# Homework Help: Collisions, Hooke's Law.

1. Jan 17, 2005

### futb0l

A 450kg bumper car, with a spring which have a spring constant of 3x10^7 N/m collides at a speed of 2m/s with a solid wall. It gives a maximum compression of 7.7mm. At what speed will the car rebound of the wall?

I am having trouble with this one... I don't know how to go about solving the problem. The answer btw is 1.6m/s

2. Jan 17, 2005

### HallsofIvy

Do you know how to find the potential energy from the spring constant and compression? You should have a formula for that and a formula for kinetic energy as a function of speed. Once the car has rebounded, all that potential energy becomes kinetic energy.

3. Jan 17, 2005

### stunner5000pt

Since the final speed is not equal to the initial speed isnt there some friction involved in this question??

DOes the question say anything about the surface upon which this car travels??

4. Jan 17, 2005

### futb0l

Nope, it doesnt say anything about the surface, it says its just a solid wall... which is why it is strange.

5. Jan 18, 2005

### Gokul43201

Staff Emeritus

I get 1.9762 m/s

Use energy conservation.

KE (before collision) = PE (at max compression) + E (lost to friction)

Plugging in the numbers, you can find E (lost).

During the rebound, you will lose this same amount of energy to friction, so KE (final) = PE - E (lost)

6. Jan 18, 2005

### Andrew Mason

I agree. The car has 900 Joules of energy (.5mv^2=.5*450*2*2). A spring compression of .0077 m contains 899.35 joules of energy. If it loses another 10.65 joules in converting it back to kinetic energy, you end up with 878.7 J, so v^2=2*878.7/450; v=1.9762. A speed of 1.6 m. gives the car 576 J. The problem contains no information to account for such a loss of energy.

AM

7. Jan 18, 2005

### Gokul43201

Staff Emeritus
That (1.6 m)answer would require either a spring constant of about 2.5 * 10^7 N/m or a compression of about 7.0 mm or just a whole new set of numbers.

8. Jan 18, 2005

### futb0l

Thanks, probably something wrong with this question, I am stunned myself.