Answer:
thats a really cool design or whatever you got there.
Explanation:
niceeeeeeee :)
A 1-ft rod with a diameter of 0.5 in. is subjected to a tensile force of 1,300 lb and has an elongation of 0.009 in. The modulus of elasticity of the material is most nearly:
Answer:
E = 8.83 kips
Explanation:
First, we determine the stress on the rod:
[tex]\sigma = \frac{F}{A}\\\\[/tex]
where,
σ = stress = ?
F = Force Applied = 1300 lb
A = Cross-sectional Area of rod = 0.5[tex]\pi \frac{d^2}{4} = \pi \frac{(0.5\ in)^2}{4} = 0.1963\ in^2[/tex]
Therefore,
[tex]\sigma = \frac{1300\ lb}{0.1963\ in^2} \\\\\sigma = 6.62\ kips[/tex]
Now, we determine the strain:
[tex]strain = \epsilon = \frac{elongation}{original\ length} \\\\\epsilon = \frac{0.009\ in}{12\ in}\\\\\epsilon = 7.5\ x\ 10^{-4}[/tex]
Now, the modulus of elasticity (E) is given as:
[tex]E = \frac{\sigma}{\epsilon}\\\\E = \frac{6.62\ kips}{7.5\ x\ 10^{-4}}[/tex]
E = 8.83 kips
For a turbine, it is seen that work is done by the fluid at the expense of its enthalpy. Explain with mathematical proof.
Answer:
The work of the turbine is done at the expense of the enthalpy of the fluid.
Explanation:
Ideally speaking, a turbine is a steady-state devices that has no heat interactions and generates works at the expense of enthalpy. By the First Law of Thermodynamic, we have the following definition for steady-state conditions: (all energy components are measured in joules)
[tex]E_{in} - E_{out} + E_{gen} = 0[/tex] (1)
Where:
[tex]E_{in}[/tex] - Inlet energy.
[tex]E_{out}[/tex] - Outlet energy.
[tex]E_{gen}[/tex] - Generated energy.
Generated energy is associated with endothermic and exothermic chemical reactions and fission processes in radioactive elements and isotopes. Since fluids used in turbines are usually inert, the generated energy is zero and each remaining componets of the expression are defined:
[tex]E_{in} = U_{g,in}+K_{in}+H_{in}[/tex] (2)
[tex]E_{out} = U_{g,out}+K_{out}+H_{out}+W_{out}[/tex] (3)
Where:
[tex]U_{g,in}[/tex], [tex]U_{g,out}[/tex] - Inlet and outlet gravitational potential energies.
[tex]K_{in}[/tex], [tex]K_{out}[/tex] - Inlet and outlet translational kinetic energies.
[tex]H_{in}[/tex], [tex]H_{out}[/tex] - Inlet and outlet enthalpies.
[tex]W_{out}[/tex] - Energy generated by the turbine.
Usually, turbines at steady state does not report significant changes in translational and gravitational potential energies and (2) and (3) can be reduced into this form:
[tex]E_{in} = H_{in}[/tex] (2b)
[tex]E_{out} = H_{out}+W_{out}[/tex] (3b)
And we find the following equation of work by substituting on (1):
[tex]W_{out} = H_{in}-H_{out}[/tex] (4)
In a nutshell, the work of the turbine is done at the expense of the enthalpy of the fluid.
Merchants get commission from selling products that are consigned to them true or false
Answer:
true
Explanation:
Who is responsible for providing working conditions which are free from fall dangers?
Answer:
I am pretty confident it is the Employer!
Explanation:
They have the responsibility to provide a safe workplace that is free from serious hazards, according to the General Duty Clause of the OSH Act (OSHA Standards)
I hope this helped you!! :D
Answer:
Employers
Explanation:
OSHA requires employers to: Provide working conditions that are free of known dangers. Keep floors in work areas in a clean and, so far as possible, a dry condition. Select and provide required personal protective equipment at no cost to workers.
Schrodinger equation is a ........... Equation
Answer:
linear partial differential
Explanation:
The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject.
A ball is dropped onto a step at point A and rebounds with a velocity vo at an angle of 15° with the vertical. Determine the value of vo knowing that just before the ball bounces at point B its velocity vB forms an angle of 12° with the vertical. Also determine the velocity of B, vB and the distance d.
Answer:
v₀ = 2.68 m/s.
