Question

A 0.144 kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.840 m/sm/s. It has a head-on collision with a 0.302 kg glider that is moving to the left with a speed of 2.19 m/sm/s. Suppose the collision is elastic. Find the magnitude of the final velocity of the 0.144 kg glider.

Answer 1

To find the magnitude of the final velocity of the 0.144 kg glider in an elastic collision, we can use the principle of conservation of momentum. The final velocity of the 0.144 kg glider is 3.75417 m/s.

Step-by-step explanation:

To find the magnitude of the final velocity of the 0.144 kg glider in an elastic collision, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.

The momentum of the 0.144 kg glider before the collision is given by mass (m1) multiplied by velocity (v1): (0.144 kg)(0.840 m/s) = 0.12096 kg·m/s

The momentum of the 0.302 kg glider before the collision is given by mass (m2) multiplied by velocity (v2): (0.302 kg)(-2.19 m/s) = -0.66138 kg·m/s

The total momentum before the collision is the sum of the momenta of the two gliders: 0.12096 kg·m/s + (-0.66138 kg·m/s) = -0.54042 kg·m/s

Since the collision is elastic, the total momentum after the collision is the same as the total momentum before the collision: -0.54042 kg·m/s.

The final velocity of the 0.144 kg glider can be calculated using the total momentum after the collision and the mass of the glider: 0.54042 kg·m/s / 0.144 kg = 3.75417 m/s. Therefore, the magnitude of the final velocity of the 0.144 kg glider is 3.75417 m/s.