Collision in Deep Space

https://isaacphysics.org/questions/gravity_collision?stage=a_level

how do i do part b of this?

i tried working out the gravitational potential energy for the smaller mass using U=-GMm/r
and then using conservation of energy to equate that to KE

am i supposed to add both U values and figure out from there

any help would be appreciated!

Reply 1

lordaxil

The formula for U gives the gravitational potential energy of the entire system (not just smaller mass) so you don't need to add anything. Just be careful to evaluate this for both the initial and final separations of the two masses, and then calculate the change in GPE. This is then equal to the gain in KE of both masses. You will also need a relationship between the final velocities of the two masses to eliminate that of heavier one (hint: think about the answer to first part).