[tex]v_{B}[/tex] = 3.33 m/s
d = 1.61 m
Explanation:
Searching on the internet I found the picture of the answer in which the height between point A and point B is equal to 0.2 m.
To determine the value of v₀ we need to use the following equation:
[tex] v_{f} = v_{0} - gt [/tex]
Taking the initial vertical velocity ([tex]v_{0_{y}}[/tex]) as [tex]v_{A_{y}}[/tex] and the final vertical velocity ([tex]v_{f_{y}}[/tex]) as [tex]v_{B_{y}}[/tex] we have:
[tex]v_{B_{y}} = v_{A_{y}} - gt[/tex]
We can express the time (t) in terms of the velocities of A and B:
[tex] t = \frac{v_{A_{y}} - v_{B_{y}}}{g} [/tex] (1)
Now, we can use the equation:
[tex]y_{f} = y_{0} + v_{A_{y}}t - \frac{1}{2}gt^{2}[/tex] (2)
By entering equation (1) into equation (2):
[tex]y_{f} = y_{0} + v_{A_{y}}*(\frac{v_{A_{y}} - v_{B_{y}}}{g}) - \frac{1}{2}g(\frac{v_{A_{y}} - v_{B_{y}}}{g})^{2}[/tex] (3)
Since [tex]v_{A_{x}} = v_{B_{x}} [/tex] because there is no acceleration in the horizontal movement, we have:
[tex] v_{A}sin(15) = v_{B}sin(12) [/tex]
[tex] v_{A} = \frac{v_{B}sin(12)}{sin(15)} [/tex] (4)
Taking:
[tex]y_{f}[/tex] = 0
[tex]y_{0}[/tex] = 0.2 m
g = 9.81 m/s²
[tex]v_{A_{y}} = v_{A}cos(15)[/tex]
[tex]v_{B_{y}} = v_{B}cos(12)[/tex]
Entering the above values and equation (4) into equation (3) we have:
[tex] -0.4 m*9.81 m/s^{2} = (\frac{v_{B}sin(12)cos(15)}{sin(15)})^{2} - (v_{B}cos(12))^{2} [/tex]
By solving the above quadratic equation:
[tex]v_{B} = 3.33 m/s [/tex]
Hence, the velocity of the ball [tex]v_{B}[/tex] is 3.33 m/s.
Now, we can find [tex]v_{A}[/tex] by using equation (4):
[tex]v_{A} = \frac{v_{B}sin(12)}{sin(15)} = \frac{3.33 m/s*sin(12)}{sin(15)} = 2.68 m/s [/tex]
Then, the value of v₀ of the ball is 2.68 m/s.
Finally, to find the distance between point A and point B we need to calculate the time by using equation (1):
[tex]t = \frac{v_{A_{y}} - (-v_{B_{y}})}{g} = \frac{v_{A_{y}} + v_{B_{y}}}{g}[/tex]
The minus sign in [tex]v_{B_{y}}[/tex] is because the vertical component of the vector is negative.
[tex] t = \frac{v_{A_{y}} + v_{B_{y}}}{g} = \frac{2.68 m/s*cos(15) + 3.33 m/s*cos(12)}{9.81 m/s^{2}} = 0.60 s [/tex]
Now, the distance is:
[tex] x = v_{0}*t = 2.68 m/s*0.60 s = 1.61 m [/tex]
I hope it helps you!
What is the preferred approach to risk mitigation?
-Tolerate
-Transfer
-Terminate
-Treat
Answer:
The correct option is;
Terminate
Explanation:
Termination of the risk is equivalent to elimination of the risk by avoiding the activity that brings about the risk or by using a different process that does not include the risk observed in the previous process option
When the reward far outweigh the risk, it may be decided to terminate or eliminate the risk and miss the reward and also terminate the likelihood of the losses to be incurred.
Which size lug nut would fit a metric wheel stud?
A)7/16-20 LH
B)½ X20
C)M12X 1.5
D)7/16-20RH
what is 7/8 + 1/2 on a ruler
Answer:
11/8
Explanation:
7/8+4/8=11/8 if you want it on a ruler you need to go online and type fraction to decimal converter and put in 11/8 into a decimal
Question #6 Fill in the Blank Complete the following sentence. The term describes initiatives and products that preserve the environment
Answer:
The term "green" describes initiatives and products that preserve the environment
Explanation:
In order to preserve the environment the Environmental Protection Agency has provides tips for "Being Green on the Road", which highlights the topics including, Green Vehicle Guides, guides for Fuel Economy, guides for Clean Diesel and many more ways our environmental footprint can be reduced
A green economy is an economy that focuses on the reduction of risk of economic activity on the environment, such as the reduction of carbon emission and reduction in environmental pollution, biodiversity loss prevention, and promotes a sustainable development
A green tech aims to protect the environment and to reverse previous damage done to the environment, including technology for clean energy, water purification, and waste recycling.
