You do an experiment with colliding cars on a low-friction track. Car 1 of mass 0.5 kg is moving in the direction at a speed of 2 m/s when it collides with Car 2 of mass 1.0 kg which is at rest. After the collision, Car 1 rebounds and moves to the right with a speed of 0.67 m/s. Define the system as Car 1.

1. What is the change in the momentum of the system as a result of the collision?
2. What objects in the surroundings interact with the system during the collision and what is the change in the momentum of the surroundings?
3. What is the velocity of Car 2 after the collision?

A hockey puck (A) on a level air hockey table has mass = 0.100 kg and initial velocity m/s just before it collides with another hockey puck (B), which has mass kg. Just before the collision, puck B has a velocity m/s. The pucks stick together (because they are wrapped in velcro) upon colliding. What is the velocity of the system after the collision? Define the system as both hockey pucks, and assume that there is no net external force on the system.

You toss a nerf basketball of mass 0.002 kg into the air. At t = 0, the ball leaves your hand. At t = 0.11 s, the net force on the ball is , its velocity is , and its position is . What is its position at t = 0.13 s?

In a mass spectrometer (an instrument used in chemistry to measure the mass and therefore identity of unknown atoms) positively charged ions are accelerated between two charged plates. Suppose that a proton is nearly at rest at the positively charged plate on the left. It is accelerated toward a negatively charged plate on the right, as shown below. The plates are 5 cm apart.

Figure: A proton accelerated between charged plates.

The electric force by the charged plates on the proton is in the +x direction. This is the only significant force acting on the proton.

1. If the initial velocity of the proton is zero, what is the velocity of the proton after a time interval of ?
2. If you define the origin to be at the initial location of the proton, what is the position of the proton at ?

Cart A has a speed of 1.5 m/s in the +x direction and Cart B is at rest when they collide. After the collision, Cart A rebounds in the –x direction with a speed of 0.75 m/s, and Cart B travels in the +x direction with a speed of 0.75 m/s. The mass of Cart A is 0.50 kg, and the mass of Cart B is 1.5 kg.

1. Define Cart A to be the system. What is the change in momentum of the system due to the collision?
2. Define Cart B to be the system. What is the change in momentum of the system due to the collision?
3. Define Cart A and Cart B, together, to be the system. What is the change in momentum of the system due to the collision?

While playing air hockey, the puck comes toward you with a speed of 0.8 m/s at an angle of above the –x axis. You strike it with your paddle, and after the collision, the puck travels in the +x direction with a speed of 2 m/s toward the opponent's goal. The mass of the puck is 0.020 kg.

Figure: An air hockey puck before being struck by the air hockey paddle.

1. What was the impulse on the puck?
2. What is the direction of the net force on the puck during the collision?
3. What must be measured if you want to calculate the net force on the puck during the collision?

What impulse is required to accelerate a proton of mass from 0.95c to 0.99999999c (which is the maximum speed achieved with the Large Hadron Collider)? Assume that the proton travels along a straight line in the +x direction.

Earth orbits Sun in a nearly circular orbit with a speed m/s. Suppose that at a certain instant, Earth's velocity is in the –x direction. At this instant, the force by Sun on Earth is . What will be Earth's momentum 1 day later? During this time interval, the only significant force acting on Earth is the gravitational force by Sun on Earth.

Figure: The gravitational force by Sun on Earth.

An alpha particle has a speed of m/s in the +x direction when it collides with a gold nucleus. and deflects at an angle above the +x axis. Its speed after the collision nearly the same as its speed before the collision because the gold nucleus is so massive compared to the alpha particle. What is the impulse on the alpha particle due to the collision with the gold nucleus?

The thrust of a certain model rocket engine as a function of time is shown below. Here, the word "thrust" refers to the force by the exhaust on the rocket as the rocket engine is firing.

Figure: The thrust curve of a certain model rocket engine.

The total area under the curve is 1.84 N s. The total burn time of the rocket engine is 1.24 s. The peak thrust has a magnitude 8.60 N. Since force is a vector, assume that the thrust is in the +y direction.

1. Calculate the average thrust on the rocket due to the rocket engine.
2. Compare the average thrust to the peak thrust. Explain why the average thrust is so much smaller than the peak thrust.
3. If the thrust by the rocket engine on the rocket is the only force acting on the rocket, then what will be the change in the rocket's momentum during the time interval from t=0 to t=1.24 s?