Forces

In this chapter you will learn:

1. Scalar and vector quantities

2. What are Contact and non-contact forces?

3. Weight, mass and gravity

4. Resultant forces and work done

5. Forces and elasticity

6. Moments, levers and gears

7. Pressure in fluids

8. What is upthrust?

9. Atmospheric pressure

10. Distance and displacement

11. Speed, velocity and acceleration

12. What is terminal velocity?

13. What are Newton's Law's of motion?

14. Forces and braking

15. What is momentum?

Scalar and vector quantities

Scalar quantities

Scalar quantities only have magnitude, but no specific direction.

Scalar quantities examples: distance, mass, speed, time, temperature, etc.

Vector quantities

Vector quantities have both magnitude and specific direction.

Vector quantities examples: velocity, force, displacement, momentum, acceleration, etc.

Contact and non-contact forces

Forces can be either contact or non-contact.

Contact forces

In contact force the objects are physically touching for a force to act.

Examples of contact forces are: air resistance, friction, tension and normal contact force.

Non-contact forces

In non-contact force two objects do not need to be touching for a force to act.

Examples of non-contact forces are: electrostatic force, gravitational force, and magnetic force.

Weight, mass and gravity

The weight of an object may be considered to act at a single point referred to as the object’s centre of mass.

The weight of an object and the mass of an object are directly proportional. If the mass is increased the weight will also increase.

Gravitational force is a force that attracts any objects with mass.

Weight can be calculated using the following equation:

weight = mass × gravitational field strength

The units used in the equation above are as follows:

• Weight is measured in newtons, N

• Mass is measured in kilograms, kg.

• Gravitational field strength is measured in newtons per kilogram, N/kg

Resultant forces and work done

A resultant force is the overall force acting on an object.

If a number of forces acting on an object may be replaced by a single force that has the same effect as all the original forces together. This single force is called the resultant force.

Work is done when a resultant force moves an object.

The work done by a force on an object can be calculated using the following equation:

work done = force × distance

The units used in the equation above are as follows:

• Work done is measured in joules, J

• force is measured in newtons, N

• distance is measured in metres, m

Worked example:

Question 1

The drag lift pulls the skier with a constant resultant force of 200N for a distance of 25 m.

Use the following equation to calculate the work done to pull the skier up the slope.

Answer:

work done = force × distance

work done = 200 x 25

work done = 5000 J

Forces and elasticity

When you apply a force to an object, the object may change shape by bending, stretching or compressing. However, there must be more than one force acting to change the shape of a stationary object, otherwise the object would simply move in the direction of applied force.

• Objects which have a tendency to return to their original shape after the removal of applied force are called elastic e.g. springs and rubber.

• When the object doesn't return to its original shape after removing the forces, it is referred to as inelastic.

When springs or elastic material are stretched, elastic potential energy is stored in the system.

The extension of a stretched object is directly proportional to the force applied to it.

Elastic potential energy is measured in joules, J.

Moments, levers and gears

The turning effect of a force is called the moment of the force.

The object is balanced if the total clockwise moment equals the total anticlockwise moment about a pivot.

The magnitude of a moment can be calculated using the following equation:

moment of a force = force × distance

The units used in the equation above are as follows:

• Moment is measured in newton-metres, Nm

• force is measured in newtons, N

• distance is measured in metres, m

Worked example:

Question 2

A car has a mass of 800 kg. It travels south at a speed of 20 m/s. Calculate the momentum of the car.

Answer:

moment of a force = force × distance

moment of a force = 800 x 20

moment of a force = 16,000 kg m/s

Levers

Levers make work easier by reducing the force needed to move an object.

Levers increase the distance from the pivot at which the force is applied. That means less force is needed to get the same moment.

Gears

Gears are used to transmit the rotational effect.

Teeth on gears interlock so that turning one causes another to turn, in the opposite direction.

Gears of different size can be used to change the moment of the force.

A force applied to a larger gear will cause a bigger moment.

Pressure in fluids

A fluid can be either a liquid or a gas.

