# Forces (Introducing Forces)

Forces are everywhere.

When an object falls to earth from a height (think Newton’s apple) the force of gravity (9.81 m/s2 on earth) acts on the object to push it down towards the earth, when Ronaldo strikes a football there is a force from his boot exerted on the ball to propel it towards the goal, and when you push against a brick wall it doesn’t move because there is a reactive force that emanates from the wall that equals the force you exert upon it.

Where there is movement there are forces in action, and even when there is no movement… there are forces in action

To understand forces we should first start with the difference between Scalars and Vectors. A scalar quantity has magnitude only. Magnitude means size. A vector quantity has both magnitude (size) and direction.

SCALAR = Magnitude

VECTOR = Magnitude and Direction

Forces are Vector quantities. When we construct a diagram to show forces acting on an object we use arrows to show the size and direction of the force.

Forces can be classified as either contact forces or non-contact forces depending upon how two objects interact. For example, a non contact force could be gravity as it acts upon an object to push it towards the centre of the earth without physically coming into contact with it (such as a ball if dropped from a window). An example of a contact force, conversely, would be the tension on a rope as two people engage in a tug-of-war. There is clear physical contact between both the participants and the rope which we can observe.

Typical forces we can categorise in physics are:

Contact: friction, air resistance (drag), tension, normal contact force, upthrust

Non-Contact: gravity, electrostatic force, magnetic force

Gravity and its’ relationship with Weight

Gravity on earth (represented by the letter g) is the force of attraction that exists between all masses and is due to the gravitational field around our planet. The value of g on earth is constant (10m/s2 or 9.81m/s2 depending upon how accurate you want to be). The mass of an object is related to the amount of matter it contains and is constant. Weight is what we call the force that acts upon an object due to gravity.

As such, the weight of an object on earth will depend upon its’ mass and its gravitational field strength. We say that weight = massgravitational field strength

W = mg

We measure W in Newtons (after Isaac Newton) abbreviated to the capital letter N. Mass we measure in kg and gravity we measure in m/s2.

Therefore, in the example above, if the mass of the Lamborghini is 1,600kg then we can work out it’s weight (in Newtons) by using the equation w = mg

we know that the cars’ mass (m) = 1600kg

And we know that the gravitational field strength on earth (g) = 9.81m/s2

So we can calculate the weight ( W ) = 1600 x 9.81 = 15,696N

Resultant Forces

When there is more than just one force acting upon an object then we can add them together to calculate the resultant force.

When the driver is sat in his Lamborghini the upthrust (reaction) acting on the car (with driver in it) is 16,481N

The driver has a mass of 80kg.

How can we calculate the resultant force?

First we need to establish the magnitude and direction of all 3 forces. Then we add them together to find the resultant force. Simple right?

We’ll call the force of the weight of the car F1, the force of the weight of the driver F2 and the Force of upthrust F3.

As each force is a vector we also need to consider the direction upon which each force acts. Both the Lamborghini and the Driver will have the force of their weight pointing South towards the centre of the Earth. However, the force of the upthrust will be pointing North, exactly opposite to the direction of the weight of the Driver and the Car. As such we assign the Upthrust a negative value to indicate that the direction is opposite to that of the weight of the car and driver.

So our resulatnt force will be equal to (F1) + (F2) + (-F3)

We know that F1 is 15,696N from out earlier calculation.

Finding F2:

Using W = mg we can fork out the weight of the driver to be 80 x 9.81 = 785N

We know that F3 is 16,481N

By inserting these values into our calculations for resultant force we get:

FR (resultant) = (F1) + (F2) + (-F3) = 15,696 + 78516,481 = 0N

This means that the downwards force of the combined weight of the driver and the car is equal to the upwards force of the upthrust from the earth. And as a result the car stays intact on the road (it does not sink into the earth or lift into the air).

We can say that the forces are balanced.

Remember that we said at the top of the page that:

“Where there is movement there are forces in action, and even when there is no movement… there are forces in action”

Well this is an example of there being a number of forces in action despite there being no apparent movement.

Can you think of an example where forces are in action causing a net resultant force? In this instance will there be any movement? Get your thinking caps on…