A force of 25 N is needed to move automobile wheels up a smooth incline
10 m along in an automotive plant.
a. If each of the wheels weighs 125 N what work is done on each?
b. How high above the floor is the top of the incline?
a. W = F*d = 25 * 10 = 250 J.
b. Fp = 125*sinA = 25 = Force parallel with incline.
sinA = 25/125 = 0.20, A = 11.5o.
sin11.5 = h/10
h = 10*sin11.5 =
To find the work done on each wheel, we can use the formula:
Work = Force * Distance
a. Given that the force needed to move the wheels is 25 N, and the distance is 10 m, we can calculate the work done on each wheel:
Work = 25 N * 10 m
Work = 250 Nm (Newton-meters)
Therefore, the work done on each wheel is 250 Nm.
b. To determine the height of the incline, we need to use the concept of work and gravitational potential energy. The work done on the wheels is equal to the change in potential energy:
Work = Force * Distance = m * g * h
Where:
m = mass of the wheel (weight / gravitational acceleration)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the incline
Given that the weight of each wheel is 125 N, we can calculate the mass:
mass = weight / gravitational acceleration
mass = 125 N / 9.8 m/s^2 ≈ 12.76 kg
Substituting the values into the equation:
250 Nm = 12.76 kg * 9.8 m/s^2 * h
Simplifying the equation:
h = (250 Nm) / (12.76 kg * 9.8 m/s^2)
h ≈ 2.03 m
Therefore, the top of the incline is approximately 2.03 meters above the floor.