The particles in the figure below ( m 1 = 2.0 kg and m 2 = 3.5 kg) undergo an el

Question

The particles in the figure below (m1 = 2.0 kg and m2 = 3.5 kg) undergo an elastic collision in one dimension. Their velocities before the collision are

Find the velocities of the two particles after the collision. (Indicate the direction with the sign of your answer.)

I can set up the equation to get the variables v1 and v2 in the same equation, but i dont know how to solve for each independent variable or how to rearrange the equation to do so.

The particles in the figure below (m1 = 2.0 kg and m2 = 3.5 kg) undergo an elastic collision in one dimension. Their velocities before the collision are v1i = 12 m/s and v2i = ?7.5 m/s. Find the velocities of the two particles after the collision. (Indicate the direction with the sign of your answer.) I can set up the equation to get the variables v1 and v2 in the same equation, but i dont know how to solve for each independent variable or how to rearrange the equation to do so.

Explanation / Answer

Let the motion to the right be positive.

Elastic collision means :

1)Kinetic Energy is conserved.

2)Momentum is conserved.

Thus we get two equations:

m1V1 + m2V2 = m1v1 + m2v2 ..........1

V1 , V2 are initial velocities. v1 , v2 are final velocities.

(1/2)m1V1^2 + (1/2)m2V2^2 = (1/2)m1v1^2 + (1/2)m2v2^2 ............2

Put the values in equation 1

2*12 + 3.5*-7.5 =2v1 + 3.5v2

-2.25 = 2v1 + 3.5v2

v1 = -(1/2)(3.5v2 + 2.25)

Replace v1 by the above expression in equation 2 to get the quadratic in v2.

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