A shopper in a supermarket pushes a cart with a force of 48.0 N directed at an angle of 25.0° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed.(a) Find the work done by the shopper on the cart as she moves down a 45.6-m-long aisle.(b) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesn't change, would the shopper's applied force be larger, smaller, or the same?(c) What about the work done on the cart by the shopper?

Question
Asked Nov 21, 2019
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A shopper in a supermarket pushes a cart with a force of 48.0 N directed at an angle of 25.0° below the horizontal. The force is just sufficient to balance various friction forces, so the cart moves at constant speed.

(a) Find the work done by the shopper on the cart as she moves down a 45.6-m-long aisle.

(b) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the work done by frictional forces doesn't change, would the shopper's applied force be larger, smaller, or the same?

(c) What about the work done on the cart by the shopper?
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Expert Answer

Step 1

(a)

The angle between the force and displacement is 25 degrees.

Formula for the work done by the shopper on the cart is:

W = Fd cos
(48.0 N) (45.6 m) cos 25°
1 kJ
(1984 J)
1000 J
1.98 kJ
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Image Transcriptionclose

W = Fd cos (48.0 N) (45.6 m) cos 25° 1 kJ (1984 J) 1000 J 1.98 kJ

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Step 2

(b)

The speed of the cart remains same. Therefore, from work energy theorem (delta KE=W) it can be concluded that there isn’t any extra work is done on the cart.

The work done by the frictional force remains same that is the frictional force is same as earlier.

Now the force applied by the shopper is along horizontal. Therefore, the angle between the force and displacement is zero. Also, only the force by the shopper and the frictional force is acting along the direction of motion.

Therefore, the work done by the shopper is:

W F'd cos
= F'd cos 0
= F'd
help_outline

Image Transcriptionclose

W F'd cos = F'd cos 0 = F'd

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Step 3

Since the work done is same. So, shopper need to ap...

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