Two blocks can collide in a one-dimensional collision. The block on the left has

Question

Two blocks can collide in a one-dimensional collision. The block on the left hass a mass of 0.50 kg and is initially moving to the right at 2.4 m/s toward a second block of mass 0.50 kg that is initially at rest. When the blocks collide, a cooked spring releases 1.2 J of energy into the system. (For velocities, use to mean to the right to mean to the left.) (a) What is the velocity of the first block after the collision? m/s (b) What is the velocity of the second block after the collision? m/s Remember that the blocks cannot pass through each other!

Explanation / Answer

a) lets assume left side will move with v1 to the left and right side
block will move with v2 to the right after the collision.

Using momentum conservation,

0.50 * 2.4 + 0.50 * 0 = - 0.50v1 + 0.50v2

v2 - v1 = 2.4

v2 = 2.4 + v1 ......(i)

now using energy conservation,

0.50(2.4^2)/2 + 0 + 1.2 = 0.50(v1^2)/2 + 0.50(v2^2)/2

8.16 = v1^2 + v2^2

8.16 = v1^2 + (2.4 + v1)^2

2v1^2 + 4.8v1 - 2.4 = 0

v1 = 0.425 m/s ..............Ans(a)

b) v2 = 2.825 m/s

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