Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 4 / 4B (Dynamics and Relativity)

Table of contents
- Solution 4B

Solution

Put

R = R_{A} + R_{B}

,

c = R^{2} - b^{2} / R

, and

s = b / R

. At impact the unit vector from A to B is

n = (- c, s)

. The impulse is normal, so tangential velocity is unchanged, while the normal components undergo a one-dimensional elastic collision. Therefore

v_{A} = \frac{2 M _{B}}{M _{A} + M _{B}} (u e_{x} \cdot n) n = - \frac{2 M _{B} u c}{M _{A} + M _{B}} n,

v_{B} = u e_{x} - \frac{2 M _{A}}{M _{A} + M _{B}} (u e_{x} \cdot n) n = u e_{x} + \frac{2 M _{A} u c}{M _{A} + M _{B}} n .

 Ancestors (9)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version