# Combining Forces

1. Aug 4, 2015

### Zynoakib

1. The problem statement, all variables and given/known data
Hooke’s law describes a certain light spring of
unstretched length 35.0 cm. When one end is attached
to the top of a doorframe and a 7.50-kg object is hung
from the other end, the length of the spring is 41.5 cm.
(a) Find its spring constant. (b) The load and the spring
are taken down. Two people pull in opposite directions
on the ends of the spring, each with a force of 190 N.
Find the length of the spring in this situation.

I am having a small problem on (b)

2. Relevant equations
No

3. The attempt at a solution
Since the question says "Two people pull in opposite directions on the ends of the spring, each with a force of 190 N.", shouldn't the resultant force be 190N x 2 instead of just 190N (the answer)?

2. Aug 4, 2015

### BvU

Look at the end points of the spring separately and make a drawing of the forces. Newton (action = -reaction) applies. In a as well as in b. (what do you think is the force on the doorframe in a ?)

3. Aug 4, 2015

### Staff: Mentor

Since you're so good with free body diagrams, please show us your free body diagram for this situation. I'm guessing that your interpretation of the problem statement is very different from that of the rest of us.

Chet

4. Aug 4, 2015

### Zynoakib

The force on the doorframe in a should be 7.5 x 9.8 = 73.5 N

That's what I can imagine.

5. Aug 4, 2015

### BvU

That's right (plus some force from the weight of the spring itself).

(By the way, learn yourself to always include units -- and check them -- like: 7.5 kg $\times$ 9.8 m/s2 = 73.5 N -- and N = kgm/s2 )​

So for the spring constant, I hope you divide this 73.5 N by the extension (0.065 m) and not by twice 73.5 N.

Can you see the similarity with the two people pulling in opposite directions ?

I agree with your picture. Wholeheartedly: no matter what happens on the other end of the spring. It may be attached to the side of a doorframe (which then exerts a force of 190 N on the spring ! -- a mirror picture of yours) or it may be that someone holds the other end in place. If there's a curtain hanging in the middle, I won't be able to tell the difference !

Same with a rope: if the tension in the rope is 190 N, then a force of 190 N is required on both ends. Opposite and equal, so that the vector sum is zero: no acceleration (another Newton law). Again: doorframe or person -- doesn't matter.

6. Aug 5, 2015

### Zynoakib

Thank you, I get it now!!!