dynamics carts.jpgExploring momentum with dynamics carts.

In your first experiments you will use the dynamics carts to literally get a "feel" for momentum and simply one dimensional collisions. The carts come with one which has a spring-loaded "bumper". Use 1 or 2 kilogram weights to increase the mass of one of the carts in some of the experiments. For each of the following record the relative masses and velocity (don't forget the direction), and find out if your past experience is a good predictor of what happens. We can even model a simple simple two-particle explosion by compressing the spring between two carts and then releasing it.

1. Moving cart collides with stationary cart of same mass.
2. Moving heavy cart collides with stationary light cart.
3. Moving light cart collides with stationary heavy cart.
4. Two carts of equal mass "explode."
5. Light cart and heavy cart "explode."

What is momentum?

Isaac Newton spoke about momentum as he formulated his second law of motion, and said that force was proportional the rate of change of momentum. Momentum is the product of mass and velocity, and is given the symbol p. p = m x V
A change in momentum can occur if the velocity changes or the mass changes. A change in momentum which results from a change in velocity is given by Δp = mΔV

Newton's second law can be represented as F = Δp / Δt, and as F = mΔV / Δt
Since a = Δv / Δt we can say that F = ma. This is the usual way the Newton's second law is expressed.
We can also rearrange the equation above to get FΔt = mΔV which relates "impulse" and the "change in momentum".

Momentum video
More on momentum from the Mechanical Universe. (The Mechanical Universe is an "distance learning" college course in physics from Cal Tech.)

Conservation of momentum

air track.jpgWhen two objects collide along a straight line, momentum is conserved. You had little quantitative evidence for that in your first experiments, but now we will gather some numerical data to examine the concept of the conservation of momentum analytically. For these experiments we will be using a linear air track, and a pair of photogate timers. One of the timers has a memory function that allows us to record two different times. To measure the speed of the air-track gliders, each has an attached index card. By measuring the width of the card, and using the time the card breaks the light beam of the photogate timer, we can compute its speed. The speed and mass of the gliders allow us to compute their momenta.

Like the earlier experiments, we will study collisions of gliders with different mass, where one is moving and one is stationary. In an elastic collision, a rubber band is used on the "bumper". For the completely inelastic collisions each glider is equipped with a modeling clay bumper that allows the gliders to stick together -- the definition of a completely inelastic collision. Only place an index card on the glider that is moving. The will move together after to collision. The sum of the momenta before the collision equals the sum of the momenta after the collision.
m1V1 + m2V2 = m1V'1 + m2V'2
Where m1 and m2 are the masses of the gliders and V1 and V2 are the initial velocities. V2 will be zero. V'1 and V'2 are the velocities of the gliders after the collision. Your task is to be sure that momentum is conserved.
1. Heavy glider collides with stationary heavy glider - completely elastic
2. Heavy glider collides with stationary light glider - completely elastic
3. Light glider collides with stationary heavy glider - completely elastic
4. Heavy glider collides with stationary heavy glider - completely inelastic
5. Heavy glider collides with stationary light glider - completely inelastic
6. Light glider collides with stationary heavy glider - completely inelastic

Air track simulation
Since time on the air track is limited, we can each do all the experiments described above using the air track simulator found here. We can also use the collision simulation at PhET.

The final relationship to investigate is kinetic energy. Kinetic energy is energy of motion, and is defined as KE = 1/2mv2. In any completely collision, kinetic energy will be conserved. In an inelastic collision, some kinetic energy is converted into thermal energy. To investigate the conservation of energy, look at the data you collected for elastic collisions and compute the kinetic energy of the object before the collision, and the kinetic energies after the collision.

Run the PhET simulation for a two-dimensional collision (click on the "advanced" tab). Set up an experiment with a moving ball striking a stationary ball so that each goes off in a different direction. You will see how momentum in the original direction is conserved. Compute the kinetic energy for each ball after the collision and compare the sum to the kinetic energy of the original ball. How is conservation of energy different from conservation of momentum?

Worksheet on momentum and its conservation. ..... answers