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).

Forces in Two Dimensions

Often, forces will not be exactly horizontal or vertical. Instead, they may be given as vectors or at angles.

Sometimes you will need to find the resultant from two forces at right angles to one another, but more often you will be given the resultant and need to calculate the components. Use Pythagoras to do this.

When given the resultant at an angle, use trigonometry to find the components.

Moments

Moments are the turning forces acting on an object, around a pivot. 

M = Fx moment = force × perpendicular distance from pivot

The units of moments are Nm

If there is a resultant moment in either direction (clockwise or anti-clockwise), then the object will rotate in that direction about its pivot.

When an object is in equilibrium, there is neither a net force nor a net moment in any direction. The Principle of moments can be used for this: the sum of all clockwise moments must equal the sum of all anticlockwise moments for an object to be in equilibrium.

When we model a rod or object as uniform, it means we assume all the weight is evenly distributed throughout, and only acts about the centre.

Tilting

The point of tilting is the point at which a rigid body is about to pivot.

When a rigid body is at the titling point, the reaction at any other support is zero.