Question:

A 0.2 kg cricket ball moving horizontally with a speed of 15 m/s collides with a stationary 2 kg cricket bat. The collision lasts for 0.02 seconds after which the bat starts moving horizontally at a speed of 3 m/s in the same direction as the ball. Calculate the impulse experienced by the ball and the bat during the collision.

Answer:

To solve this problem, we need to use the concepts of impulse and conservation of momentum.

Step 1: First, let's calculate the initial momentum of the ball. The momentum of an object is given by the product of its mass and velocity.

Initial momentum of the ball = mass × velocity

Initial momentum of the ball = 0.2 kg × 15 m/s = 3 kg·m/s (in the positive direction since the ball is moving to the right)

Step 2: Next, let's calculate the final momentum of the ball. The final momentum of the ball can be obtained using the equation:

Final momentum of the ball = mass × velocity

Final momentum of the ball = 0.2 kg × v (where v is the final velocity of the ball after the collision)

Step 3: According to the problem, the bat and the ball stick together after the collision. This implies that the final velocity of the ball and bat will be the same. Therefore, the final momentum of the ball and the bat will be equal to the momentum of the combined system.

Final momentum of the ball and the bat = (mass of the ball + mass of the bat) × final velocity

Final momentum of the ball and the bat = (0.2 kg + 2 kg) × v

Final momentum of the ball and the bat = 2.2 kg × v (in the positive direction)

Step 4: According to the principle of conservation of momentum, the initial momentum of the ball should be equal to the final momentum of the ball and the bat.

3 kg·m/s = 2.2 kg × v

Solving for v:

v = 3 kg·m/s ÷ 2.2 kg

v ≈ 1.36 m/s

Therefore, the final velocity of the ball and the bat after the collision is approximately 1.36 m/s.

Step 5: Now, let's calculate the impulse experienced by the ball and the bat. Impulse is defined as the change in momentum of an object and can be calculated using the equation:

Impulse = Final momentum − Initial momentum

For the ball: Impulse experienced by the ball = Final momentum of the ball − Initial momentum of the ball

Impulse experienced by the ball = (0.2 kg × 1.36 m/s) − (0.2 kg × 15 m/s)

Impulse experienced by the ball = 0.272 kg·m/s − 3 kg·m/s

Impulse experienced by the ball ≈ -2.728 kg·m/s

Since the impulse is negative, it means that the ball experienced a decrease in momentum during the collision.

For the bat: Impulse experienced by the bat = Final momentum of the bat and the ball − Initial momentum of the bat

Impulse experienced by the bat = (2.2 kg × 1.36 m/s) − 0 kg·m/s

Impulse experienced by the bat = 2.992 kg·m/s

Therefore, the impulse experienced by the ball during the collision is approximately -2.728 kg·m/s and the impulse experienced by the bat is 2.992 kg·m/s.