A laboratory cart of mass is placed on a large horizontal table made of the same…
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A laboratory cart of mass m is placed on a large horizontal table made of the same rough material everywhere. Two identical carts are released from the same initial point with the same initial speed v0.
• Cart 1 is pulled straight to a point that is a distance D away.
• Cart 2 is first pulled a distance D/2 east, then a distance D/2 north so that it reaches the same final point by an L-shaped path.
Assume the pulling force is always horizontal and just large enough to keep each cart moving at constant speed along the described path. The coefficient of kinetic friction between the carts and the table is μk and remains constant.
Answer the following questions about the thermal energy produced during each trip.
(a) Identify which cart’s trip produces the greater increase in thermal energy of the cart-table system, or state if the thermal energy increases by the same amount for both carts.
(b) Using the definition of work, provide a qualitative explanation for the difference (or lack of difference) in thermal energy production that you stated in part (a).
(c) Suppose instead that the table is perfectly smooth so that the coefficient of kinetic friction is zero. Each cart is now pulled along its respective path by a light string at a constant low speed so that only static friction acts between the cart and table. Would any thermal energy be produced in this case? Explain your reasoning.
(d) If the pulling force were replaced by an ideal spring connecting the cart to the final point so that the cart moved under a conservative force, would the path taken affect the amount of mechanical energy stored (or released) in the spring when the cart arrives? Justify your answer.