Forces

Forces are all around us and are responsible for changing the motion of objects. Even when you’re sat still reading this page, there’s the force of gravity holding you down to the Earth and the contact force of the chair allowing you to sit upright. Without forces, life would be downright impossible..

Forces

When a force acts on an object, it will cause the object to speed up, slow down, change direction or change shape. For example, when a golfer hits a golf ball off a tee, he is applying a force that is going to cause the golf ball to accelerate into the air. Force is a vector quantity because it has direction.

We can categorise forces into several different types. For example, gravitational force is the force that acts between two masses, such as the moon and the Earth. An electrostatic force is one which acts between two charges. Electrostatic forces can be seen when you rub a balloon and place it near to someone’s hair. The strands of hair are raised by the balloon due to electrostatic forces. Another example is when you experience a small electric shock when getting out of a car. Friction is a force which occurs when two objects are in contact with each other and opposes motion. This means that the more friction there is, the larger the driving force needed to achieve the same speed.

Newton’s first law of motion

Isaac Newton described what happens to an object when a resultant force acts on it. It is referred to as his first law of motion and can be summarises as follows:

• Whenever forces acting on an object are unbalanced, there will be a resultant force which will cause the speed of the object to change in the direction of the resultant force.

• When the forces acting on an object are balanced, there is no resultant force which means that there will be no change to the speed of the object. If the object is a travelling at a certain speed, it will continue to do so at the same speed. If the object is stationary, it will remain stationary.

When two forces are acting on an object, the resultant force, is the difference between those two forces. Let’s say we have a car driving along a road with a driving force of 2000 newtons (N). The force caused by friction between the tyres and the road is 350 N. This means the resultant force acting on the car is 2000 - 350 = 1650 N in the forward direction.

Force, mass and acceleration

A force acting on an object can cause it to speed up, or accelerate. Acceleration is proportional to the force acting on it (so let’s say we double the force when we kick a football, it will accelerate twice as fast if the mass is constant). If we increase the mass of an object, the rate of acceleration will decrease. This is why we need to apply much more force to a football compared to a ping-pong ball to cause them to reach the same speed.

The equation linking force, mass and acceleration is:

Weight, mass and gravitational field strength

Weight is the force exerted on an object by gravity and is measured in Newtons. The Earth’s gravitational field strength is 10 N/kg which means that for each kilogram of an object’s mass, there is 10 N of force acting on it. Make sure you’re confident about the difference between weight and mass - mass is constant whereas weight changes depending on gravity. This means that a 60 kg woman will weigh more on the Earth compared to the moon, since gravitational field strength on Earth is larger. Weight and mass are directly proportional, so it the mass of an object doubles, its weight will also double providing that the gravitational field strength is constant.

The equation linking weight, mass and gravitational field strength is:

Centre of gravity

The weight of an object acts at one point of the object which is referred to as its centre of gravity or centre of mass. The centre of mass may be inside or outside of an object, depending on its shape. If an object is suspended from a string so that it can turn, it will come to rest with its centre of gravity of the object immediately below the point of suspension.

Stopping distance

In an emergency, it is important that the driver can stop the car as quickly as possible. The distance travelled when coming to a stop depends on several factors which influence both the reaction time of the driver (thinking distance) and friction between the tyres and the road (breaking distance).

stopping distance = thinking distance + breaking distance

• Factors which affect thinking distance: if the driver is tired, distracted by a mobile phone or under the influence of drugs or alcohol

• Factors which affect breaking distance: mass of the car, worn tyres or wet weather conditions.

Higher speeds will increase both thinking distance and breaking distance since the car will travel a larger distance in the same time that it takes to come to a stop.

Increasing the mass of the car will increase the breaking distance (but not the thinking distance). This makes sense if we use the equation we learnt earlier: force = mass x acceleration. Acceleration refers to the car coming to a stop, and will have a negative value since we are slowing down rather than speeding up. If we double the mass of the car, the force needed to bring the car to a stop will also double to achieve the same rate of deceleration.

Forces acting on falling objects

Falling objects have two main forces acting on them, the force of gravity pulling them towards Earth and air resistance acting in the other direction and slowing their fall. The size of these forces change as an object falls, until the object reaches a constant speed, called terminal velocity.

Imagine you are a skydiver falling out of an aeroplane:

• When you first jump out of the aeroplane, your speed is the fastest since there is little air resistance to counter the force of gravity. Because there is a large downwards force and only a small upwards force, the forces are unbalanced so there is a large resultant force acting downwards, causing you to accelerate.

• As you gain speed the air resistance increases, making the resultant force smaller and causing you to slow down.

• At one point the forces from gravity and air resistance will become equal and there will be no resultant force. When there is no resultant force, the speed of falling becomes constant and you have reached terminal velocity.

Hooke’s Law

An object which can be extended and compressed, such as a spring or a rubber band, stores elastic potential energy. Elastic behaviour is the ability of a material to recover its original shape after the forces which cause compression or extension have been removed. Robert Hooke discovered that the extension of a spring is directly proportional to the force acting on it, which means that if we pull on a spring twice as hard then it will extend to twice the length. The equation for Hooke’s law is:

This law is true for the straight part of the graph shown on the right, which shows how extension increases when increasing force is applied. When the graph begins to curve, the spring has exceeded its elastic limit and will not return to its original length.

Worked example: using Hooke’s Law equation

A spring is pulled with a force of 8 N which causes it to stretch 14 cm. Calculate the spring constant.

• Rearranging the equation gives us: spring constant (k) = force (F) / extension (e)

• Extension is always in meters so we convert 14 cm to 0.14 m

• k = 8/0.14 = 57.1 N/m