A force is a push, pull or a twist.

Simple formula:

Force = mass x acceleration

F = m x a

The unit of force is Newton (N).

1 Newton is defined as the force that would give a mass of 1 kg an acceleration of 1 m/s².

1 N = 1 kg m/s²

Force is a **vector** quantity.

This means that it has magnitude and direction. Since it has direction, it can either be positive and negative.

**Example:
**A car, weighing 500 kg, has a constant acceleration of 2 m/s². What is the force produce by its engine?

Using the formula F = ma,

F = 500 x 2

F = 1000 kg m/s² = 1000 N

### Resultant Force (∑F)

Resultant force is the sum of forces acting on a body.

Let us say two people were pushing a box from opposite directions. One person applies a force of 20 N and the other person applies a force of 10 N.

The person applying a force of 10 N is doing it in the opposite direction of the other person. Since force is a vector quantity, the person applying the force of 10 N would have a negative value (i.e. -10 N).

**REMEMBER: **

A force from left to right would be positive.

A force from right to left would be negative

A downward force is positive. (Gravity or Weight)

An upward force is negative. (Air resistance)

∑F = [20 + (-10)] = (20 – 10) = 10 N to the right

### Weight

The weight of a body or an object is also a force. The weight is measure in Newtons.

In order to measure your weight, you must take your mass in kilograms and multiply it by 10. This is because the acceleration of gravity on Earth is 10 m/s².

Let us say a person’s mass is 60 kg.

Weight (Force) = Mass x Gravitational acceleration

Weight = 60 x 10

Weight = 600 N

Ever object and person on Earth has mass and hence a weight.

**REMEMBER: **

Acceleration due to gravity on different planets and other Celestial objects have a different value. Moon’s acceleration due to gravity is 6 times less than Earth’s.

Therefore, a person weighing 600 N on Earth weighs 100N on Moon.

However, a person’s mass remains the same. A person who has mass of 60 kg on Earth will have a mass of 60 kg on Moon.

### Free Fall

Free fall is when a person or an object moves downward under the force of gravity only.

The best and most popular example of free fall is a skydiver.

As soon a skydiver jumps out of the plane, the only force acting on him/her is gravity. The person falls with an acceleration of 10 m/s². There is a constant gain of velocity.

If a person weighs 90 kg, their downward force would be their weight, i.e. 900 N.

The increase in velocity is accompanied by increase in air resistance. Air resistance acts against force of gravity. Using the Newton’s third law of motion, air resistance has an equal but opposite force on the person.

Air resistance = -900 N

Resultant Force (∑F) = 900 + (-900) = 900 – 900 = 0

Once the magnitude of air resistance becomes equal to the magnitude of force of gravity, (∑F = 0), the person’s acceleration becomes zero and they move downward with constant velocity. This is known as **terminal velocity**.

When the skydiver opens their parachute, the force of air resistance greatly increases as it acts on a much larger surface area (a parachute is very big). This air resistance overwhelms the force of gravity. This causes the skydiver to slow down.

As the skydiver begins to slow down, the air resistance also decreases until the skydiver reaches a terminal velocity again.

A graph of a free fall looks like this:

**Example:**

A skydiver of mass 50 kg opens his parachute and the magnitude of air resistance becomes 800 N.

What is the size of acceleration? What is the direction of acceleration?

Solution:

Skydiver’s weight = 50 x 10 = 500 N

Force downwards = 500 N

Force upwards = 800 N

Net force = 800 + (-500) = 800 – 500 = 300 N

Upward force > Downward force.

Therefore the **direction of acceleration would also be upwards**.

We know F = ma

a = F ÷ m

Net force = 300 N

m = 50 kg

a = 300 ÷ 50 = 6 m/s²

Size of acceleration = 6 m/s²

Direction of acceleration = Upwards