Suppose you lift a 15 kg box by a height of 1.9 m. How much work do you do in li

Question

Suppose you lift a 15 kg box by a height of 1.9 m. How much work do you do in lifting the box? Instead of lifting the box straight up, suppose you push it up a 1.9-m-high ramp that makes a 27 degrees angle with the horizontal, as shown in the figure below. Being clever, you choose a ramp with no friction. How much force F is required to push the box straight up the slope at a constant speed? How long is the ramp? Use your force and distance results to calculate the work you do in pushing the box up the ramp. How does this compare to your answer to part (a)? (Assume answers are the same if they are within 6% of each other.) The answer to part (d) is less than part (a). The answer to part (d) is greater than part (a). Both answers are the same.

Explanation / Answer

(a)

work done = force * displacement = m*g*h = 15*9.8*1.9 = 279.3 J

(b)

along the ramp

Fnet = F - m*g*sinsintheta

from newtons second law

Fnet = m*a

as speed v is constant a = 0

Fnet = 0

F - m*g*sinsintheta = 0

F = m*g*sinsintheta = 15*9.8*sin27 = 140.6 N

(c)

sin27 = h/L

L = h/sin27 = 1.9/sin27 = 1.98

(d)

W = F*L = m*g*sintheta*L = m*g*h = 279.3 J

both are same

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