# Compression of Spring

1. May 20, 2010

### roam

1. The problem statement, all variables and given/known data
A 2kg block is dropped from a height of 40 cm onto a spring of force constant k=1960 N/m. Find the maximum distance the spring is compressed.

(The answer must be 10 cm)

3. The attempt at a solution

Well, I know that if a spring is stretched "y", it will be compressed "y". The problem is that I can't find out how long will the spring stretch once it is dropped from that height. Therefore I tried to use the formula

$$F = ky$$

Where $$F= mg = 2 \times 9.81$$ and k =1960 N/m which is 196000 N/cm

$$2 \times 9.81 = (196000) k$$

$$y= \frac{2 \times 9.81}{196000}$$

But this gives me the wrong answer. Why is that??

By the way, I know that the tension is $$T= 2 \pi \sqrt{\frac{m}{k}} = 2 \pi \sqrt{\frac{2}{196000}}= 0.02 N$$.

2. May 21, 2010

### rock.freak667

It is best to consider energy for this problem, graviational pe = potential pe of spring

Also that T is period time and not the tension.

3. May 21, 2010

### roam

I tried that, it doesn't seem to work:

$$mgh= \frac{1}{2} k x^2$$

2 (9.81) 40 = 1/2 (196000) x2

x=0.089 cm

Because the correct answer should be 10 cm! Is there anything wrong with my calculations?

Yep, my mistake.

4. May 21, 2010

### rock.freak667

Not sure, the only way to get 10cm exact is if the mass was dropped from 50cm.

Normally, the energy method should work.