PHYS4A/ Fall 2014; Impulse Momentum Energy

 Purpose: For this experiment, we are trying to determine an object's impulse and show that impulse is equal to momentum.

Based on the impulse-momentum theorem, the impulse of an object is equal to the change in momentum of the same object. Momentum is the the idea that it takes a force in order to stop a moving object and is similar to the idea of inertia which is a resistance to change. When an object has a large momentum, it is moving very fast or has a very large mass meaning that it would take a great force in order to slow it down to a stop.

Momentum = p = m*v

Impulse is the quantity of an applied force over a period of time. This can be derived from Newton's Second Law where....

F = m*a = m*v/t

Which becomes

F*t = m*v

Impulse = J = F*t = m*v = Momentum

Based on the derivation above, the impulse is equal to the change in momentum of an object which is what we will be trying to prove in the experiment below. But first, meet Bob, the clay model who will be assisting us today in the experiment. 

Bob and his dog Spot. No animals were harmed in the execution of this experiment.

For the experiment, we were creating different types of collisions to measure the changes in momentum. This was done by creating inelastic and elastic collisions between two carts on a frictionless track. These are collisions where the objects either stick together or bounce off each other after the collision. In order to simulate an inelastic collision, two carts were gathered with one set up on its side with a plastic bumper sticking out. A secondary cart (blue in the picture) was also set on the track with a force sensor which had a rubber stopper at the end in order to measure force from the impact and to protect the equipment from any unnecessary damage. Two runs were done, first with no mass and then with a 500g mass added to it for the second run.

Cart prepared for second run with 500g mass added on top.

Force vs Time for Trial 1

Velocity vs Time for Trial 1

Once the inelastic collisions were done, Logger pro was used to analyze the data. When looking at the force vs time graph, it is apparent that there was suddenly a force within a small amount of time. The integral of this curve can be taken and the resulting value is impulse. This value was then compared to the velocity graph in order to see if impulse is equal to the change in momentum. As seen in the velocity vs time graph, velocity suddenly drops at the same time that the impulse occurred. This change signifies the impact that occurred and is the relation used to prove the theory mentioned earlier. Since the velocity dropped, that means momentum also dropped which is what also occurred to the impulse.

Set-up for the inelastic collision.

For the next part, an inelastic collision was set up by replacing the rubber stopper on the force sensor with a metal nail. A wooden post was set up at one end of the track and Bob was placed on the post acting as a clay ball which would create an inelastic collision. The idea for this part of the experiment is that the cart would stick to the clay to drop the velocity to 0. Energy would no longer be conserved in this situation, however momentum still would be, The same method of data collection and analysis was used to see the relation in an inelastic collision.

Bob being stuck by the nail. His eyes were covered so he wasn't scared.

Force vs Time for Trial 3(Inelastic)

Velocity vs Time for Trial 3 (Inelastic)

As you can see in the graphs, just like before the force vs time graph and the velocity vs time graph both followed a common trend of decrease at the same time. This proves that they have some correlation and due to the the nature of the experiment, there is some error so the graphs are not perfect. However, this shows that in all cases, impulse is directly proportional to the change in momentum of an object.