Calculation of Final Velocity in an Elastic Collision
Problem Statement:
A 0.149 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.710 m/s. It has a head-on collision with a 0.308 kg glider that is moving to the left with a speed of 2.27 m/s. Suppose the collision is elastic.
Questions:
- Find the magnitude of the final velocity of the 0.149 kg glider.
- Find the magnitude of the final velocity of the 0.308 kg glider.
Answer:
v1 = −2.201946 m/s (to the left)
v2 = 0.7780534 m/s (to the right)
Explanation:
Given the following :
Mass of first glider (m1) = 0.149 kg
Initial Speed of first glider (u1) = 0.710 m/s
Mass of second glider (m2) = 0.308 kg
Initial Speed of second glider (u2) = 2.27 m/s
For elastic collision:
m1u1 + mu2u2 = m1v1 + m2v2
Where V1 and v2 are the final velocities of the bodies after the collision.
Taking right as positive and left as negative.
u1 = 0.710 m/s ; u2 = -2.27 m/s
From the equation u1 - u2 = - (v1 - v2)
0.710 - (-2.27) = - v1 + v2
v2 - v1 = 2.98
From the equation (0.149 * 0.710) + (0.308 * -2.27) = (0.149 * v1) + (0.308 * v2)
0.10579 + (-0.69916) = 0.149 v1 + 0.308 v2
−0.59337 = 0.149 v1 + 0.308 v2
Dividing both sides by 0.149
v1 + 2.067 v2 = −0.59337
After solving the equations, we get:
v1 = −2.201946 m/s (to the left)
v2 = 0.7780534 m/s (to the right)