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• A-Level Maths

# Forces, Friction & Motion

As seen in the Notes Sheet on Modelling in Mechanics, forces on an object can be expressed with a force diagram:

### Newton's 1st Law:

On this diagram, you can see that T, the tension force pulling the object to the right, is equal to F, the friction between the the object and the surface - friction is the force that opposes motion.

This means that there is no resultant force to the left nor right, so the object remains motionless (it is in equilibrium). This is Newton's first law:

An object will stay at a constant velocity, or motionless, unless it experiences a resultant force.

### Newton's 2nd Law:

Here, the surface is smooth (no friction). This means the object experiences a resultant force, T, to the right. According to Newton's second law, the resultant force on an object is directly proportional to the rate of change of momentum of the object, and acts in the same direction.

This is commonly expressed as:

F = ma Resultant Force = Mass x Acceleration (in direction of resultant force)

### Newton's 3rd Law:

In this example, the object sits at rest on the surface with no horizontal forces acting on it. However, its weight, W, (mass x g) is a force acting down. If this were the only force, you would expect the object to accelerate down through the surface but it does not.

This means there is an equal but opposite force acting upwards: the normal reaction, R.

For every action, there is an equal but opposite reaction (equal in magnitude and type of force).