Question

7. Carrie's group is analyzing the motion of a cart that moves up a ramp. Carrie claims that when the cart slows down the kinetic energy is negative. She justifies this claim by stating that "the work-energy theorem for an object says that when a force pushes an object the kinetic energy increases but now the force is pulling the object." Andrea disagrees and claims that the kinetic energy of the cart is never negative anywhere on the ramp but doesn't provide reasoning to support her claim. a. Treating the cart as an object upon which Earth exerts a gravitational force, justify Andrea's claim. b. Carrie responds by claiming that by treating the cart- Earth pair as an isolated system, no work is done and so according to the work-energy theorem the kinetic energy of the system cannot change. And since the total kinetic energy of the system is the sum of the kinetic energies of the components, for the sum to be zero one of the terms in this sum must be negative. Evaluate Carrie's explana- tion of why kinetic energy can be negative.

Answer 1

a)

Work done by net force on a body is equal to change in its kinetic energy.

In the above case the cart is moving up the plane. The gravitational force is pulling the cart down.Hence work done by gravity on the cart is negative. And kinetic energy may be decreasing, but kinetic energy cannot be negative.

Hence Andrea's statement is correct.

b)

Now cart-earth system is isolated. But net work done on the system may be due to internal as well as external forces.

In this case, gravitational force is an internal force and can lead to change in kinetic energy. (which may be negative)

Since the kinetic energy of the earth is not changing and the cart is slowing down, change in total kinetic energy of system is negative. Hence Carrie's explanation is wrong.