A shopper in a supermarket pushes a cart with a force of 35.0 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 50.0-m-long aisle. (b) The shopper goes down the next aisle, pushing horizontally and maintaining the same speed as before. If the friction force 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?
(a)
The work done by the shopper on the cart.
Answer to Problem 1P
The work done by the shopper on the cart is
Explanation of Solution
The force exerted by the shopper on the cart is
Write the formula to calculate the work done by the shopper
Here,
Conclusion:
Substitute
Therefore, the work done by the shopper on the cart is
(b)
Whether the force applied by the shopper will be larger, smaller or same by pushing the cart horizontally at same speed.
Explanation of Solution
The work done by the force is equal to the dot product of the applied force vector to the displacement vector of the body.
Write the formula to calculate the work done by the shopper on the cart
Rearrange the above equation,
Since the shoppers moves with the constant velocity therefore the distance travel by the shopper is same. Also the change in kinetic energy of the cart is zero that corresponds to work done must be same. So the applied force by the shopper is depends upon the slope of the aisle.
The value of
Conclusion:
Therefore, the applied force by the shopper will be smaller in compare to the applied force on the cart in part (a).
(c)
Whether the work done by the shopper will change or remains same by pushing the cart horizontally at same speed.
Explanation of Solution
From the work energy theorem, the work done by the shopper on the cart is equal to the change in kinetic energy of the cart. Since the cart is moving with the same speed so, its kinetic energy remains same and hence the work done by the shopper on the cart remains same as that of part (a).
Conclusion:
Therefore, the work done by the shopper to push the cart horizontally remains same. It does not change.
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Physics for Scientists and Engineers
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