In mechanics we always start with a simple model and then gradually get closer to a realistic situation by making it more complicated. We will do this now by introducing forces.

• A force is anything that can change the motion of an object. e.g.:
  • Tension: Pulling a string or a rod;
  • Thrust: Pushing in from the end of a rod;
  • Friction: Including resistance from a fluid such as air;
  • Gravity: The pull of earth due to its mass.

All of the forces we meet in this course, except for gravity, require physical contact with the object in motion.

Newton’s Laws

Isaac Newton revolutionised physics and our understanding of the world in general. His “laws” are the foundations of modern science. Here we introduce the first two, the second of which will be used repeatedly throughout the course.

Newton’s First Law: A particle is at rest or constant velocity unless it is acted on by a net force.

Newton’s Second Law: Net Force, F = m x a (a force of 1 Newton accelerates a mass of 1kg by 1 ms^-2)

Note: We will use the word light when we wish to refer to an object of negligible mass.

Worked Examples

Exercise – Impact of a single force

Answers

Combining Forces

Acceleration is generated by the net force on the particle. If net force is zero, the object will be in equilibrium (i.e. at rest or at constant velocity (Newton’s First)).

Good force diagrams are very useful in mechanics (and sometimes specifically required in examination questions). Do not include resultant forces on diagrams (i.e. draw a separate diagram if you want to show these). Acceleration should be indicated using a double headed arrow.

Worked Examples

Exercise

Answers

Weight and Gravity

Gravity makes objects fall with a constant acceleration independent of their mass. On earth, gravity varies based on the distance from the core, but is always 9.81ms^-2, or about 10ms^-2.

Air resistance (proportional to the square of the speed) means that some objects fall slower than others.  But its effect is much smaller than the effect of gravity, so is often ignored in models and is outside the scope of this course.

Depending on the context of the question, we can treat upwards as positive, so that W=-mg or downwards as positive, so that W=mg.  We must always be consistent in the question, so all positive values are referring to the same direction.

Worked Example

Exercise

Answers

Normal Contact Force

There is a reaction force (“R”) or normal contact force, on an object.  This is a reaction to the weight of the object and acts perpendicular to the surface to maintain equilibrium;

In a static situation on a vertical surface, this will be equal to the weight of the object;

If there is vertical acceleration, this will not equal weight (due to NII);

If R=0, the object will lose contact with the surface.

Worked Examples

Exercise and Combined Exercise

Answers