Inelastic Collision homework problem

In summary, an inelastic collision is a type of collision where kinetic energy is not conserved and the objects involved typically stick together after colliding. It is different from an elastic collision, where kinetic energy is conserved. The conservation of momentum equation and the coefficient of restitution formula are used to solve inelastic collision problems. The mass of the objects involved affects the resulting velocities after the collision, with heavier objects experiencing a smaller change in velocity. An example of an inelastic collision in real life is when a car collides with a wall, resulting in a loss of kinetic energy and a decrease in velocity.
  • #1
court2011
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Homework Statement


Two 75.0 kg hockey players skating at 6.15 m/s collide and stick together. If the angle between their initial directions was 130°, what is their speed after the collision? (Let the motion of player 1 be in the positive x-direction and the motion of player 2 be at an angle of 130° measured counterclockwise from the positive x-axis.)


Homework Equations





The Attempt at a Solution

 
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  • #2
Draw a picture and apply the conservation of momentum.
 
  • #3


To solve this problem, we can use the conservation of momentum and conservation of kinetic energy equations. Since the two players stick together after the collision, this is considered an inelastic collision. We can also use the fact that the total momentum before the collision is equal to the total momentum after the collision.

Let's first find the initial momentum of each player. Since player 1 is moving in the positive x-direction, their initial momentum is 75.0 kg * 6.15 m/s = 461.25 kg*m/s. For player 2, we can use the angle given to find their initial momentum in the x-direction. Using trigonometry, we can find that their initial momentum in the x-direction is 75.0 kg * 6.15 m/s * cos(130°) = -215.87 kg*m/s.

Now, using conservation of momentum, we can set the total initial momentum equal to the total final momentum. This gives us the equation 461.25 kg*m/s + -215.87 kg*m/s = (75.0 kg + 75.0 kg) * vf. Solving for vf, we get vf = 1.73 m/s.

Next, we can use conservation of kinetic energy to find the final speed. Since the players stick together, their final kinetic energy is equal to the initial kinetic energy. Using the equation KE = 1/2 * m * v^2, we can set the initial kinetic energy equal to the final kinetic energy and solve for vf. This gives us vf = 1.73 m/s.

Therefore, the final speed of the two players after the collision is 1.73 m/s. This is a significantly slower speed than their initial speeds, which makes sense since this was an inelastic collision. In an inelastic collision, some kinetic energy is lost due to deformation or other factors.
 

Related to Inelastic Collision homework problem

1. What is an inelastic collision?

An inelastic collision is a type of collision in which 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. Inelastic collisions typically involve objects that stick together after colliding.

2. How is an inelastic collision different from an elastic collision?

In an elastic collision, kinetic energy is conserved, meaning that the total kinetic energy of the objects involved before and after the collision is the same. Inelastic collisions, on the other hand, result in a loss of kinetic energy due to deformation or other factors.

3. What equations are used to solve inelastic collision problems?

The equations used to solve inelastic collision problems include the conservation of momentum equation, which states that the total momentum before the collision is equal to the total momentum after the collision, and the coefficient of restitution formula, which relates the initial and final velocities of the objects involved in the collision.

4. How does the mass of the objects involved affect an inelastic collision?

The mass of the objects involved in an inelastic collision will affect the resulting velocities after the collision. The heavier object will generally experience a smaller change in velocity compared to the lighter object, as the total momentum must still be conserved. However, the change in velocity will also depend on the initial velocities of the objects and the coefficient of restitution.

5. Can you provide an example of an inelastic collision in real life?

An example of an inelastic collision in real life is when a car collides with a wall. The car and the wall will stick together after the collision, and the resulting velocity of the car will be much less than its initial velocity due to the loss of kinetic energy during the collision.

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