Suppose you lift a 30 kg box by a height of 2.0 m. How much work do you do in li

Question

Suppose you lift a 30 kg box by a height of 2.0 m. How much work do you do in lifting the box? J Instead of lifting the box straight up, suppose you push it up a 2.0-m-high ramp that makes a 17 degree 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? N How long is the ramp? m Use your force and distance results to calculate the work you do in pushing the box up the ramp. J How does this compare to your answer to part (a)? (Assume answers are the same if they are within 6% of each other.) Both answers are the same. The answer to part (d) is greater than part (a). The answer to part (d) is less than part (a).

Explanation / Answer

(a) Work done in lifting the box, W = mgh = 30*9.81*2.0 = 588.6 J

(b) The box is required to push with constant speed, means no acceleration

I this case -

F cos theta = mg sin theta

=> F cos17 = 30x9.81 sin17

=> F = 89.98 N

(c) Consider the length of the ramp = L

So, sin theta = h/L

=> L = h/sin theta = 2/sin17 = 6.84 m

(d) Work done in pushing the box up the ramp = F*L = 89.98*6.84 = 615.46 J

(e) Difference of the two work done = 615.46 - 588.6 = 26.86 J

this value is 26.86*100/588.6 = 4.56 %

So as per the condition, we can assume that both the values are same.

So, first option is correct.

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