Lab 14: April 19,2017: Impulse-Momentum Activity

Lab 14: Impulse-Momentum Activity

Amy, Chris, and John

April 19,2017

Today's lab is to verify the impulse-momentum theorem by elastic and inelastic collisions.

Theory: The impulse-momentum theorem states that the amount of momentum change for the moving cart is equal to the amount of the net impulse acting on the cart. With the inelastic collision the cart has a ribber stopper measuring the force of impact, wherein the force is not constant. We can measure the area under our force vs time graph during this collision to find the change in momentum this in by knowing the carts mass and measuring its velocity before and after the collision.
Whilst in a perfect elastic collision between a cart and a wall, the cart would recoil with the same magnitude of momentum, in this lab we can only imitate that so much.
By recognizing the force to be non constant we can integrate the function of force.

Apparatus and Procedure: For this lab we needed two carts (one with a spring plunger), a rubber stopper, macbook, force probe, clamps, leveled track, and a motion sensor. This are all the materials needed for the elastic collision. In this set up we have one cart aligned so it hits the spring plunge from the cart that is clamped on the table.

As discussed in theory/introduction, impulse can be obtained through a graph of Force vs time. The spike in the amount of force in the graph for the time interval is our impulse, and we can find this quantity using the integration function in LoggerPro. We take this value and compare it to our calculated value for impulse using the change in momentum (note that while the magnitude of velocity for initial and final is expected to be almost the same, the directional component of velocity in our momentum equation should give us a value subtracted by a negative value, or simply a sum of the two). The velocity we obtain through the motion sensor can be plugged into our delta p equation and we compare the two values to verify the impulse-momentum theorem.

Our second set up involved most of the equipment from the last experiment, except 

instead of having the other cart clamped we have a wooden block clamped to the table and our force probe has a sharpened screw connected. For this part of the activity we tried to imitate the same speed for both collisions. 

Data and Graphs: 

The data we obtain from the above graphs show that the initial velocity of the cart was -0.364 m/s (as mentioned previous, the direction away from the spring plunger is positive so initial velocity is modeled as negative). Making the final velocity 0.246 m/s after collision. 

The value for impulse we obtained using the integration function on LoggerPro gives the value to be 0.3168 Ns.

Conclusion: We initially assumed that for the nearly elastic collision the energy in the system was supposed to be conserved but reviewing our data for initial and final velocity we see that there is already a big discrepancy between 0.364 m/s and 0.246 m/s. While we did initially assume there would be some speed loss, it was much more than we had initially thought. One source for this "error" is the fact that our graph examination for the initial velocity was taken further away from the collision point. 

We could also make an argument that some energy was lost at the spring plunge.

While ideal conditions would be if our cart's initial velocity is constant, simply looking at the trend in the velocity vs time graph before the collision we see that there is a slight slope. This shows that our "friction-less" track isn't quite friction-less as the cart slows down as it gets closer to the spring plunger. It would have been more accurate to take the value of velocity closest to the point just before it comes in contact with the spring. This is a detail we overlooked which was a major source of error in our values. Comparing the impulse found via Force vs time in our graph of 0.3168 to the calculated of 0.413 we see that the calculated value is much greater. I believe this has to do with the initial velocity reading mentioned above, if we were to use a value closer to the collision point we should have gotten closer values for our momentum.