Two pendulums banging into each other problem.

[tjhero123]

Homework Statement

A system contains two metal balls hanging from strings of length !.0 m. Pendulum A has a mass of 2.0 kg and B has a period of 2.0s. They are released from the same height at the same time and collide right in the middle of their arcs. If pendulum A comes to a complete stop while B moves backwords with half of its original speed, what is the mass of pendulum B?

Homework Equations

Conservation of momentum.

The Attempt at a Solution

My first thought was the conservation of momentum. 2Va+MbVb=-(1/2)MbVb. Of course there's 3 variables so i couldn't solve it but then i thought that since the balls were colliding in the middle of their arcs that maybe they're velocities were the same. So Va=Vb. From that logic I get that the mass of B is -4/3 which obviously makes no sense... I am not sure what I am doing wrong. I am gratful for any help. Thanks in advance

 

[ehild]

Homework Statement

A system contains two metal balls hanging from strings of length !.0 m. Pendulum A has a mass of 2.0 kg and B has a period of 2.0s. They are released from the same height at the same time and collide right in the middle of their arcs. If pendulum A comes to a complete stop while B moves backwords with half of its original speed, what is the mass of pendulum B?

Homework Equations

Conservation of momentum.

The Attempt at a Solution

My first thought was the conservation of momentum. 2Va+MbVb=-(1/2)MbVb. Of course there's 3 variables so i couldn't solve it but then i thought that since the balls were colliding in the middle of their arcs that maybe they're velocities were the same. So Va=Vb. From that logic I get that the mass of B is -4/3 which obviously makes no sense... I am not sure what I am doing wrong. I am gratful for any help. Thanks in advance

The momentum is a vector. The balls move in opposite directions just before they collide. Va is not equal to Vb.


ehild

 

[tannerbk]

Use the equation for the period of a pendulum to help you find Vb.

 

[haruspex]

Use the equation for the period of a pendulum to help you find Vb.

The time taken is irrelevant. You cannot deduce any actual velocity since you do not know the original height. ehild's hint is the way forward.

 

[Nickie]

You are on the right track by using the conservation of momentum equation, but there are a few things that need to be clarified.

First, the equation should be written as MaVa + MbVb = (Ma+Mb)Vf, where Ma and Mb are the masses of pendulums A and B respectively, Va and Vb are their initial velocities, and Vf is their final velocity after the collision.

Second, in your attempt at a solution, you have used the same variable (Vb) for both the initial and final velocities of pendulum B. This is incorrect as the final velocity of pendulum B would be different from its initial velocity after the collision.

Third, the negative sign in front of (1/2)MbVb should be positive, as the final velocity would be in the opposite direction from the initial velocity.

With these corrections, the equation should look like this:

2kg(0m/s) + Mb(2m/s) = (2kg+Mb)(1m/s)

Solving for Mb, we get Mb = 4kg.

This means that pendulum B has a mass of 4kg.

In summary, the mass of pendulum B is 4kg.