Help on 2 Physics Problems: Proton-Helium Collision & Tennis Ball Impulse

[jdword]

Hey all, I am in need of desperate help, any comments would be a huge help! thanks.

A proton moving at 3x10^5 m/s [E], strikes a helium nucleus at rest. If the collision is perfectly elastic, find the velocities of each after the collision. Assume the collision is 1 dimensional.

A tennis ball of mass m and speed v strikes a wall at 45degree angle and rebounds with the same speed at 45degrees. What is the impulse given the wall? [Hint: Magnitude and Direction are needed]

Thanks for any help,
Jeremy

 

[Astronuc]

For 1, try conservation of momentum and conservation of energy.

So m_Hv_H is the momentum before, and must equal the momentum after, and

1/2 m_Hv²_H is the KE before and must equal the KE of both particles after.

Use the relationship of momentum to partition the KE. The problem stated represents a head-on collision with full recoil.

For 2, the change in momentum normal to the plane of the wall contributes to the impulse. The momentum parallel to the wall does not contribute to the impulse.

 

[quicknote]

Sure, I'd be happy to help with these physics problems.

For the first problem, we can use the conservation of momentum and energy to solve for the velocities after the collision. Since the collision is perfectly elastic, the total momentum and total kinetic energy before and after the collision should be the same.

We can set up the equations as follows:

Initial momentum = Final momentum
(mass of proton)(initial velocity of proton) = (mass of proton + mass of helium)(final velocity of proton) + (mass of helium)(final velocity of helium)

Initial kinetic energy = Final kinetic energy
1/2(mass of proton)(initial velocity of proton)^2 = 1/2(mass of proton + mass of helium)(final velocity of proton)^2 + 1/2(mass of helium)(final velocity of helium)^2

Solving these equations simultaneously will give us the final velocities of the proton and helium. Remember to use the correct units for mass and velocity (kg and m/s).

For the second problem, we can use the definition of impulse, which is the change in momentum. Since the tennis ball rebounds with the same speed, we can assume that the change in momentum is equal to the initial momentum. We can also use the law of reflection to determine the direction of the impulse.

Impulse = Change in momentum = Initial momentum
= (mass of tennis ball)(initial velocity of tennis ball)

The direction of the impulse will be opposite to the direction of the initial velocity, so we can use vector notation to represent it.

Impulse = - (mass of tennis ball)(initial velocity of tennis ball) in the direction of the wall's normal vector.

I hope this helps. Let me know if you have any further questions. Good luck with your physics problems!