Answer:
The correct answer is stressor. The durability of building products and structures is affected by stressors such as rain, heat, snow, and hurricanes. Construction standards consider these potential stressors.
3. Which of the following statements is false?
a. The condenser is normally mounted just in front of the radiator.
b. The receiver/dryer is a storage tank for the liquid refrigerant from the condenser.
c.An accumulator is not used in a system with a receiver/dryer.
d All of the above
Answer: c.An accumulator is not used in a system with a receiver/dryer
Explanation:
In a refrigeration system, a condenser is used to transfer heat and this occurs from the refrigerant to the air or water.
Then, the refrigerant then condenses to liquid when the hear has been transferred.
We should note that the condenser is normally mounted in front of the radiator. The receiver/dryer is a storage tank for the liquid refrigerant from the condenser.
The statement that an accumulator is not used in a system with a receiver/dryer is not true. This is because, the accumulator gives protection to the compressor which helps to prevent the failure of the compressor.
Therefore, the answer is C.
a. Briefly describe the microstructural difference between spheroidite and tempered martensite. Explain why tempered martensite is much stronger.
b. Explain why tempered martensite is much harder and stronger.
Answer:
Answered below.
Explanation:
A) Both spheroidite & tempered martensite possess sphere - like cementite particles within their microstructure known as a ferrite matrix. However, the difference is that these particles are much larger for spheroidite than tempered.
B) Tempered martensite is much harder and stronger than spheroidite primarily because there is much more ferrite - cementite phase boundary area for its sphere - like cementite particles.
This is because the greater the boundary area, the more the hardness.
Tech A says that you can test for defective ignition wires by using a spray bottle and water. Tech B says that you can test for defective ignition wires with a grounded test lead. Who is correct?
A) Tech A
B) Tech B
C) Both Techs A and B
D) Neither Tech A nor B
Answer: C) Both Techs A and B
Explanation:
Technician A and Technician B are both very right. Using a spray bottle and water, the ignition wire test can be carried out using any of the methods described above. Or, by using a grounded test lead that is connected to a multimeter, you can also conduct the test for faulty ignition wires.
Answer: Either A or B
Explanation:
Considering only (110), (1 1 0), (101), and (10 1 ) as the possible slip planes, calculate the stress at which a BCC single crystal will yield if the critical resolved shear stress is 50 MPa and the load is applied in the [100] direction.
Solution :
i. Slip plane (1 1 0)
Slip direction -- [1 1 1]
Applied stress direction = ( 1 0 0 ]
τ = 50 MPa ( Here slip direction must be perpendicular to slip plane)
τ = σ cos Φ cos λ
[tex]$\cos \phi = \frac{(1,0,0) \cdot (1,1,0)}{1 \times \sqrt2}$[/tex]
[tex]$=\frac{1}{\sqrt2 }$[/tex]
[tex]$\cos \lambda = \frac{(1,0,0) \cdot (1,-1,1)}{1 \times \sqrt3}$[/tex]
[tex]$=\frac{1}{\sqrt3 }$[/tex]
τ = σ cos Φ cos λ
∴ [tex]$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $[/tex]
σ = 122.47 MPa
ii. Slip plane --- (1 1 0)
Slip direction -- [1 1 1]
[tex]$\cos \phi = \frac{(1, 0, 0) \cdot (1, -1, 0)}{1 \times \sqrt2} =\frac{1}{\sqrt2}$[/tex]
[tex]$\cos \lambda = \frac{(1, 0, 0) \cdot (1, 1, -1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$[/tex]
τ = σ cos Φ cos λ
∴ [tex]$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $[/tex]
σ = 122.47 MPa
iii. Slip plane --- (1 0 1)
Slip direction --- [1 1 1]
[tex]$\cos \phi = \frac{(1, 0, 0) \cdot (1, 0, 1)}{1 \times \sqrt2} =\frac{1}{\sqrt2}$[/tex]
[tex]$\cos \lambda = \frac{(1, 0, 0) \cdot (1, 1, -1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$[/tex]
τ = σ cos Φ cos λ
∴ [tex]$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $[/tex]
σ = 122.47 MPa
iv. Slip plane -- (1 0 1)
Slip direction ---- [1 1 1]
[tex]$\cos \phi = \frac{(1, 0, 0) \cdot (1, 0, -1)}{1 \times \sqrt2}=\frac{1}{\sqrt2}$[/tex]
[tex]$\cos \lambda = \frac{(1, 0, 0) \cdot (1, -1, 1)}{1 \times \sqrt3} =\frac{1}{\sqrt3}$[/tex]
τ = σ cos Φ cos λ
∴ [tex]$50= \sigma \times \frac{1}{\sqrt2} \times \frac{1}{\sqrt3} $[/tex]
σ = 122.47 MPa
∴ (1, 0, -1). (1, -1, 1) = 1 + 0 - 1 = 0
A 1,040 N force is recorded on a hemispherical vane as it redirects a 2.5 cm- blade diameter water jet through a 180 angle. Determine the velocity of the flowing water jet if the blade diameter water jer through a 180' angle. Determinethe velcity of the flowing water jet if is assumed to be frictionless.
This question is incomplete, the complete question is;
A 1,040 N force is recorded on a hemispherical vane as it redirects a 2.5 cm- blade diameter water jet through a 180 angle.
Determine the velocity of the flowing water jet if the blade is assumed to be frictionless.
Answer: the velocity of the flowing water jet is 32.55 m/s assuming the blade is frictionless
Explanation:
Given that;
Force Ft = 1040 N
diameter d = 2.5 cm = 0.025 m
we know that; force acting on Hemispherical plate is;
Ft = 2δav²
where
a is area = π/4(0.025)²
δ is density of water = 1000 kg/m³
v is velocity = ?
now we substitute
1040 = 2 × 1000 × (π/4(0.025)²) × v²
1040 = 0.9817v²
v² = 1040 / 0.9817
v² = 1059.3867
v = √1059.3867
v = 32.5482 ≈ 32.55 m/s
Therefore the velocity of the flowing water jet is 32.55 m/s assuming the blade is frictionless
is used to change physical objects and 3-D ideas into 2-D drawing that effectively describe the design and features of an object, so the object can be documented and manufactured.
Answer:
2D CAD Software Application
Explanation:
Two Dimensional Computer-Aided Design Software Application is otherwise known as 2D CAD software application such as AutoCAD or MicroStation is used to change physical objects and 3-D ideas into a 2-D drawing that effectively describe the design and features of an object, so the object can be documented and manufactured.
The utilization of a 2D CAD software application saves time and revision to construction drawings can quickly be made without having to redesign the whole drawings from the scratch.
For some transformation having kinetics that obey the Avrami equation, the parameter n is known to have a value of 2. If, after 100 s, the reaction is 40% complete, how long (total time in seconds) will it take the transformation to go to 95% completion
This question is incomplete, the complete question is;
For some transformation having kinetics that obey the Avrami equation, the parameter n is known to have a value of 2. If, after 100 s, the reaction is 40% complete, how long (total time in seconds) will it take the transformation to go to 95% completion
y = 1 - exp( -ktⁿ )
Answer: the time required for 95% transformation is 242.17 s
Explanation:
First, we calculate the value of k which is the dependent variable in Avrami equation
y = 1 - exp( -ktⁿ )
exp( -ktⁿ ) = 1 - y
-ktⁿ = In( 1 - y )
k = - In( 1 - y ) / tⁿ
now given that; n = 2, y = 40% = 0.40, and t = 100 s
we substitute
k = - In( 1 - 0.40 ) / 100²
k = - In(0.60) / 10000
k = 0.5108 / 10000
k = 0.00005108 ≈ 5.108 × 10⁻⁵
Now calculate the time required for 95% transformation
tⁿ = - In( 1 - y ) / k
t = [- In( 1 - y ) / k ]^1/n
n = 2, y = 95% = 0.95 and k = 5.108 × 10⁻⁵
we substitute our values
t = [- In( 1 - 0.95 ) / 5.108 × 10⁻⁵ ]^1/2
t = [2.9957 / 5.108 × 10⁻⁵]^1/2
t = [ 58647.22 ]^1/2
t = 242.17 s
Therefore the time required for 95% transformation is 242.17 s
A motorist is driving his car at 60km/hr when he observes that a traffic light 250m ahead turns red. The traffic light is
timed to remain red for 20 seconds before it turns green. The motorist wishes to pass the traffic lights without stopping to wait for it to turn green. make calculations for
(a) the required uniform acceleration of the car
(b) the speed of the car as it passes the traffic light in km/hr
Explanation:
Okay soo-
Given-
u = 60 km/hr = 60×1000/3600=50/3 m/s
t = 20 s
s = 250 m
a = ?
v = ?
