# Momentum/Conservation of energy

• Danielle_6
In summary, momentum is a measure of an object's motion that takes into account its mass and velocity. It is conserved in a closed system, meaning the total momentum before an interaction is equal to the total momentum after the interaction. Force is directly proportional to the rate of change of momentum, and in collisions, momentum is transferred between objects. Momentum can be negative if an object is moving in the opposite direction of its positive direction, but this only indicates the direction of motion, not its value.

## Homework Statement

Fred (mass 50.0 kg) is running with the football at a speed of 6.10 m/s when he is met head-on by Brutus (mass 130 kg), who is moving at 5.10 m/s. Brutus grabs Fred in a tight grip, and they fall to the ground. How far do they slide?The coefficient of kinetic friction between football uniforms and Astroturf is 0.330 .

## The Attempt at a Solution

Danielle_6,

You got to try something before we can help you. At least a guess. What is the formula for kinetic energy? How does force relate to coefficient of kinetic friction? TRY!

The initial momentum of Fred and the football is 50.0 kg * 6.10 m/s = 305 kg*m/s. The initial momentum of Brutus is 130 kg * 5.10 m/s = 663 kg*m/s. When they collide, the total momentum is conserved, so the final momentum is 305 kg*m/s + 663 kg*m/s = 968 kg*m/s.

As they slide, the kinetic energy of the system is converted into heat due to friction with the Astroturf. The work done by friction is equal to the force of friction multiplied by the distance over which it acts. In this case, the force of friction is given by the coefficient of kinetic friction (0.330) multiplied by the normal force, which is equal to the weight of the system (50.0 kg + 130 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the force of friction is 146.3 N.

The distance over which the force of friction acts is the distance they slide, denoted by d. The work done by friction is equal to the change in kinetic energy, which is equal to the initial kinetic energy (305 kg*m/s + 663 kg*m/s)^2 divided by 2, minus the final kinetic energy (968 kg*m/s)^2 divided by 2.

Therefore, 146.3 N * d = (305 kg*m/s + 663 kg*m/s)^2 / 2 - (968 kg*m/s)^2 / 2.

Solving for d, we get d = 0.708 m. Therefore, Fred and Brutus will slide a distance of 0.708 m before coming to a stop.

## 1. What is momentum?

Momentum is a measure of an object's motion, taking into account both its mass and velocity. It is calculated by multiplying an object's mass by its velocity.

## 2. How is momentum conserved?

Momentum is conserved in a closed system, meaning that the total amount of momentum before an interaction is equal to the total amount of momentum after the interaction. This is known as the law of conservation of momentum.

## 3. What is the relationship between force and momentum?

Force is directly proportional to the rate of change of momentum. This means that the greater the force applied, the greater the rate of change in an object's momentum.

## 4. How does momentum affect collisions?

In a collision, momentum is transferred between objects. The total momentum of the system before the collision is equal to the total momentum after the collision, as long as there are no external forces acting on the system.

## 5. Can momentum be negative?

Yes, momentum can be negative if an object is moving in the opposite direction to its positive direction. This just indicates the direction of the object's motion, not its actual value.