# How Fast Was Kevin Skating Before the Inelastic Collision?

In summary, Kevin, with a mass of 84.2 kg, is skating at a speed of 1.74m/s when he grabs his 23.2-kg brother from behind, causing them to roll off together. Ignoring friction, Kevin's speed just before grabbing his brother can be found using conservation of momentum.

## Homework Statement

Kevin has a mass of 84.2 kg and is skating with in-line skates. He sees his 23.2-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 1.74m/s. Ignoring friction, find Kevin's speed just before he grabbed his brother.

## Homework Equations

V= d/t ?
I have no idea how to solve this eqn!
The only eqn i have for perfectly inelastic collision involves center of mass.

## Homework Statement

Kevin has a mass of 84.2 kg and is skating with in-line skates. He sees his 23.2-kg younger brother up ahead standing on the sidewalk, with his back turned. Coming up from behind, he grabs his brother and rolls off at a speed of 1.74m/s. Ignoring friction, find Kevin's speed just before he grabbed his brother.

## Homework Equations

V= d/t ?
I have no idea how to solve this eqn!
The only eqn i have for perfectly inelastic collision involves center of mass.

In an inelastic collision, kinetic energy is lost, but momentum is still conserved. Use conservation of momentum.

Hello Kevin, thank you for your question. I am happy to provide you with an explanation of the concept of perfectly inelastic collision and how it applies to your scenario.

First, let's define what a perfectly inelastic collision is. It is a type of collision where two objects collide and stick together after the collision, resulting in a loss of kinetic energy. This means that the final velocity of the two objects after the collision is the same.

In your scenario, Kevin is skating with a speed of 1.74 m/s and his brother is standing still. When Kevin grabs his brother, the two objects stick together and roll off at the same speed of 1.74 m/s. This is a perfectly inelastic collision because the two objects have become one and there is a loss of kinetic energy.

To find Kevin's speed just before he grabbed his brother, we can use the conservation of momentum principle. This principle states that the total momentum before a collision is equal to the total momentum after the collision. In this case, the total momentum before the collision is equal to the mass of Kevin (84.2 kg) multiplied by his initial velocity (V) and the total momentum after the collision is equal to the combined mass of Kevin and his brother (84.2 kg + 23.2 kg) multiplied by their final velocity (1.74 m/s).

Mathematically, this can be represented as:

84.2 kg * V = (84.2 kg + 23.2 kg) * 1.74 m/s

Solving for V, we get:

V = (84.2 kg + 23.2 kg) * 1.74 m/s / 84.2 kg

V = 1.74 m/s * (107.4 kg / 84.2 kg)

V = 1.74 m/s * 1.276

V = 2.22 m/s

Therefore, Kevin's speed just before he grabbed his brother was 2.22 m/s.

I hope this explanation helps you understand the concept of perfectly inelastic collision and how it applies to your scenario. Let me know if you have any further questions. Keep up the good work in your studies!

## 1. What is a perfectly inelastic collision?

A perfectly inelastic collision is a type of collision in which two objects stick together after colliding and move as one combined mass. This means that the kinetic energy of the system is not conserved and is converted into other forms of energy, such as thermal energy or deformation energy.

## 2. How is a perfectly inelastic collision different from an elastic collision?

In an elastic collision, the objects bounce off each other and retain their individual identities and velocities after the collision. In a perfectly inelastic collision, the objects stick together and move with a common velocity after the collision. This means that the kinetic energy is conserved in an elastic collision, but not in a perfectly inelastic collision.

## 3. Can a perfectly inelastic collision occur in real life?

Yes, perfectly inelastic collisions can occur in real life. Examples include a car crashing into a wall and sticking to it, or two pieces of clay colliding and sticking together. However, most real-life collisions are not perfectly inelastic, as some kinetic energy is usually lost due to factors such as friction and deformation.

## 4. How is the coefficient of restitution related to perfectly inelastic collisions?

The coefficient of restitution is a measure of the elasticity of a collision. In a perfectly inelastic collision, the coefficient of restitution is zero, as there is no bouncing or separation of the objects after the collision. The closer the coefficient of restitution is to 1, the more elastic the collision is.

## 5. What are the applications of perfectly inelastic collisions?

Perfectly inelastic collisions are commonly used in industries such as car manufacturing and sports equipment design. They can also be used in physics experiments to study the conservation of momentum and energy. In addition, perfectly inelastic collisions are important in understanding the dynamics of celestial bodies, such as when two planets collide and merge to form a larger planet.

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