Conservation of Momentum and Kinetic Friction: How Far Do Fred and Brutus Slide?

Question:

If Fred (mass 65 Kg) is running with a football at a speed of 5.9 m/s and is met head-on by Brutus (mass 130 kg) moving at 4.4 m/s, how far do they slide on the ground? The coefficient of kinetic friction between their football uniforms and Astroturf is 0.30.

Answer:

The distance they slide is 0.16 meters.

First, we need to find the combined velocity of Fred and Brutus after the collision using the law of conservation of momentum. We calculate the final combined velocity to be -0.97 m/s, which indicates the direction of their movement.

Next, we calculate the deceleration due to the frictional force on Fred and Brutus as they slide together, which is -2.94 m/s². Using the equation for distance covered during deceleration, we find that they slide a total distance of 0.16 meters before stopping.

This problem demonstrates the conservation of momentum during a collision and the impact of kinetic friction on motion. By understanding these principles, we can determine how far objects will slide on a surface due to frictional forces.