What Happens When a Sliding Block Collides with Another on a Flat Surface?

[lando45]

Hey,

I got this question, and I don't really know how to solve it, I'm stuck:

A block of mass m = 2.80 kg slides down a 30.0° incline which is 3.60 m high. At the bottom, it strikes a block of mass M = 6.80 kg which is at rest on a horizontal surface, Fig. 7-41. (Assume a smooth transition at the bottom of the incline, an elastic collision, and ignore friction.)

Determine the speeds of the two blocks after the collision.

I worked out the length traveled down the slope using basic trigonometry and got a value of 7.2m, but now I am completely lost and don't know what the next step is...any help?

Thanks a lot,

Rory

 

[Tide]

Start by finding the speed of the small block using energy conservation and go from there. :)

 

[quicknote]

Hi Rory,

Thanks for reaching out for help with your question. It seems like you have made a good start by calculating the distance traveled down the slope.

To determine the speeds of the two blocks after the collision, we will need to use the principles of conservation of momentum and conservation of kinetic energy. These principles state that in a closed system, the total momentum and total kinetic energy before and after a collision must be equal.

In this case, the closed system is the two blocks (mass m and M) before and after the collision. We can set up the following equations:

Conservation of momentum: mvi + MVi = mvf + MVf

Conservation of kinetic energy: 1/2mvi^2 + 1/2MVi^2 = 1/2mvf^2 + 1/2MVf^2

Where vi and vf are the initial and final velocities of the blocks, respectively.

Since we know the masses (m and M) and the initial velocity of the block on the incline (vi), we can solve for the final velocities (vf and Vf) using these equations.

I hope this helps guide you in the right direction. Let me know if you have any further questions or need clarification on any of the steps. Good luck!

Best,