So I had an exam today and one of the questions is bugging me. Our professor is out of town for a few days, so we had a proctor and I still can't figure it out using my notes. It was a question about two carts and deals with momentum. Cart A is at rest between two photogates, while cart B is off to the right and it's pushed. An elastic collision occurs. Mass of cart A is 100 g and the first photogate time is 0.2 seconds and second time is 0.5 seconds going back through. Find mass of cart B and the initial and final energy of the system.
I didn't think there was enough info supplied, so I was really lost. Maybe I missed something in the question, but this is what I believe it was. Help Please.
I don't exactly understand what you mean by "photogate" time. Those times tells you relative velocity of the carts after/before collision (twice the time, half the velocity). With that, you should be able to solve it. It really depends on what Photogate time means.
This is a long problem for an exam.
Unless someone on here knows exactly what your experiment was, I do not see how we can help. I do not know where these photogates are for example.
If you go to google and type "conservation of momentum photogate lab penn state" this is just like the experiment we performed. It should be the top result "Physics 250 Laboratory: Conservation of Momentum. Hope this helps.
You need the velocities of both masses before and after the collision.
Since the initial velocity of the big mass is zero, you need to measure 3 velocities with the two photogates
You need the length of the two masses that pass through the photogates (your Penn state link calls them "flag lengths)
Then you can get for your initially moving mass (B) its initial velocity = +L1/(t forward)
and its final velocity on rebound = -L1/(t back)
However you need that third velocity, the velocity forward of A after it is hit. +L2/t mass A after)
Then mB * VinitialB = mB * VfinalB + 100 * VfinalA
solve that for mB
Note that Vfianal B must be negative or the photogate for B will not trigger the second time.
That means the stationary mass must be much bigger than the moving mass, or the moving one would not rebound.
Now since the collision was elastic the initial and final energies should be the same. However the world is not perfect
masses should now be in kilograms and lengths in meters so Joules result.
.5mB *VBi^2 + 0 and compare to .5mB * vBf^2 + .5mA * vAf^2
To solve this problem, we'll need to use the principles of conservation of momentum and conservation of kinetic energy.
Let's start by understanding the information given in the question:
1. Cart A is at rest between two photogates.
2. Cart B is off to the right and is pushed.
3. An elastic collision occurs.
4. The mass of cart A is 100 g.
5. The first photogate time is 0.2 seconds, and the second time is 0.5 seconds going back through.
Based on this information, we can assume that the collision between cart A and cart B is one-dimensional. Since the collision is elastic, both momentum and kinetic energy will be conserved during the collision.
Let's proceed with finding the mass of cart B and the initial and final energies of the system:
1. Mass of cart A: Given as 100 g.
2. Initial momentum of the system: Since cart A is at rest, its initial momentum is zero. The momentum of cart B can be calculated using the formula p = m * v, where p is momentum, m is mass, and v is velocity. Here we need to be careful as we don't have the velocity value directly. However, we have timing information from the photogates.
- The time it takes for cart B to pass through the first photogate is 0.2 seconds. This provides us with the time it takes for cart B to travel a certain distance.
- The distance traveled can be calculated using the formula d = v * t, where d is distance, v is velocity, and t is time.
- Assuming the initial speed of cart B is constant, the distance traveled through the first photogate is also the distance traveled in the collision.
- We'll use this distance to find the initial velocity of cart B.
3. Calculating the initial velocity of cart B:
- Using the distance traveled and the time taken, we can rearrange the formula d = v * t to solve for initial velocity as v = d / t.
- Plug in the distance from the first photogate and the time of 0.2 seconds to calculate the initial velocity.
4. Calculating the final velocity of cart B:
- Since the collision is elastic, momentum is conserved. Therefore, the initial momentum of cart B will be equal to its final momentum.
- Calculate the momentum of cart B after the collision using the equation p = m * v, where p is momentum, m is mass, and v is velocity.
- Rearrange the equation to solve for final velocity.
5. Calculating the mass of cart B:
- Now that we have the final velocity of cart B, we can calculate its mass using the equation p = m * v, where p is momentum and v is velocity.
- Rearrange the equation to solve for mass.
6. Calculating initial and final energies of the system:
- To find the initial energy of the system, we can use the formula for kinetic energy: KE = 0.5 * m * v^2, where KE is kinetic energy, m is mass, and v is velocity.
- Plug in the values of mass and velocity to calculate the initial kinetic energy.
- For the final kinetic energy, use the same formula, but with the final mass and velocity.
By following these steps, you should be able to solve the problem and find the mass of cart B as well as the initial and final energy of the system.