# Homework Help: Hooks Law F = kx Book answer wrong I think

1. Sep 30, 2015

### Barclay

1. The problem statement, all variables and given/known data

Hello, two basic questions on the same topic and I think the book answer is wrong so I've posted both here if that's okay.

Q1. What force is required to stretch a spring with spring constant 0.2 N/cm a distance of 5 cm?

Q2. A vertical spring stretches 5 cm under a load of 100 g. Determine the spring constant.

2. Relevant equations

F = kx k = spring contant x = extension in spring

3. The attempt at a solution

Q1. F = kx
F = 0.2 x 5
F = 1 N

1 Newton is my answer but the book says 0.01 N.

Q2. 100g = 0.1kg therefore weight (force) = 0.1 x 10 = 1 N

F = kx
1 = 5k
k = 0.2 N/cm

0.2 N/cm is my answer but the book says 0.05 N/cm.

2. Sep 30, 2015

### stockzahn

Are you sure the dimension of the spring constant is N/cm and not N/m?

The solution in the book seems to be the inversed value of the spring constant, again using the common dimension N/m for it.

3. Sep 30, 2015

### Barclay

Yes absolutely sure

4. Sep 30, 2015

### stockzahn

Your calculations seem to be correct to me.

Q1:

If you take k = 0.2 N/m, then

F = 0.2 N/m ⋅ 0.05 m = 0.01 N

Q2:

If you take k in N/m, then

k = 1 N / 0.05 m = 20 N/m → 1/k = 0.05 m/N

Maybe this is where the answers are coming from, but they have to have messed up several times.

5. Sep 30, 2015

### dmcdaniel5253

1 Newton is equal to 1 kg m/s2. The cm and m cannot cancel each other out. Change the cm to m first, then solve.

6. Oct 1, 2015

### rude man

1N is correct unless somebody meant k = 0.2N/m.
The book here is wrong no matter what. Your answer is correct.

7. Oct 1, 2015

### Barclay

Thanks all. The book authors were trying to explain (somewhere earlier in the text) that the "spring constant can be in N/cm or N/mm as long as the extension is measured in the same units". So I think the authors go mixed up with all the units somewhere because they've been working in metres up to that point in the book

8. Oct 1, 2015

### Barclay

I just read this and seems to make sense.
So for Q1 What force is required to stretch a spring with spring constant 0.2 N/cm a distance of 5 cm?

0.2N/cm = 20N/m
5 cm = 0.05 m

F = kx
F = 20 x 0.05
F = 1 N

So the same answer as mine. This book is just wrong.

9. Oct 1, 2015

### rude man

Ya. get a new book!