Collisions and changing frame of reference?

[twenty5]

collisions and "changing frame of reference?"

Homework Statement

A 6.0Kg trolley moving at 6.0 m/s right overtakes and collies with a 2kg trolley moving 2m/s right in the same direction on the same track. The collision is cushioned by a perfectly elastic bumper attached to one of the trolleys.

A) what is the speed and direction of each trolley after the collision?

B) What is the maximum amount of potential energy stored in the bumper during the collision?

Homework Equations

V₁' = v₁ (m₁ - m₂) / ( m¹ + m₂ )

V2f = 2*m1v1 / (m1+m2)

The Attempt at a Solution

for A) I tried that by substituting in values from the question and It gave me 3m/s and 9m/s... yet the answer says 4m/s and 8 m/s... am I doing anything wrong? =/

**my friend said something about change frame of reference...**

didn't start B yet because I didn't get A yet =/

 

[twenty5]

help please...

 

[nlightner]

I would like to clarify the concept of "changing frame of reference" in the context of this problem. In physics, a frame of reference is a coordinate system used to describe the position and motion of objects. In this problem, the initial frame of reference is the ground, where both trolleys are moving towards the right.

However, after the collision, the trolleys will have different velocities and therefore, a different frame of reference. To accurately determine the velocities after the collision, we need to use the frame of reference attached to one of the trolleys. This means that the speeds and directions calculated in this frame of reference may be different from those calculated in the ground frame of reference.

Now, coming to the solution for part A, your calculations seem to be correct. However, it is important to specify the frame of reference being used. If we use the ground frame of reference, the speeds after collision will be 3m/s and 9m/s as you have calculated. But if we use the frame of reference attached to the 6kg trolley, the speeds will be 4m/s and 8m/s, as mentioned in the answer.

For part B, we can calculate the maximum potential energy stored in the bumper using the formula for elastic potential energy: PE = 1/2*k*x^2, where k is the spring constant of the bumper and x is the maximum displacement of the bumper during the collision. This can be calculated using the conservation of momentum and kinetic energy equations. I leave it to you to try and solve it, keeping in mind the correct frame of reference.

In conclusion, it is important to understand the concept of frame of reference and choose the appropriate one while solving problems involving collisions. I hope this helps.