Elastic collisions and gravitational forces

[mickellowery]

Homework Statement

Two blocks are on a frictionless ramp. The first block has a mass of 5.00kg and is released from the top of the ramp 5.00m. It has a magnet on the front with the north pole facing out. The second block is at rest at the bottom of the ramp and has a mass of 10.00kg. The two blocks never touch. Calculate the maximum height block 1 rises back up the ramp after the collision.

Homework Equations

I assume I need to use m₁v_1i+m₂v_2i= m₁v_1f+m₂v_2f and the 1/2m₁v_1i²... equations. I'm having trouble with coming up with initial velocity for block 1 coming down the ramp.

The Attempt at a Solution

 

[collinsmark]

I'm having trouble with coming up with initial velocity for block 1 coming down the ramp.

Ignore the second block for just a moment. How fast would the first block be traveling when it reached the ground, if it simply fell 5 m straight down? Now how fast would the block be traveling when it reached the end of a frictionless ramp, if it slid down the ramp, and the top of the ramp was 5 m high?

 

[mickellowery]

OK I might be doing this wrong. I assumed that an object accelerating at 9.8m/s² would travel 5m in .51s. This gave me a velocity of 7.30m/s. Am I on the right track? I'm still a little lost on how to get to how high it goes up.

 

[collinsmark]

OK I might be doing this wrong. I assumed that an object accelerating at 9.8m/s² would travel 5m in .51s. This gave me a velocity of 7.30m/s. Am I on the right track?

Umm, no. Not quite.

You could, if you really wanted to, use kinematics to find the first block's velocity when it reaches the bottom of the ramp. But conservation of energy is a much better way to go about problems like this.

The ramp is frictionless. So you can ignore friction. That means conservation of kinetic and potential energy is conserved, as the first block slides down the ramp. How much potential energy does the block have when it is at the top of the 5 m ramp? Thus, how much kinetic energy does it have when it reaches the bottom (remember we can ignore friction)? If you know the block's kinetic energy, what does that tell you about its velocity?

I'm still a little lost on how to get to how high it goes up.

Now is where you need to bring conservation of momentum into the picture, and model the collision. You've listed the relevant equations in the original post. You should be able to use them to find the velocity of the first block after the collision.

One more application of conservation of potential and kinetic energy should guide you to your final answer of how high the block goes back up the ramp.