Our goal in this lab was to show that in elastic and inelastic collisions, momentum is conserved.
The experiment had 3 separate trails, all of them involving the conventional cart and track system that we have employed in many previous labs.
First, we attach a force sensor to the cart, and motion sensor and spring system on one end of the track, We then gave the cart an initial push and recorded the data of its collision with the spring system, obtaining a time/position chart from the motion sensor and a force/time chart from the force sensor.
The second experiment is identical to the first in all but one respect, a 500 gram weight was added to the cart. The setup for the second experiment is shown below, the first experiments, setup as I said, is identical except for the weight.
Finally, for the third and final experiment, the rubber cap that was on the force sensor previously is replaced with a nail (as shown below) and the spring system is replaced with a lump of clay that this nail will impact in a (hopefully) inelastic collision. As in the first experiment, there was no weight added to the cart expect for the force sensor and metal plate used to fasten it.
In order to prove that mometum is conserved, it was rather helpful to know what momentum was exactly. Essentially, it is the value p=mv. A second value, impulse which is equal to F(t), affects momentum in a way very simular to the relationship between work and energy. That is that initial momentum plus the total impulse exerted on the system will equal the final momentum of the system. Or.
Mvi +F(t) = Mvf
We are able to measure the initial and final momentum of the system by way of the motion sensor (charting position with respect to time and deriving velocity immediately before and after the collision). Likewise we are able to measure impulse through the force sensor on the cart by plotting the force with respect to time and taking the integral the resulting function during the collision. Below is a description of each experement in chronological order where we followed this method.
TRIAL 1
Is described above, from the motion and force sensors we gathered the following data.
As we can see, the velocity of the cart before the collision is 0.834 m/s and immediately after is -0.759 m/s. The force range of the force/time graph we chose to treat as "durring the collision" was determined by the sudden increase in force that occurs at 1.66 seconds. That, we assumed was the first moment that the force sensor (and therefore the cart) came in contact with the spring system. Our integration of this range gives us a value of -0.7389. Our carts mass was 43 grams, so our equation (manuplated) gives us the following:
M(vi) + I = M(vf)
I = M(vf-vi)
I = 0.43(-0.759-0.834)
I = -0.68499
This theoretical value for impulse is lower than the actual observed value by about 7 percent. This is probably due to some friction in the spring system, or issue with data collection.
TRIAL 2
This trail was run in exactly the same way as the first, save that a weight of 500 grams was added to the cart. The data collected is as follows.
Here the values are as follows:
M=0.43+0.5
vi=0.464 m/s
vf=-0.401 m/s
I=-0.8591
Plugging the first 3 values into the equation derived below
I=0.93(-0.401-0.464)
I=-0.80445
This value for I is, once again, lower than the actual observed value of -0.8591, this time by a margin of 6.3 percent. I suspect the same sources for this error as listed above.
Trial 3
Finally, in trail 3, our data was as folllows
We have the values
M= 0.43
vi= 0.861
vf= 0
I=-0.3178
plugging these values into our equation we get
I=0.43(0-0.861)
I=-0.37023
This time, the value for impulse that we predict is much higher than the one we observed, in contrast to the previous experiments. This error may be due to some issue of the cart hitting the back of the object the clay was stuck to and ricocheeing, making the clay have to impart more force on the nail than it would in a purely inelastic collision. This idea is supported by the fact that the force fluctuates between positive and negitive durring the colllision, while in the previous trails it remained negitive the entire time.
The experiment had 3 separate trails, all of them involving the conventional cart and track system that we have employed in many previous labs.
First, we attach a force sensor to the cart, and motion sensor and spring system on one end of the track, We then gave the cart an initial push and recorded the data of its collision with the spring system, obtaining a time/position chart from the motion sensor and a force/time chart from the force sensor.
The second experiment is identical to the first in all but one respect, a 500 gram weight was added to the cart. The setup for the second experiment is shown below, the first experiments, setup as I said, is identical except for the weight.
 |
| pictured, a chair, and also our lab setup |
Finally, for the third and final experiment, the rubber cap that was on the force sensor previously is replaced with a nail (as shown below) and the spring system is replaced with a lump of clay that this nail will impact in a (hopefully) inelastic collision. As in the first experiment, there was no weight added to the cart expect for the force sensor and metal plate used to fasten it.
 |
| cart of unholy death |
Mvi +F(t) = Mvf
We are able to measure the initial and final momentum of the system by way of the motion sensor (charting position with respect to time and deriving velocity immediately before and after the collision). Likewise we are able to measure impulse through the force sensor on the cart by plotting the force with respect to time and taking the integral the resulting function during the collision. Below is a description of each experement in chronological order where we followed this method.
TRIAL 1
Is described above, from the motion and force sensors we gathered the following data.
As we can see, the velocity of the cart before the collision is 0.834 m/s and immediately after is -0.759 m/s. The force range of the force/time graph we chose to treat as "durring the collision" was determined by the sudden increase in force that occurs at 1.66 seconds. That, we assumed was the first moment that the force sensor (and therefore the cart) came in contact with the spring system. Our integration of this range gives us a value of -0.7389. Our carts mass was 43 grams, so our equation (manuplated) gives us the following:
M(vi) + I = M(vf)
I = M(vf-vi)
I = 0.43(-0.759-0.834)
I = -0.68499
This theoretical value for impulse is lower than the actual observed value by about 7 percent. This is probably due to some friction in the spring system, or issue with data collection.
TRIAL 2
This trail was run in exactly the same way as the first, save that a weight of 500 grams was added to the cart. The data collected is as follows.
Here the values are as follows:
M=0.43+0.5
vi=0.464 m/s
vf=-0.401 m/s
I=-0.8591
Plugging the first 3 values into the equation derived below
I=0.93(-0.401-0.464)
I=-0.80445
This value for I is, once again, lower than the actual observed value of -0.8591, this time by a margin of 6.3 percent. I suspect the same sources for this error as listed above.
Trial 3
Finally, in trail 3, our data was as folllows
We have the values
M= 0.43
vi= 0.861
vf= 0
I=-0.3178
plugging these values into our equation we get
I=0.43(0-0.861)
I=-0.37023
This time, the value for impulse that we predict is much higher than the one we observed, in contrast to the previous experiments. This error may be due to some issue of the cart hitting the back of the object the clay was stuck to and ricocheeing, making the clay have to impart more force on the nail than it would in a purely inelastic collision. This idea is supported by the fact that the force fluctuates between positive and negitive durring the colllision, while in the previous trails it remained negitive the entire time.
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