How to find the unknown mass of an object in a 2d collision?

In summary, the problem involves finding the mass of a second puck in a collision, given the masses and velocities of the two pucks before and after the collision. Using the conservation of momentum equations, the mass of the second puck can be derived from the velocities in the x and y directions. However, the results obtained may be inconsistent and require double-checking of the data to ensure accuracy.
  • #1

Homework Statement


I have two pucks colliding. PUck 1 has a mass of .545 kg. Puck two has the same puck mass, but also has a weight added onto it. I need to find the mass of puck two.

Velocity before and after for puck 1:
V1i = 2.0m/s[19°Below the Horizontal]
V1f = 3.0m/s[31°Above the Horizontal]

Velocity before and after for puck 2:
V2i = 4.33m/s[19°Above the Horizontal]
V2f = 3.36m/s[16°Below the Horizontal]

Homework Equations



Conservation of momentum:

[itex]\vec{Pi}[/itex] = [itex]\vec{Pf}[/itex]

The Attempt at a Solution

m1[itex]\vec{vi}[/itex] + m2[itex]\vec{vi}[/itex] = m1[itex]\vec{vf}[/itex] + m2[itex]\vec{vf}[/itex]

m1[itex]\vec{vf}[/itex] - m1[itex]\vec{vi}[/itex] = m2[itex]\vec{vf}[/itex] - m2[itex]\vec{vi}[/itex]

m2/m1 = (v1f - v1i)/(v2f-v1i)

Now, I am supposed to draw vector diagrams for this but after that I get stuck. What do I do once I have drawn the vector diagrams for (v1f - v1i) and (v2f-v2i) ? I don't need someone to give me a full solution or anything, I just need some help to continue on the right track. I really appreciate any help!

Here is what I am getting by the vector diagrams by the way:
(v1f - v1i) = 2.3m/s [83° Above the horizontal]
(v1f - v1i) = -2.5m/s [78° Belowthe horizontal]
 
Last edited:
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  • #2
Hmm. One would expect momentum to be conserved in the collision. In fact, momentum in the x-direction and momentum in the y-direction should be conserved independently. Since you have the vectors for both objects before and after collision, you can write the momentum equations for both components.

When I do so and solve for the mass of the second puck I get different results for that mass from the x and y component equations. Furthermore, both results are LESS than the mass of the puck 1.

I would expect some variation due to experimental error, but the results seem to be a bit wonky even so. Can you check your data to make sure that you transcribed it correctly?
 

1. What is the equation for calculating unknown mass in a 2d collision?

The equation for calculating unknown mass in a 2d collision is m1v1 + m2v2 = (m1 + m2)vf, where m1 and m2 are the masses of the two objects colliding, v1 and v2 are their initial velocities, and vf is the final velocity after the collision.

2. What information is needed to calculate the unknown mass in a 2d collision?

In order to calculate the unknown mass in a 2d collision, you will need the masses of the two objects involved, as well as their initial velocities and the final velocity after the collision.

3. Can the unknown mass be calculated if only one object's mass is known?

No, in order to calculate the unknown mass in a 2d collision, you will need the masses of both objects involved.

4. How does the angle of collision affect the calculation of unknown mass in a 2d collision?

The angle of collision does not affect the calculation of unknown mass in a 2d collision, as long as the initial and final velocities are known.

5. Are there any limitations to using this equation to calculate unknown mass in a 2d collision?

This equation assumes that the collision is elastic (meaning no energy is lost during the collision) and that the objects are point masses (meaning their size and shape do not affect the collision). If these assumptions do not hold true, the calculated value for unknown mass may not be accurate.

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