Hooks Law F = kx Book answer wrong I think

[Barclay]

Homework Statement

[/B]
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. Homework Equations

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

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. I can't see where I've gone wrong. Please advise.

 

[stockzahn]

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

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

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

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

 

[Barclay]

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.

Yes absolutely sure

 

[stockzahn]

Yes absolutely sure

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.

 

[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.

 

[rude man]

Q1: 1 Newton is my answer but the book says 0.01 N.

1N is correct unless somebody meant k = 0.2N/m.

Q2: 0.2 N/cm is my answer but the book says 0.05 N/cm.

The book here is wrong no matter what. Your answer is correct.

 

[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

 

[Barclay]

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.

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.

 

[rude man]

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

Ya. get a new book!