A ball B of mass m is projected with some velocity from a block A of mass 2m kept on a smooth horizontal surface. The ball strikes the wall elastically and comes back to the block A. Find the distance of block A from the wall when ball reaches back to it. Velocity in B is generated by a compressed spring fixed to block A. When the ball leaves spring, the distance of block from wall is d. (Neglect gravity)
- 2d
- 3d2
- 3d
- d
Let velocity of ball be v1 and velocity of block be v2
Applying the conservation of momentum for the bigger block and ball
mv1=2mv2
v2=v12
Let the block travel a distance x in time t
t=xv1/2=2d+xv1
⇒2x=2d+x
x=2d
∴ Final distance of block A from the wall =d+x=3d
mv1=2mv2
v2=v12
Let the block travel a distance x in time t
t=xv1/2=2d+xv1
⇒2x=2d+x
x=2d
∴ Final distance of block A from the wall =d+x=3d
A block of mass m attached to an ideal spring of spring constant K is placed on a smooth horizontal surface between two fixed elastic walls AB and CD as shown. The block is at a distance d from CD and spring is in its natural position. The maximum velocity with which the block can be projected towards CD so that block performs complete SHM.
One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x0 from the block. The spring is then compressed by 2x0 and released. The time taken to strike the wall is
A block of mass m attached to an ideal spring of spring constant K is placed on a smooth horizontal surface between two fixed elastic walls AB and CD as shown. The block is at a distance d from CD and spring is in its natural position. The maximum velocity with which the block can be projected towards CD so that block performs complete SHM.
