Using a string, you pull a box along a low-friction table with a constant force of 100 N, starting from rest. The box is full of fluid and is a cube of dimensions 1m x 1m x 1m with a total mass of 2.0 kg. When the box was at rest, the center of mass of the system was located at relative to the left, lower corner of the box. At some time later, your hand has pulled through a distance of 0.5 m, and the center of mass has shifted to relative to the left, lower corner of the box.

Figure: A box with fluid being pulled by a constant force.

The box is thermally insulated and the table is nearly frictionless, so assume that there is no energy transferred thermally between the box and its surroundings.

1. Define the box and fluid to be the system. What is of the system?
2. What is of the system?
3. What is the speed of the system (after your hand has moved through a distance of 0.5 m)?
4. What is the change in the thermal energy of the system?

A car of mass 500 kg and a truck of mass 1200 kg are moving directly toward each other at the same speed of 20 m/s. Define the +x direction to the direction of the car.

1. What is the velocity of the center of mass of the system, defined to be the car and truck?
2. At the moment when the vehicles are 100 m apart, what is the location of the center of mass of the system? Treat the vehicles as point particles.

While playing around with identical hockey pucks on an air hockey table, you push one puck so that it collides with another stationary puck. Before the collision, puck B is at rest and puck A is moving with a speed of 0.500 m/s. After the collision, puck A's velocity is at an angle of 20 (below the horizontal) and puck B has a velocity at 65 (above the horizontal). What are the speeds of puck B and puck A after the collision?