# Homework Help: Normal force by a spring

1. Nov 25, 2013

### Leong

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

A vertical spring is fixed on a table. A book is put on the spring. The book compresses the spring until static equilibrium is reached. Question: Is there a normal force exerted by the spring on the book? Why or why not?

2. Relevant equations

3. The attempt at a solution
I think there is because normal force is a contact force. As long as two bodies are in contact, I think it exists. But I never see books mention normal force in this kind of problem.

2. Nov 25, 2013

### Staff: Mentor

Hi Leong. What do you understand by the meaning of the word "normal" here?

3. Nov 26, 2013

### Leong

Perpendicular

4. Nov 26, 2013

### Staff: Mentor

If you put the book on a table, would there be a 'normal' force supporting it? It's the same idea here. The term 'normal force' is commonly used to describe the support force on an object from some surface. (Imagine the top of the spring has a platform for resting the book on.)

5. Nov 26, 2013

Let the mass of the book be 'm' and the spring constant be 'k'. When the book has achieved static equilibrium we know two things.
1) The force of gravity is trying to pull the book downwards. This force = m*g ( g is the gravitational constant for earth and equals 9.81m per second squares )
2) There has to be a force which cancels the force of gravity otherwise the book will start accelerating under the influence of unbalanced force.

Now, the spring will definitely have to exert a force on the book because it is at rest and gravity acts towards the center of earth (i.e. downwards towards the table). The spring applies a force which equals mg in order to cancel the force of gravity.

Hope this Helped

6. Nov 26, 2013

### Leong

If there is no platform, just the book on the spring, will there still be a normal force on the book other than spring force and the weight of the book?

7. Nov 26, 2013

### Leong

Do you mean spring force or normal force or both as the force on the book exerted by the spring on the book?

8. Nov 27, 2013

### Staff: Mentor

The spring force is the normal force.

The upward force that the spring exerts on the book to support it is the normal force. And that force is given by Hooke's law, since it is a spring.

There are only two forces acting on the book: The downward force of gravity and the upward force of the spring (which you can call the normal force, if you like).

9. Nov 27, 2013

### Leong

Thanks for the explanation which I cannot find anywhere. Thanks to everyone who replied to my post.