2.1 Mechanics - Forces

A force is a push or a pull on an object. Forces are vectors (they have magnitude and direction) and are measured in newtons (N).

Forces can make an object:

• Speed up (accelerate)
• Slow down (decelerate)
• Change direction
• Change shape

Contact vs. Non-Contact Forces

All forces can be sorted into two groups:

• Contact Forces: The objects must be touching for the force to act (e.g., Friction, Air Resistance, Tension, Normal Contact Force).
• Non-Contact Forces: The objects do not have to touch; the force acts at a distance (e.g., Gravity, Magnetism, Electrostatic force).

Gravity is a non-contact force of attraction between all objects that have mass. The more mass an object has, the stronger its gravitational pull.

Mass is the amount of "stuff" an object is made of. Your mass is the same whether you are on Earth or on the Moon. It is measured in kilograms (kg).

Weight is the force of gravity acting on an object's mass. Your weight is different on the Moon because the Moon's gravity is weaker. Weight is a force, so it is measured in newtons (N).

You can calculate weight using this equation:

Weight = Mass × Gravitational Field Strength

W = m × g

Where:

• W is Weight in newtons (N)
• m is Mass in kilograms (kg)
• g is Gravitational Field Strength in newtons per kilogram (N/kg). On Earth, g ≈ 9.8 N/kg.

Usually, more than one force acts on an object. The resultant force is the single force that has the same effect as all the individual forces combined.

• If forces are balanced, the resultant force is 0 N. The object will either stay stationary or move at a constant velocity (this is Newton's First Law).
• If forces are unbalanced, the resultant force is not 0 N. The object will accelerate (speed up, slow down, or change direction).

For example, if you push a ball with a force of 10 N to the right, and air resistance pushes back with 2 N to the left, the resultant force is 5 N to the right (10 N – 5 N = 5 N).

You can use free body diagrams to help visualise and analyse these situations:

Free-Body Diagrams

A free-body diagram is a simple drawing used to show all the forces acting on a single object. We draw the object as a simple box and use arrows to show the forces.

Below is a more complex example, when the ball is being pulled by a string with 10 Newtons of tension. In this case they are to scale, and you can simply measure the length of the 10N line (100 pixels) this means the ratio of Newtons to pixels is 0.1. If we make a right angled triangle, and measure the horizontal element, we find it is 91 pixels. Therefore 91 x 0.1 = 9.1N. In an exam you would do the same but with a ruler and centimeters, not pixels.

When you apply a force to an object (like a spring or a rubber band), you can deform it.

• Elastic Deformation: The object returns to its original shape after the force is removed (e.g., stretching a spring a little bit).
• Inelastic Deformation: The object is permanently deformed and does not return to its original shape (e.g., stretching a spring too far).

Hooke's Law

For elastic objects like springs, the extension is directly proportional to the force applied. This means if you double the force, you double the extension. This is known as Hooke's Law.

Force = Spring Constant × Extension

F = k × x

Where:

• F is the Force in newtons (N)
• k is the Spring Constant in newtons per metre (N/m). A "stiffer" spring has a higher k-value.
• x is the Extension in metres (m)

This law only works up to a certain point, called the limit of proportionality. If you apply too much force, the spring will stretch inelastically and the graph of force vs. extension will no longer be a straight line. The elastic limit is the maximum extension before permanent deformation occurs, and is always after the limit of proportionality.

The area of a Force vs Extension graph represents the work done in stretching the spring.

If we take a look at the spring extension above, we see its 10cm, and if 10N is the force applied we can find the work done stretching the spring using the formula:

Work Done = 0.5 × Force × Extension

W = 0.5 × F × x = 0.5J

We can also find the spring constant using Hooke's law:

k = F / x = 10N / 0.1m = 100N/m