Setup
For this lab my group and I prove the Impulse (J) of a cart colliding with a stationary object. To do this we set up a ramp with a motion sensor on one side and a force sensor on the other side. We connected both of them to logger pro and gave the cart a push towards the force sensor and measured the velocity before and after, as well as the force over time of the force sensor.
Graphs of data
Our data was unfortunately lost, but I was able to write down our results before we lost them. These graphs are group Zach Pabis and his group, and are the most similar to our data.
This is the momentum graph of our data, graphed in desmos
Evaluation and Calculations
Impulse is defined as the force applied over a certain time, and thus can be measured by the integral of a Force vs. Time graph. Our group did this and got a value of 0.3981 kg*m/s (J). This is enough to measure the impulse, but to prove that this is true we calculated the change in momentum (ΔP). To do this we use the equation: ΔP = J = Pf-Pi = mf*vf-mi*vi since mf = mi = m, we can factor to simplify: J = m (vf - vi). for our experiment, we got an initial velocity of 0.688 m/s and a final velocity of -0.649 m/s, with a mass of 0.25 kg.
Simplifying we get: J = 0.25(-0.649-0.688) J = 0.334 kg m/s
This is our answer using momentum. Using the integral function in logger pro you can find the area under the graph of the force vs. time graph. This method gives us J = 0.3981 kg m/s
Using the percent difference formula, we get a 19.19% difference between the impulse integral and the change in momentum method.
Simplifying we get: J = 0.25(-0.649-0.688) J = 0.334 kg m/s
This is our answer using momentum. Using the integral function in logger pro you can find the area under the graph of the force vs. time graph. This method gives us J = 0.3981 kg m/s
Using the percent difference formula, we get a 19.19% difference between the impulse integral and the change in momentum method.
Conclusion
All of these graphs as well as our data matches up with the definition of impulse: Since impulse is both the change in momentum and the area of the force time graph, both of those calculations only having a percent difference of 19.19%, they prove each other. This experiment was relatively straightforward, so there isn't very much room for uncertainty.