1Normal1 No Spac... Heading 1 Paragraph a) A cart of mass m; moving to the right

Question

1Normal1 No Spac... Heading 1 Paragraph a) A cart of mass m; moving to the right collides with a cart of mass ma that is at rest. If m2 is significantly larger than mi, consider the following two different inelastic collisions (the amount of energy lost is different in each and does not matter in the problem), then several scenarios are possible. In one scenario the cart on the left rebounds as illustrated in Fig. 5 Before collision After collision Rest Figure 5: Rebound 4/2/2018 Phys 111L Name: In another scenario the cart on the left is at rest after the collision as illustrated in Fig. 6. After collision Rest Before collision Rest Figure 6: No rebound In which scenario does the cart on the right move with greater velocity, assuming that the initial velocity of the cart on the left is the same? Explain your answer.

Explanation / Answer

In the case of no rebounce,

The first cart hits the second, which is at rest. After collison, the first cart comes to rest and second car move with some velocity.

Let momentum of system before the collision

P before = m1u1 + m2 u2 = m1u1 + m2 ( 0 ) = m1u1

After the collision, the mometum is

P after = m1( v1 ) + m2 ( v2 ) = m1( 0 ) + m2 ( v2 ) = m2 v2

In accordance with the law of conservation of momnetum, the total momentum before

the collision is equal to total momentum after the collision

m1u1 =  m2 v2

If masses of carts is the same, m1 = m2 = m (say)

u1 = v2

This implies that the initial speed of first cart is equal to final speed of second cart, vice versa.

Speeds are exchanged , what the given in above case ( Figure 6 )

To satisfy this , the masses of carts must be equal, means m1 = m2

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