A body with a mass of 490kg is pulled along a horizontal plane at a constant velocity.the pulling force is 1.2 kN is making an angle of 20degrees with the plane.
A.determine the coefficient of friction
Draw the free body diagram which reveals the net forces on the body.
The force F at 20 degrees with horizontal has an upward component of Fsin(20) which has the effect of reducing the normal reaction N from mg to mg-Fsin(20).
The horizontal component of Fcos(20) is the only force that resists friction, so may be equated with the frictional force of μN.
So equating horizontal forces,
μN=Fcos(20), or
μ(mg-Fsin(20))=Fcos(20).
Solve for μ.
Coefficient of friction is 13.0? Am I correct?
I do not see how you can get 13.0.
Please show your work (must use consistent units, kg, N, s, m)
F=1.2kN=1200N
m=490 kg
g=9.8 or 9.81 m/s^2
Perhaps it was a mistake on the calcultor, so please try again.
μ should be between 0 and 1.
To determine the coefficient of friction, we can follow these steps:
Step 1: Find the vertical component of the pulling force.
The vertical component of the pulling force can be calculated using trigonometry. Since the pulling force is making an angle of 20 degrees with the plane, we can find the vertical component using the formula:
Vertical component = Pulling force * sin(angle)
Vertical component = 1.2 kN * sin(20 degrees)
Step 2: Find the weight of the body.
The weight of the body can be calculated using the formula:
Weight = mass * gravity
where gravity is approximately 9.8 m/s^2.
Weight = 490 kg * 9.8 m/s^2
Step 3: Compare the vertical component and the weight.
Since the body is moving at a constant velocity, the vertical component of the pulling force must be equal to the weight. If it is not, there would be an acceleration in the vertical direction.
If the vertical component of the pulling force is equal to the weight, then the friction force between the body and the plane (which opposes the motion) can be calculated using the formula:
Friction force = Pulling force * cos(angle)
Friction force = 1.2 kN * cos(20 degrees)
Step 4: Calculate the coefficient of friction.
The coefficient of friction (μ) can be calculated using the formula:
Coefficient of friction = Friction force / Weight
Coefficient of friction = (1.2 kN * cos(20 degrees)) / (490 kg * 9.8 m/s^2)
Now, substitute the values and solve for the coefficient of friction.
Note: Remember to convert the pulling force to Newtons and ensure that all units are consistent throughout the calculation.