# Contact forces – definition, examples & equations

Newton’s second law of motion tells that a sufficient amount of net force can move an object from one place to another. For example, If you push an object placed on the floor, it will go away. Similarly, if you pull it, it will come closer to you. In either case, you have to touch the object. Therefore, push and pull are two examples of contact force. Advanced placement physics 1 (AP 1) in USA covers this topic under the dynamics unit (unit 2). In this article, I’m going to explain the definition, examples, equation and diagrams of Contact forces.

1. Definition of Contact force
2. Examples of contact forces
3. Equations of Contact force

## What are Contact forces?

The contact forces are the forces between the objects that act when the objects come into contact with each other. An object can exert contact force on another object only if it touches that object physically. Contact forces are observable in the objects at the macroscopic level.

All the macroscopic forces are categorized into two types –

• Contact force
• Non-contact or long-distance force

Here we are interested in contact force only. You might be thinking about examples of non-contact forces. Here are three of them –

## Examples of contact forces

Here is a list of six examples of contact forces –

• Push and Pull
• Friction
• Tension
• Normal reaction
• Elastic force of spring
• Buoyant force

In the above diagram of contact force, F is the applied force (Pull or Push), f is the friction force and N is the normal reaction.

Now it’s time for short notes on these forces. Let’s start!

### Push and Pull

In the introduction of this article, I’ve told you that push and pull are the contact forces. The simplest way to move an object is by pushing or pulling it. In both cases, an external agent needs to touch the object. Hence, push and pull are two basic touch forces. Sometimes push-pull is generalized as the applied force.

### Friction force

When we try to move an object by pulling or pushing it on a rough surface, the friction force acts on the object in the opposite direction of the applied force (push or pull). The friction force acts on the surface of the object which is in contact with the rough surface. Hence, the friction force is another good example of contact force. Here is a full article on Friction force.

### Tension force

If an object is pulled by attaching it to a rope, the tension of the rope arises. Since the rope touches the object, the tension of a string or rope is a contact force. Note that the tension will not arise in the string in absence of external force (pulling) at the free end. I’ve written a complete article on Tension of a string. You can go through it.

### Normal reaction

The normal reaction is another example of contact force. Newton’s third law of motion tells us that to every action there is an equal and opposite reaction. Any surface exerts a normal reaction force on the surface of an object that is in contact with it. For example, when we stand on the floor, the floor exerts a normal reaction to us. In this case, the action force is our weight which acts on the floor. The same case happens when two blocks become in contact with each other.

### The Elastic Force of a Spring

The force exerted by a compressed spring on an object placed at the free end of the spring is also a contact force. A spring can apply this type of force due to its elastic property. A compressed spring always tends to gain its actual length and tries to be enlarged. During this time it pushes objects that are placed on its free end.

### Buoyant force

When an object is immersed in a liquid or gas medium, the object feels an upward thrust while falling. This is nothing but the buoyant force. Note that the object feels this force when it is in contact with the fluid (liquid or gas). Hence, the buoyant force is a contact force. Air resistance is also a contact force which is nearly the same as the buoyant force.

## Equations of contact forces

1. The equation of push-pull is the same as an external force. If an object of mass m achieves an acceleration a due to the applied force F then the equation of the force is F = ma. Here the surface is considered to be smooth and hence no friction force acts on the object.
2. If an object moves in a rough surface of friction coefficient $\color{Blue} \mu$ and the normal reaction of the surface to the object is N , then the equation of friction force is $\small\color{Blue} f = \mu N$.
3. If a block of mass m is placed on a horizontal surface, then the normal reaction on the block is, N = mg and the equation of normal reaction on an object placed on an inclined plane of angle $\small\color{Blue} \theta$ is $\small\color{Blue} N = mgcos\theta$.
4. The equation for the elastic force of a spring of spring constant k, compressed by a distance x is, F = – kx.
5. At the equilibrium condition, the tension of a string becomes equal to the net applied force at its free end. See all equations here: Tension of a string.
6. The buoyant force is equal to the weight of displaced fluid by the immersed object. If an object displaces fluid of volume V and density d then the equation of buoyant force is B = Vdg.

This is all from this article about the contact force, its definition, examples and equations. If you still have any doubts on this topic you can ask me in the comment section.

Thank you!

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