A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):
A ball of mass 'm' moves normal to a wall with a velocity 'u' and rebounds with a velocity 'v'. The change in momentum of the ball is (surface of the wall is smooth):
The correct option is B m(u+v) away from the wall
A ball of mass, m, moving with initial velocity, u to the right towards a wall.
It will have momentum →pi=m→u towards the right.
The ball bounces off the wall. It will now be moving to the left, with the same mass, but a different velocity, v and therefore, a different momentum,→pf=m→v towards the left.
The final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, △→p=m−→△v .
Using tail to head vector addition, △→p, must be the vector that starts at the head of →pi and ends on the head of →pf, hence the resultant change in momentum vector will point towards the left, that is, away from the wall.
We also know from algebraic addition of vectors that:
→pf=→pi+△→p
→pf−→pi=△→p
Magnitude of the change in momentum = mv−(−u)=m(v+u)
Direction of change in momentum is towards the left, away from the wall.
A ball of mass, m, moving with initial velocity, u to the right towards a wall.
It will have momentum →pi=m→u towards the right.
The ball bounces off the wall. It will now be moving to the left, with the same mass, but a different velocity, v and therefore, a different momentum,→pf=m→v towards the left.
The final momentum vector must be the sum of the initial momentum vector and the change in momentum vector, △→p=m−→△v .
Using tail to head vector addition, △→p, must be the vector that starts at the head of →pi and ends on the head of →pf, hence the resultant change in momentum vector will point towards the left, that is, away from the wall.
We also know from algebraic addition of vectors that:
→pf=→pi+△→p
→pf−→pi=△→p
Direction of change in momentum is towards the left, away from the wall.
