What is the rebound speed of a bumper car after colliding with a wall?

[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

 

[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.

 

[stunner5000pt]

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.

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

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

 

[futb0l]

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

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

Nope, it doesn't say anything about the surface, it says its just a solid wall... which is why it is strange.

 

[Gokul43201]

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

Are you sure about this ?

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)

 

[Andrew Mason]

Are you sure about this ?

I get 1.9762 m/s

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

 

[Gokul43201]

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.

 

[futb0l]

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