Electrostatic collision between two masses

[unscientific]

Homework Statement

Homework Equations

The Attempt at a Solution

I've done part (a) and (b) using conservation of momentum and energy..for part (c) I'm not sure how to find the minimum angle ∅. I have also worked out the velocities of m₁ and m₂ just before the collision as required in part (a).

I've done a sketch that shows something like:

I know that in the zero-momentum-frame the total momentum must be zero, so their momentum are aligned. (different masses results in them having different velocities, in order to ensure Ʃp = 0)

 

[Mandelbroth]

I've done part (a) and (b) using conservation of momentum and energy..for part (c) I'm not sure how to find the minimum angle ∅. I have also worked out the velocities of m₁ and m₂ just before the collision as required in part (a).

Just for the math folk, let's use $\varphi$ rather than the empty set for our variable.

You have the velocities of the two masses. Velocity is a vector. The question you need to ask yourself is "how do you find the angle between two vectors?"

You probably meant speed, in which case...how do you relate speed and velocity?

 

[unscientific]

Just for the math folk, let's use $\varphi$ rather than the empty set for our variable.

You have the velocities of the two masses. Velocity is a vector. The question you need to ask yourself is "how do you find the angle between two vectors?"

You probably meant speed, in which case...how do you relate speed and velocity?

I know the answers to all your questions, but I'm not sure if they're helpful in this question...

 

[unscientific]

bumpp

 

[paranormal]

Using conservation of energy, we can write:

1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2

Where v1 and v2 are the initial velocities of m1 and m2 respectively, and v1' and v2' are the velocities just after the collision.

To find the minimum angle ∅, we can use the law of cosines:

v1'^2 = v1^2 + v2^2 - 2v1v2cos∅

Then we can substitute this into the conservation of energy equation to solve for cos∅:

1/2m1v1^2 + 1/2m2v2^2 = 1/2m1(v1^2 + v2^2 - 2v1v2cos∅) + 1/2m2v2'^2

Solving for cos∅, we get:

cos∅ = (m1v1^2 + m2v2^2 - m2v2'^2)/(2m1v1v2)

Using this equation, we can calculate the minimum angle ∅ for the given masses and velocities.