Elastic collision question: two marbles

[GFWD]

I just want to know if I am approaching this question correctly.

Homework Statement

Two marble spheres of masses 30 and 20 grams, respectively, are suspended from the ceiling by massless strings (.95m long). The lighter sphere is pulled aside through an angle of 75 degrees and let go. It swings and collides elastically with the other sphere at the bottom of the swing.
a) To what maximum angle will the heavier sphere swing.
b) To what maximum angle will the lighter sphere swing.

Homework Equations

Conservation of mechanical energy
Conservation of momentum
Conservation of kinetic energy

The Attempt at a Solution

1. Calculate the height the small sphere is above the "rest" state. Use this height and conservation of mechanical energy to get the velocity.
2. Use conservation of momentum and conservation of kinetic energy to get the velocity of the larger and smaller spheres after the collision.
3. Use conservation of mechanical energy to get the new heights of the large and small sphere.
4. use trig to get the angles of each sphere.

Does that approach make sense?

Thanks.

 

[Astronuc]

That approach will work.

Here are some useful references -

http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html

http://hyperphysics.phy-astr.gsu.edu/hbase/colsta.html

 

[m2003]

Your approach is generally correct. However, there are a few things to consider.

1. Step 1: When calculating the height of the small sphere, make sure to use the angle of 75 degrees in your calculation. This will give you the initial potential energy of the small sphere.

2. Step 2: When using conservation of momentum, make sure to account for the direction of the velocities. The small sphere will have a velocity in the horizontal direction after the collision, while the larger sphere will have a velocity in the vertical direction.

3. Step 3: When using conservation of mechanical energy, make sure to account for the new heights of the spheres after the collision. The smaller sphere will now have a lower maximum height due to the collision, while the larger sphere will have a higher maximum height.

4. Step 4: Your use of trigonometry is correct, but make sure to account for the new heights of the spheres in your calculations. This will give you the final maximum angles for each sphere.

Overall, your approach is on the right track. Just make sure to account for all the variables and consider the changes in energy and height after the collision.