork in place? (Area of cork =5.2 cm 2 )
(a) The pressure in the bottle just before the cork is popped is approximately 1.204 atm.(b) The magnitude of the friction force holding the cork in place is 0.000626 m²·atm.
a) To find the pressure in the bottle just before the cork is popped, we can use the ideal gas law, which states:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
Since the volume of the bottle remains constant, we can write:
P₁/T₁ = P₂/T₂,
where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
P₁ = 1 atm,
T₁ = 25°C = 298 K,
T₂ = 86°C = 359 K.
Substituting the values into the equation, we can solve for P₂:
(1 atm) / (298 K) = P₂ / (359 K).
P₂ = (1 atm) * (359 K) / (298 K) = 1.204 atm.
b) The magnitude of the friction force holding the cork in place can be determined by using the equation:
Friction force = Pressure * Area,
where the pressure is the pressure inside the bottle just before the cork is popped.
Pressure = 1.204 atm,
Area of the cork = 5.2 cm².
Converting the area to square meters:
Area = (5.2 cm²) * (1 m^2 / 10,000 cm²) = 0.00052 m².
Substituting the values into the equation, we can calculate the magnitude of the friction force:
Friction force = (1.204 atm) * (0.00052 m²) = 0.000626 m²·atm.
Please note that to convert the friction force from atm·m² to a standard unit like Newtons (N), you would need to multiply it by the conversion factor of 101325 N/m² per 1 atm.
To know more about friction force refer here
brainly.com/question/30280206
#SPJ11