Two blocks move along a linear path on a nearly frictionless air track. One bloc

Question

Two blocks move along a linear path on a nearly frictionless air track. One block, of mass 0.104 kg, initially moves to the right at a speed of 5.10 m/s, while the second block, of mass 0.208 kg, is initially to the left of the first block and moving to the right at 7.50 m/s. Find the final velocities of the blocks, assuming the collision is elastic.

The option the select box are:

to the right

to the left

no direction

Please explain...

velocity of the 0.104 kg block =1 2 ---Select--- to the right to the left no direction velocity of the 0.208 kg block =3 4 ---Select--- to the right to the left no direction

Explanation / Answer

Momentum conservation: 0.104*5.1 + 0.208*7.5 = 0.104*v1 + 0.208*v2

or, 0.104*v1 + 0.208*v2 = 2.0904

KE conservation: 1/2*0.104*5.1^2 + 1/2*0.208*7.5^2 = 1/2*0.104*v1^2 + 1/2*0.208*v2^2

or,  0.104*v1^2 + 0.208*v2^2 = 14.40504

Solving both thes equations, v1 = 8.3 m/s and v2 = 5.9 m/s

Veloity of 0.108 kg mass = 8.3 m/s towards right

Velocity of 0.208 kg mass = 5.9 m/s to the right

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