# Spring theory

1. Nov 26, 2004

### Kissinor

Hi

A skater with mass m = 80 kg and speed v = 8 m/s hits (colides with ) a spring with spring constant 40 N/m.
a .What is the maximum compression of the spring or in other words , how far will the sping be strecthed?

b. What is the speed of the skater after the spring has been compressed 5 m?

The same spring is now hung vertically from a tower on a bridge such that the free end is at the same level with the road , the skater hangs on to the free end of the spring and jumps over the bridge with an initial velocity v = 0 .

c How far is the spring extended when the skater has attained maximum speed?
d. What energy transfers occur when the skater falls towards the water?

Calculate the following :
1. The skater's maximum speed during the fall
2. How far under the road does the skater stops?
3 The geatest force the skater will experience form the spring during the fall.

2. Nov 26, 2004

### Astronuc

Staff Emeritus
a. Convert the kinetic energy of the skater 1/2mv^2 into the energy stored by the spring at maximum displacement, i.e. when the skater stops. For the spring F=kx and total energy absorbed = $$\int F dx$$. Find the appropriate limits.

b. Determine spring energy at displacement of 5m and determine kinetic energy of skater.

c. 1. Skater achieves maximum velocity when acceleration = 0, i.e when spring force balances force of gravity. Determine distance at this point, and speed.

2. From point of maximum velocity, spring force exceeds gravity force so skater is decelerating, and reaches maximum distance from starting point when speed is zero.

3. If spring force, F=kx, where should the maximum force occur?

3. Nov 26, 2004

### Kissinor

Thanks Astronuc , but I am still confused. I would need a little more detail like how I go about solving for the length of spring in question .

what formula do i use to determine the spring energy?

I don't know how to apply antidifferention in this case .

4. Nov 26, 2004

### Kissinor

What is the acceleration of the skater after he hits the spring?

5. Nov 27, 2004

### fannemel

$$F = kx$$
$$E_p = \int F dx = \frac{1}{2} k x^2$$ Energy in spring

The only force working on the object is the force from the spring

Last edited: Nov 27, 2004