Consider the following two cases: In case 1 a ball of mass m is thrown horizonta

Question

Consider the following two cases:

In case 1 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball bounces off the box and after the collision the box is moving to the right with V1 and the ball is moving to the left with speed vf .

In case 2 a ball of mass m is thrown horizontally with speed v0 at a stationary box of mass M. The ball sticks to the box and after the collision the box (with the ball stuck to it) is moving to the right with speed V2. In both cases the box slides without friction. Assume all motion is horizontal.

In which case is the change in momentum of the ball the biggest?

Which one of the following statements best describes V1 and V2?

In case 2 it is observed that V2 = v0/3. What is the ratio of masses M/m ?

In Case 1 it is observed that vf = v0/2. What V1/v0?

Explanation / Answer

here

the case 1 is the change in momentum of the ball the biggest

V1 >V2

here the momentum is conserved

so , m * v0 = (m + M) *v0/3

v0 cancels on both sides

then we divide the whole equation by m

1 = ( 1 + M/m) / 3

3 = 1 + M/m

M/m = 2

from this we get M/m = 2

then

momentum before collision = momentum after collision

m*v0 = M*V1 - m*vf
vf = v0 / 2

So
m*v0 = M*V1 - m*(v0 / 2)

(3/2) m*v0 = M*V1

(3/2)(m/M) = V1 / v0

3m / 2M = V1 / v0

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects