Inelastic Collision Problem. Help

In summary, a cart of mass 1.2 kg moving at 3m/s collides with a block of wood of mass 0.8 kg at rest on a frictionless table. Since the collision is inelastic, kinetic energy is not conserved but momentum is. By using momentum conservation and knowing the masses and velocities before and after the collision, the velocity of the composite body can be calculated.
  • #1
blue_bee29
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Homework Statement



A cart of mass 1.2 kg that is moving to the right qt 3m/s collides on a block of wood of mass 0.8 kg that is lying at rest on top of a frictionless table. if the collision is inelastic, find the velocity of the composite body.

Homework Equations





The Attempt at a Solution


 
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  • #2
Well..

you know that the collision is inelastic, so kinetic energy will not be conserved, but momentum will be. You know the masses and the velocities before the collision as well as their velocities, and you can safely assume that mass is conserved, you can use momentum conservation to find the velocity of the composite body.
 
  • #3


In inelastic collisions, kinetic energy is not conserved. This means that after the collision, the total kinetic energy of the system will be less than the initial kinetic energy. In this problem, we can use the conservation of momentum to find the final velocity of the composite body.

First, we need to calculate the initial momentum of the system. The cart has a mass of 1.2 kg and is moving with a velocity of 3 m/s to the right, so its initial momentum is 1.2 kg * 3 m/s = 3.6 kg*m/s.

The block of wood has a mass of 0.8 kg and is at rest, so its initial momentum is 0 kg*m/s.

The total initial momentum of the system is therefore 3.6 kg*m/s.

After the collision, the two objects will stick together and move with a common final velocity. Let's call this velocity v.

Using the conservation of momentum, we can set up the equation:

Initial momentum = final momentum

3.6 kg*m/s = (1.2 kg + 0.8 kg) * v

Solving for v, we get v = 2 m/s.

Therefore, the final velocity of the composite body after the inelastic collision is 2 m/s to the right.

I hope this helps with your homework problem. It's important to remember that inelastic collisions result in a decrease in kinetic energy, so the final velocity will always be less than the initial velocity.
 

FAQ: Inelastic Collision Problem. Help

What is an inelastic collision?

An inelastic collision is a type of collision where kinetic energy is not conserved. This means that after the collision, the total kinetic energy of the objects involved is less than the initial total kinetic energy.

How is an inelastic collision different from an elastic collision?

In an elastic collision, both momentum and kinetic energy are conserved, whereas in an inelastic collision, only momentum is conserved. This is because some of the kinetic energy is converted into other forms, such as heat or sound, during the collision.

What factors affect the outcome of an inelastic collision?

The mass, velocity, and elasticity of the objects involved all play a role in the outcome of an inelastic collision. The greater the mass and velocity of the objects, the more energy will be lost during the collision. The elasticity, or ability to deform and return to its original shape, also affects the amount of energy lost.

How is the coefficient of restitution used in inelastic collisions?

The coefficient of restitution is a measure of the elasticity of a collision. In an inelastic collision, the coefficient of restitution is less than 1, indicating that some of the kinetic energy is lost. The lower the coefficient, the less elastic the collision is.

How can I solve inelastic collision problems?

To solve inelastic collision problems, you can use the principles of conservation of momentum and conservation of energy. You will also need to apply the coefficient of restitution to determine how much energy is lost during the collision. It is also helpful to draw a diagram and use equations to represent the motion of the objects before and after the collision.

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