A 0.156 glider is moving to the right on a frictionless, horizontal air track wi

Question

A 0.156 glider is moving to the right on a frictionless, horizontal air track with a speed of 0.900 . It has a head-on collision with a 0.303 glider that is moving to the left with a speed of 2.10 . Suppose the collision is elastic. 1) Find the magnitude of the final velocity of the 0.156 glider. 2) Find the magnitude of the final velocity of the 0.303 glider. 3) Find the direction of the final velocity of the 0.303 glider. *THE FULL RATING DEPENDS ON CLEAR EXPLANATION IN DETAILS, WITH NUMERICAL ANSWERS.

Explanation / Answer

For elastic collision

Applying conservation of momentum since no external force is present

Let right side is positive and left negative and final velocities of 0.156 kg and 0.303 kg be v1, v2

0.156*0.9 - 0.303*2.1 = 0.156*v1 + 0.303*v2

0.156*v1 + 0.303*v2 = -0.4959

v2 = (-0.4959 - 0.156*v1)/0.303

By conservation of energy since no external work is done

0.156*0.9*0.9/2 + 0.303*2.1*2.1/2 = 0.156*v1*v1/2 +0.303*v2*v2/2

0.156*(v1)^2 +0.303*((-0.4959 - 0.156*v1)/0.303)^2 = 1.4626

v1 = 0.9 or v1 = -3.06

v2 = -2.1 or v2 = -0.06

This gives -3.06 of 0.156kg glider and -0.06 of 0.303 kg glider

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