# Conservation of Momentum Lab (Carts Collide and Stick Together)

• kenzieleigh
In summary, the conversation discussed a lab where two carts with different masses collided and the students used photogate timers to determine velocities and calculate the unknown mass of one of the carts. However, their calculated mass was significantly different from the actual mass. They also discussed potential sources of error and suggested redoing the experiment with a different method to verify the results.
kenzieleigh

## Homework Statement

We did a lab where we had one cart with an unknown mass stationary on a friction-less surface. Another cart with a mass of 378.9g, was pushed down the track (which moves at a constant speed due to the friction-free surface) and collides with the second cart - so it is a hit and stick collision. We used photogate timers to determine time values immediately before and after which allowed us to find initial and final velocities. We graphed these values, found the best fit line and the slope from that. Then stacked the equations y=mx + b with m1v1 + m2v2 = (m1 + m2)vf to try and find the second mass. So we ended up having a slope of 0.8, thus we had the equation: 0.8 = 378.9 / (378.9 + m2). We calculated the second cart's mass to be 94.73 g, but after weighing it our mass is almost half of the actual mass. I attached a picture of our data and a diagram of the lab.

## Homework Equations

- y = mx + b
- slope = rise/run
- hit and stick collision

## The Attempt at a Solution

We now have to explain why we got the results we did. Momentum is clearly not conserved or we would have been able to determine the second mass accurately. The question is why not? Could it be air drag? Or is there some other force acting?

#### Attachments

• image.jpg
26.9 KB · Views: 431
• image.jpg
26.5 KB · Views: 454
Last edited by a moderator:
Can you explain exactly what you plotted? How are the x and y values in your plot related to what you measured?

kuruman said:
Can you explain exactly what you plotted? How are the x and y values in your plot related to what you measured?

We got the time value from before and after the collision with the timers. Found the length of the antennae on the first cart and used v=d/t to find the initial and final velocity. Then plotted the velocities with initial on the x-axis and final on the y.

kenzieleigh said:
Then plotted the velocities with initial on the x-axis and final on the y.
And why should that give you a straight line when plotted? What is the theoretical equation that you used?

kuruman said:
And why should that give you a straight line when plotted? What is the theoretical equation that you used?

Because the slope is equal to m1/(m1+m2) which were kept constant in the lab. Therefore there should be a straight line.

OK. Now how did you extract the unknown mass from the slope?

kuruman said:
OK. Now how did you extract the unknown mass from the slope?
We used that equation. We got the slope through rise/run and since we knew the mass of the first cart we could use the equation above (slope=m1/(m1+m2) ) to find the m2, but it wasn't the correct mass. It was about 90g when it actually has a mass of 180g (as calculated by a scale)

OK. You probably found the slope by using some kind of canned linear regression and set the intercept equal to zero because that makes sense theoretically. What if you redid the regression and let it find an intercept. What kind of slope and value for the mass do you get then?

kenzieleigh said:
Momentum is clearly not conserved or we would have been able to determine the second mass accurately. The question is why not? Could it be air drag? Or is there some other force acting?
Your problem is the opposite, too little speed was lost.
The plot looks suspiciously like two separate plots. The first three datapoints have a slope closer to 0.7, the rest being more like 0.9.
That might not sound much, but do the error analysis: 0.7 gives the unknown mass as 3/7 of the known mass, so quite close to the right value, while 0.9 gives 1/9. This suggests to me some experimental error crept into the set-up.
(Should such an exercise arise again, I recommend finishing with a run without the second cart, to verify the photogates still agree.)

Looking at the diagram, is it possible the carts were making contact before the first cart had cleared the first photogate? Maybe the antenna got bent back a little.

## 1. What is conservation of momentum?

Conservation of momentum is a fundamental law in physics that states that the total momentum of a closed system remains constant over time. This means that in any given interaction, the total momentum before the interaction is equal to the total momentum after the interaction.

## 2. How does the conservation of momentum apply to the "Carts Collide and Stick Together" lab?

In the lab, two carts with different masses collide and stick together. According to the law of conservation of momentum, the total momentum of the two carts before the collision must be equal to the total momentum of the combined carts after the collision. This means that the final velocity of the combined carts will be less than the initial velocity of the heavier cart, as the lighter cart will transfer some of its momentum to the heavier one.

## 3. How can we experimentally verify the conservation of momentum in this lab?

In order to verify the conservation of momentum in this lab, we can measure the initial velocities and masses of the carts, and then measure the final velocity of the combined carts after the collision. By plugging these values into the equation p = mv, where p is the momentum and m and v are the mass and velocity respectively, we can see if the total momentum before the collision is equal to the total momentum after the collision.

## 4. What are some potential sources of error in this lab?

Some potential sources of error in this lab include friction between the carts and the surface, which can affect the final velocities, as well as imprecise measurements of mass and velocity. Additionally, external forces such as air resistance or an uneven surface can also affect the accuracy of the results.

## 5. How can we improve the accuracy of the results in this lab?

To improve the accuracy of the results in this lab, we can minimize sources of error by using carts with lower friction, ensuring precise measurements of mass and velocity, and conducting the experiment on a smooth, level surface. Additionally, we can repeat the experiment multiple times and take the average of the results to reduce the impact of random errors.

• Introductory Physics Homework Help
Replies
40
Views
3K
• Introductory Physics Homework Help
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
6K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
6
Views
999
• Introductory Physics Homework Help
Replies
15
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
24
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
1K