Calculating Initial Speed in an Inelastic Collision with Friction

In summary, the problem involves a completely inelastic collision between a drunk driver's car and a parked car with a coefficient of sliding friction between the tires and the road of 0.59. Using the conservation of linear momentum, the speed of the drunk driver's car can be determined after the collision. Then, using the work-energy theorem and assuming uniform friction, the distance required to stop the cars can be calculated and equated with the given data to find the initial speed of the drunk driver's car.
  • #1
Oliviam12
28
0

Homework Statement


A drunk driver strikes a parked car. During the collision the cars become entangled and slide to a stop together. The drunk driver's car has a total mass of 742 kg, and the parked car has a total mass of 776 kg. If the cars slide 18 m before coming to rest, how fast was the drunk driver going? The coefficient of sliding friction between the tires and the road is 0.59.


Homework Equations


Err?


The Attempt at a Solution


Not any idea really? Just that I think its inelastic... and that I can't use the equation v1`=m1-m2/m1+m2 V1 to get the answer... How do I incorporate the friction?
 
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  • #2
Yes, it's a completely inelastic collision. (What's conserved during the collision?) Treat the problem in two parts: (1) the collision (What's the speed of the two cars immediately after the collision?) (2) the slowing down due to friction.

Work backwards from the given information.
 
  • #3
Energy is conserved, but I don't know how to find the speed of the two cars after the collision :/
 
  • #4
Energy is not conserved (that's what inelastic means). Work backwards. Hint: What's the force of friction that slows the cars? The acceleration? The speed just after the collision?
 
  • #5
I am sorry but, I don't understand this problem at all... Can you redirect me to an example problem or a tutorial?
 
  • #6
Go through your text. You should find there that during inelastic collision, only thing that remains conserved is linear momentum. (Here, we are not concerned with rotaion and all.)
So assume initial speed to be 'v' and conserve momentum, to get speed of the two cars, just after the collision. (Note, after collision the two cars stick -- entangle -- to each other.) After obtaining this speed, you can apply work-energy theorem to know the work done by the friction. And, assuming uniform friction, you can get the distance required to stop the cars. Equate it with the given data (18m) to get initial speed 'v'.
 

FAQ: Calculating Initial Speed in an Inelastic Collision with Friction

1. What is an inelastic collision?

An inelastic collision is a type of collision in which energy is not conserved. In this type of collision, some of the kinetic energy of the colliding objects is converted into other forms of energy, such as heat or sound.

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

In an elastic collision, kinetic energy is conserved and the colliding objects bounce off each other. In an inelastic collision, kinetic energy is not conserved and the colliding objects stick together or deform.

3. What is the equation for calculating the final velocity in an inelastic collision?

The equation for calculating the final velocity in an inelastic collision is v = (m1v1 + m2v2)/(m1 + m2), where v is the final velocity, m1 and m2 are the masses of the colliding objects, and v1 and v2 are their initial velocities.

4. Can two objects with the same mass have different final velocities after an inelastic collision?

Yes, two objects with the same mass can have different final velocities after an inelastic collision. This is because the final velocity depends not only on the masses of the objects, but also on their initial velocities.

5. How does the coefficient of restitution affect an inelastic collision?

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. A lower coefficient of restitution results in a greater loss of kinetic energy and a slower final velocity for the colliding objects.

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