Solution -
Here, acceleration is uniform.
(a) According to 2nd kinematics equation,
s = ut + ½at^2
250 = 50/3 ×20 + 0.5×a×20×20
250-1000/3=200a
(750-1000)/3=200a
a = -250/(3×200)
a = -5/12
a = 0.4167 m/s^2
The required uniform acceleration of the car is 0.4167 m/s^2.
(b) According to 1st kinematics equation
v = u + at
v = 50/3 + (-5/12)×20
v = 50/3-25/3
v = 25/3
v = 8.33 m/s
The speed of the car as it passes the traffic light is 8.33 m/s.
Good luck!
Which of the following is the use and study of liquid fluids and their motions, properties, behaviors, and interactions?
O pneumatics
O hydraulics
O torque
O fluid power
Answer:
hydraulics
Explanation:
Answer:
b
Explanation:
Creep occurs by:_________
a. constant stress at room temperature
b. high temperatures over 1000°C
c. constant stress at temperatures over 0.5 TM in K
d. none of these
Answer:
The answer is "Option C".
Explanation:
The creep depends on temperature and stress whenever the temperature rise, for failure generosity, its core symptoms can be increased between about 0,5 and 0,7 TM in k (melting point of temperature). It is indeed a metal puncturing type, typically at high temperatures with stresses below the yields of a metal.
Explanation:
Creep occurs by constant stress at temperatures over 0.5 TM in K.
Creep is a phenomenon in which a material or an object is elongated over a time period under constant temperature and stress for a long period of time. For example, a belt used for a year or so, is elongated.
A genetically engineered hormone.
increasing muscle mass.
can treat Mary's child for growth hormone deficiencies by stimulating body growth and increasing muscle mass.
Answer:
the answer is scientifically science chemistry biochemistry aerospace engineering plato english history world ap history yes
Explanation:
que
A reversible steady-state device receives a flow of 1 kg/s air at 400 K, 450 kPa and the air leaves at 600 K, 100 kPa. Heat transfer of 900 kW is added from a 1000 K reservoir, 50 kW is rejected at 350 K, and some heat transfer takes place at 500 K. Find the heat transferred at 500 K and the rate of work produced.
Answer:
41 kW
690.2 kW
Explanation:
Given the following data
T1 = 400 K
P1 = 350 kPa
T2 = 600 K
P2 = 100 kPq
m = 1 kg/s
Q1 = 900 kW
Q2 = 50 kW
T(amb1) = 1000 K
T(amb2) = 350 K
T(amb3) = 500 K
We also will be using tables to solve the question.
R = 0.287 kJ/kgk
C(p) = 1.004 kJ/kgk
To find Q3, we'd use the formula
Q3 = m.T(amb3).[C(p).In(T2/T1) - R.In(P2/P1)] - [T(amb3)/T(amb1) * Q1] + [T(amb3)/T(amb2) * Q2]
Q3 = 1 * 500 * [1.004 * In(600/400) - 0.287 * In(100/450)] - 500/1000 * 900 + 500/350 * 50
After simplification, we find that
Q3 = 41 kW
Next, we use the equation
Q3 - Q2 + Q1 = W + m.C(p).(T2 - T1)
41 - 50 + 900 = W + 1 * 1.004 * (600 - 400)
891 = W + 1.004 * 200
891 = W + 200.8
W = 891 - 200.8
W = 690.2 kW
If we make W the subject of the formula, we have
I tried this question but my teacher said it was wrong so Can y’all describe y’all’s answers to this question
Answer:
R=v/i.... So V=R*i=10*1.7=17 volt
Which sentence is correct about the exergy of an empty (pressure around zero Pascal) tank with a volume of V, located in an environment with a pressure and temperature of P0 and T0?
a. The exergy of the tank is positive and equal to PoV.
b. Since the system receives work from the environment the exergy of the tank is negative and equal to -PoV
c. The exergy of the tank can be anything between zero to PoV.
d. Since the pressure of the tank is almost zero the tank has no exergy.
