Impulse-Momentum Activity
(Is Impulse equal to the change in Momentum?)
Purpose: To demonstrate that impulse (J) is equal to the change in momentum of an object (in this case a cart along a frictionless track).
Procedure: We first leveled a cart track on top of our table. We placed one cart on top of the track, and another (this one with a spring bit extended from its end) at one end of the track, with the spring bit facing inward towards the track. We also placed a motion sensor at the end opposite the spring bit containing cart. This setup is shown below:
(Apparatus setup w/o force sensor)
In order to determine the impulse of the coming collisions, a force sensor is required. We attached this force sensor to the cart on top of the track. Additionally, we attached a flashcard to the back of the cart on the track, which would allow the motion sensor to record data from the moving object. This is depicted below, however, before running the experiments, we opted to remove the flashcard, and instead placed a small board attachment via velcro.
(Cart with force sensor and flashcard attached)
With the motion sensor tracking the object's position over time, we can determine the cart's velocity as the hook on the force sensor collides with the spring bit from the other cart, this can be used to determine the change in momentum (given that we know the mass of the cart and it's initial and final velocities). The force sensor allows us to record the varying force over the time of the collision (which gives us the impulse by integration).
We ran 3 experiments using this equipment. The 1st being a collision between the setup cart shown above and the spring bit cart. The 2nd being the same as the 1st with an added amount of mass to the cart on the track. For the 3rd experiment, we attached a needle to the end of the force sensor, and collided it with a piece of clay instead of the second cart (an inelastic collision).
EXP 1)
mass of cart system = m = 0.764 kg
The recorded data from this first collision is show below:
(LoggerPro data from Exp 1)
The top graph represents the cart's velocity over time, while the bottom represents the varying force over time. From the velocity v. time graph, we can determine the cart's velocity just before and just after the collision occurs.
initial velocity = vi = 0.2867 m/s
final velocity = vf = -0.2394 m/s
Having these values enables us to calculate the change in momentum of the cart:
mvf - mvi = (0.764)(-0.2394) - (0.764)(0.2867) = -0.4019 kg * m/s
From the lower graph, we can utilize the integration function in LoggerPro to determine the Impulse of the collision:
J = -0.4175 kg * m/s
Our calculations for Impulse were off slightly from the value given by integrating the force v. time graph over the collision time interval. We then proceeded to do the experiment with additional mass added to the cart system.
EXP 2)
m = 1.264 kg
Below are the graphs from the second experiment:
(LoggerPro data from Exp 2)
From the velocity graph, we have:
mvf - mvi = (1.264)(-0.3748) - (1.264)(0.3989) = -0.9779 kg * m/s
From the force v. time graph we have:
J = -0.9678 kg * m/s
Once again, our values are slightly off from one another. This could be to sources of uncertainty, such as improper recording of mass value of the cart system, or even a improperly leveled track.
EXP 3)
For this experiment, we removed the dynamics cart and replaced it with a wooden object which we then attached a bit of clay to (in order to create an inelastic collision). We also removed the hook from the end of the forces sensor and replaced it with a nail. This is shown below:
(Exp 3 setup)
m = 1.28 kg
Below is the data from this collision:
(LoggerPro data from Exp 3)
From these graphs, we have:
mvf - mvi = 0 - (1.28)(0.4277) = -0.5475 kg * m/s
J = -0.4671 kg * m/s
This last experiment contains the largest error with respect to the above values. I believe this occurred due to improper recording of the new cart system mass. We simply recorded the mass of the nail and rubber stopper used to attach it and added it to the entire system's mass from the previous experiment, as opposed to replacing the items and then measuring the new mass as a while system (which would've yielded better results in our change in momentum calculation).
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