Relating forces to changes in kinetic energy and momentum Two carts, A and B, are initially at rest on a horizontal frictionless table as shown in the top-view diagram below. A constant force of magnitude F., is exerted on each cart as it travels between two marks on the table. Cart B has a greater mass than cart A.

A. Three students discuss the final momentum and kinetic energy of each cart.

Student l: "Since the i:;ame force fr; exerted on both carts, the cart with the smaller mass will move quickly, while the cart with the larger mai:;i:; will move slowly. The momentum of each cart is equal to its mass times its velocity."

Student 2: "This mw;t mean that the speed compensates for the mai:;i:; and the two carts have equal final momenta."

Student 3: "I was thinking about the kinetic energies. Since the velocity is squared to get the kinetic energy but mass isn't, the cart with the bigger speed must have more kinetic energy."

In the space below, write down whether you agree or disagree with the statements made by each student.

B. Which cart takes longer to travel between the two marks? Explain your reasoning.

C. Use Newton's second law and the definition of acceleration to derive an equation for each cart relating the net force on the cart to the change in velocity of the cart (l:!..v A or l:!..v 8 ) and the time interval (l:!..tA or l:!..t8) that the cart spends between the two marks.

1. Is the quantity mAIA.vAI greater than, less than, or equal to m8 IA.v81? Explain how you can tell

For a constant net force, the quantity F ... flt is called the impulse imparted to the object.

2. Is the magnitude of the impulse imparted to cart A greater than, less than, or equal to the magnitude of the impulse imparted to cart B? Explain your reasoning.

mg>MA F 14 F Top view Frictionless table First mark Second mark