Calculating Maximum Compression and Acceleration in a Car-Spring Collision

[ellyb]

A 1300-kg car starts at rest and rolls down a hill from a height of 10.0-m. It moves across a level surface and collides with a spring-loaded guard rail designed to bring the car safely to a stop. The spring has a spring constant of 2.0E6N/m.
Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed.

Calculate the maximum acceleration of the car after contact with the spring (again ignore brakes, friction, etc.). Comment on the possibility of injury to the driver.

If the spring is compressed by only 0.30-m, find the change in the mechanical energy due to friction.

*I am really not sure where to start with this quesion can someone please help me?

 

[Jebus_Chris]

$$E_o = E_f$$
That will get you the first part

 

[nocturnus]

First you should be asking yourself, "what is going on?". You have an object starting from rest at a certain height, and then it proceeds downward toward a flat surface. Energy is needed to make the object move. Where does this energy come from? Is energy conserved? And finally, What happens to this energy as the object moves down the hill and compresses the spring?

As for the second part, you are analyzing the part where the car is traveling on the flat surface, and then continues to compress the spring. You can solve this part using F = ma. What forces are acting on the car? We know a spring force is acting on it.. when is this spring force maximum?

 

[Jebus_Chris]

$$E_o = E_f$$
$$mgh = \frac {1}{2} k x^2$$
I don't know why you have mgx in the second part. The car is moving horizontally once it hits the spring.

 

[ellyb]

oh right...so it would be
x= squar(127400(2)/2.0E6)=.4 m

 

[Jebus_Chris]

You messed up on your calculations.

 

[ellyb]

How do i find the maximum acceleration?

 

[Jebus_Chris]

F = -kx = ma

 

[ellyb]

Is this right?
f=-kx=-2.0E6*0.4=8.0E5N
a=F/m=8.0E5N/1300Kg=615.4 kg.n

 

[ellyb]

If the spring is compressed by only 0.30-m, find the change in the mechanical energy due to friction.
How do i find this part?

 

[ellyb]

KE= 1/2 2.0E6 N/m * (.3)^2
Is this the right formula to use for the mechanical energy last part?