Suppose you lift a 35 kg box by a height of 1.6 m (a) How much work do you do in

Question

Suppose you lift a 35 kg box by a height of 1.6 m

(a) How much work do you do in lifting the box?

Instead of lifting the box straight up, suppose you push it up a 1.6-m-high ramp that makes a 26° angle with the horizontal, as shown in the figure below. Being clever, you choose a ramp with no friction.

(b) How much force F is required to push the box straight up the slope at a constant speed? in Newton

(c) How long is the ramp? in meters

(d) Use your force and distance results to calculate the work you do in pushing the box up the ramp. in Joules

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 greater than part (a).

Both answers are the same.

The answer to part (d) is less than part (a).

Explanation / Answer

here,

mass of box, m = 35 kg
height, h = 1.6 m

Part A:
Work in liftiung, w = f*h = mg*h
w = 35*9.81*1.6
w = 549.36 J

Part B:
Angle, A = 26 degrees

From newton Second law, SUM(f) = 0
F -mgSinA = 0
F = mg*Sin26
F = 35*9.81*Sin26
F = 150.515 N

Part C:
From trignometry,
SinA = h/d

solving for length of ramp, d
d = h/sinA
d = 1.6/sin26
d = 3.65 m

Part d:
Work done = Force * Dispalcement
w = 15.515*3.65
w = 56.63 J

Work done in puishing box on ramp is less the lifting, for pushing less work has to be done.

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