Elastic Collision: Find Velocity of 2 Bodies

[TheAce3317]

1. A steel ball of mass 0.400 kg is fastened to a cord 60.0 cm long and fixed at the far end, and is released when the cord is horizontal. At the bottom of its path, the ball strikes a 2.00 kg steel block initially at rest on a frictionless surface. The collision is elastic.

Assuming the positive direction is to the right, find, just after the collision,
Velocity of the ball
Velocity of the block

I don't know how to start this one, never the less do it.

2. A body of mass 2.4 kg makes an elastic collision with another body at rest and continues to move in the original direction but with one-fourth of its original speed. The struck block has a mass of 1.44kg.

What is the speed of the two-body center of mass if the initial speed of the 2.4 kg body was 4.5 m/s?

I plugged in the numbers into the equation (m1v1+m2v2)/(m1+m2) and got 3.234375 which I know is wrong. Don't even know how I got v2.

 

[guitarphysics]

First, a bit of a tip. When looking at a physics problem, don't limit it to a problem of just one concept (i.e. conservation of momentum); as you'll see, these problems you posted are about more than just one concept, so you can't just plug and chug equations willy-nilly (think about each situation and the relevant equations for those situations. Only then should you plug :) )

For the first question- think about conservation of energy. What's the energy of the steel ball at the beginning? Is it gravitational potential energy, kinetic energy, what? And what's the energy at the bottom, when it crashes with the block? If you consider these questions you'll be able to find the initial velocity of the ball during the collision. If the collision is elastic, kinetic energy is conserved. So, use conservation of momentum and conservation of kinetic energy to wrap everything up :).

Once you get that one let's discuss question 2.
Have fun

 

[TheAce3317]

At the beginning, I believe it has GPE, and when it hits it has KE, but i don't know how to find the initial velocity. I have been looking over my notes from class for quite some time, but I am just not seeing the right equations. Could you give me a bit of a hint?

 

[guitarphysics]

Yep, you're right. Initially, it's just standing still at some height so it will have energy equal to mgh. Afterwards (if we set the point of zero GPE to be the maximum downwards extension of the rope, or the point where the collision occurs) it will only have KE for the collision, equal to 1/2mv^2. Remember that energy is conserved, and you should be able to find it.

 

[TheAce3317]

I have to stop working for now, so I don't want to make you wait for nothing. You have helped with what you told me though, so thanks for that.

 

[guitarphysics]

No problem! If you need any more help don't hesitate to ask.