- #1
nokia8650
- 219
- 0
A smooth sphere A of mass 4m is moving on a smooth horizontal plane with speed u. It
collides directly with a stationary smooth sphere B of mass 5m and with the same radius as A.
The coefficient of restitution between A and B is 1/2
(a) Show that after the collision the speed of B is 4 times greater than the speed of A.
Sphere B subsequently hits a smooth vertical wall at right angles. After rebounding from the
wall, B collides with A again and as a result of this collision, B comes to rest.
Given that the coefficient of restitution between B and the wall is e,
(b) find e. For part (b), I receive an answer of 1/14. This is due to the fact that I have equated the coefficient of resisution of the two balls in the following way for the final collision:
0.5 = v/(u+4eu)
where v = velovity of ball A after the final collision, and u = the velocity of ball A before the collision (and hence the velocity of B is -4eu).
This results in a result of e = 1/14 after solving simultaneously with a linear expression for the conservation of momentum.
However, the markscheme has done the above as: 0.5 = (0-v)/(u+4eu) - note the presence of the negative sign. This results in a result of 0.5 for the second coefficient of resistution. Can someone please explain the logic behind this?
Thanks
collides directly with a stationary smooth sphere B of mass 5m and with the same radius as A.
The coefficient of restitution between A and B is 1/2
(a) Show that after the collision the speed of B is 4 times greater than the speed of A.
Sphere B subsequently hits a smooth vertical wall at right angles. After rebounding from the
wall, B collides with A again and as a result of this collision, B comes to rest.
Given that the coefficient of restitution between B and the wall is e,
(b) find e. For part (b), I receive an answer of 1/14. This is due to the fact that I have equated the coefficient of resisution of the two balls in the following way for the final collision:
0.5 = v/(u+4eu)
where v = velovity of ball A after the final collision, and u = the velocity of ball A before the collision (and hence the velocity of B is -4eu).
This results in a result of e = 1/14 after solving simultaneously with a linear expression for the conservation of momentum.
However, the markscheme has done the above as: 0.5 = (0-v)/(u+4eu) - note the presence of the negative sign. This results in a result of 0.5 for the second coefficient of resistution. Can someone please explain the logic behind this?
Thanks