Answer:
The correct option is;
c. the exergy of the tank can be anything between zero to P₀·V
Explanation:
The given parameters are;
The volume of the tank = V
The pressure in the tank = 0 Pascal
The pressure of the surrounding = P₀
The temperature of the surrounding = T₀
Exergy is a measure of the amount of a given energy which a system posses that is extractable to provide useful work. It is possible work that brings about equilibrium. It is the potential the system has to bring about change
The exergy balance equation is given as follows;
[tex]X_2 - X_1 = \int\limits^2_1 {} \, \delta Q \left (1 - \dfrac{T_0}{T} \right ) - [W - P_0 \cdot (V_2 - V_1)]- X_{destroyed}[/tex]
Where;
X₂ - X₁ is the difference between the two exergies
Therefore, the exergy of the system with regards to the environment is the work received from the environment which at is equal to done on the system by the surrounding which by equilibrium for an empty tank with 0 pressure is equal to the product of the pressure of the surrounding and the volume of the empty tank or P₀ × V less the work, exergy destroyed, while taking into consideration the change in heat of the system
Therefore, the exergy of the tank can be anything between zero to P₀·V.
Solve for R.
What is the current going through the 6 ohms light bulb?
Answer:
9A
Explanation:
The peak voltage of a 240 vrms sine wave is approximately
Answer:
339.4625
Explanation:
correct me if i am wrong
What can be used as a tracing powder when checking for small oil leaks
Answer:
Talcum powder!
Explanation:
How to find the source of an oil leak:
This method simply involves using Talcum Powder as a visual aid to help pinpoint the location of an oil leak,
so you use Talcum powder for small oil leak :]
Have a wonderful day!
determine the wattmeter reading when it is connected to resistor load.
Answer:
Each wattmeter measures a line-to-line voltage between two of the three power supply lines. In this configuration, the total power, watts is accurately measured by the algebraic sum of the two wattmeter values. Pt = P1 + P2. This holds true if the system is balanced or unbalanced.
Which two statements about professional technical jobs in the energy industry are correct?
A. Energy careers offer limited prospects.
B. Certifications are often necessary to be employed in the energy sector.
C. Continuing education and certifications must be done in a classroom setting.
D. Continuing education is important to have a long-term energy career.
E. Energy technology is static.
Answer: the answer is B and D
Explanation:
Find the resultant of two forces 130 N and 110 N respectively, acting at an angle whose tangent
is 12/5.
Answer:
[tex]F_r = 200N[/tex]
Explanation:
Given
Let the two forces be
[tex]F_1 = 130N[/tex]
[tex]F_2 = 110N[/tex]
and
[tex]\tan(\theta) = \frac{12}{5}[/tex]
Required
Determine the resultant force
Resultant force (Fr) is calculated using:
[tex]F_r^2 = F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)[/tex]
This means that we need to first calculate [tex]\cos(\theta)[/tex]
Given that:
[tex]\tan(\theta) = \frac{12}{5}[/tex]
In trigonometry:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
By comparing the above formula to [tex]\tan(\theta) = \frac{12}{5}[/tex]
[tex]Opposite = 12[/tex]
[tex]Adjacent = 5[/tex]
The hypotenuse is calculated as thus:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
[tex]Hypotenuse^2 = 12^2 + 5^2[/tex]
[tex]Hypotenuse^2 = 144 + 25[/tex]
[tex]Hypotenuse^2 = 169[/tex]
[tex]Hypotenuse = \sqrt{169[/tex]
[tex]Hypotenuse = 13[/tex]
[tex]\cos(\theta)[/tex] is then calculated using:
[tex]\cos(\theta)= \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(\theta)= \frac{5}{13}[/tex]
Substitute values for [tex]F_1[/tex], [tex]F_2[/tex] and [tex]cos(\theta)[/tex] in
[tex]F_r^2 = F_1^2 + F_2^2 + 2F_1F_2\cos(\theta)[/tex]
[tex]F_r^2 = 130^2 + 110^2 + 2*130*110*\frac{5}{13}[/tex]
[tex]F_r^2 = 16900 + 12100 + 11000[/tex]
[tex]F_r^2 = 40000[/tex]
Take square roots of both sides
[tex]F_r = \sqrt{40000[/tex]
[tex]F_r = 200N[/tex]
Hence, the resultant force is 200N