The pressure in fluids causes a force normal (at right angles) to any surface in contact with the fluid.

Pressure is the force per unit area.

The pressure at the surface of a fluid can be calculated using the equation:

The units used in the equation above are as follows:

• pressure is measured in pascals, Pa

• force is measured in newtons, N

• area is measured in metres squared,

Pressure in a liquid depends upon the depth of the fluid and the density of the fluid.

Upthrust

When an object is partially, or completely, submerged in a fluid it experiences an upward force; this force is known as upthrust. Therefore, the force of upthrust acts in the opposite direction to weight. Wheather the submurged object will float or sink depends on the megnitude of upthrust with respect to its weight.

If the weight of the object is more than the upthrust, the object will sink.

If the weight of the object is less than the upthrust, the object will rise.

Atmospheric pressure

The atmosphere is a thin layer of air round the Earth. It is thin compared to the size of the Earth.

When air molecules colliding with a surface, atmospheric pressure is created.

When the height increases, atmospheric pressure decreases.

As the altitude increases, the atmosphere gets less dense, hence there are less air molecules to collide with the surface.

Distance and displacement

Distance is just how far an object moves. Distance does not involve direction.

Distance is a scalar quantity.

Displacement measures both the distance and direction an object moves, in a straight line from the starting point to the finishing point.

Displacement is a vector quantity.

Speed, velocity and acceleration

Speed is how fast an object is moving but no direction. The speed of a moving object is rarely constant

Speed is a scalar quantity.

The distance travelled by an object at constant speed can be calculated using the following equation:

distance travelled = speed × time

The units used in the equation above are as follows:

• distance travelled is measured in metres, m

• speed is measured in metres per second, m/s

• time is measured in seconds, s

Velocity

The velocity of an object is its speed in a particular direction.

Velocity is a vector quantity.

Velocity is measured in metres per second (m/s)

Acceleration

Acceleration is the change in speed (or velocity) in certain time.

Constant acceleration is also called uniform acceleration.

The uniform acceleration can be calculated using the following equation:

(final velocity)2 − (initial velocity)2 = 2 × acceleration × distance

The units used in the equation above are as follows:

• final velocity is measured in metres per second, m/s

• initial velocity is measured in metres per second, m/s

• time acceleration is measured in metres per second squared, m/s2

• distance is measured in metres, m

Terminal velocity

At terminal velocity, the object falling through a fluid initially accelerates due to the force of gravity. Eventually, due to the increase in the force of friction, the resultant force will be zero and the object will move at its terminal velocity.

Terminal velocity depends on the shape of object and area.

Drag is the resistance force you get in a fluid.

Drag increases as speed increases.

Newton's First Law

Newton's first law says that a resultant force is needed to change motion.

The velocity of an object will only change if a resultant force is acting on the object.

Newton's Second Law

Newton’s Second Law: The acceleration of an object is proportional to the resultant force acting on the object, and inversely proportional to the mass of the object.

Acceleration (a) is measured in metres per second squared (m/s²).

The acceleration of an object increases if the resultant force on it increases.

Acceleration is inversely proportional to the mass. So for a given force an object with a larger mass will accelerate less than one with a smaller mass.

Newton's Second Law of motion can be described by this equation:

resultant force = mass × acceleration

The units used in the equation above are as follows:

• force is measured in newtons, N

• mass is measured in kilogram, kg

• acceleration is measured in metres per second squared, m/s²

Worked example:

Question 3

Calculate the force needed to accelerate a 30 kg object at 15 m/s².

Answer:

resultant force = mass × acceleration

resultant force = 30 x 15

resultant force = 450 N

Newton's Third Law

Newton's third law: When two objects interact, the forces they exert on each other are equal and act in opposite directions.

If you pushes a shopping trolley forwards the trolley pushes you backwards.

Forces and braking

Stopping distance

Many factors affect total stopping distance.

Stopping distance = thinking distance + braking distance.

Thinking distance is the distance your car travels after you have spotted a hazard, before you apply the brakes.

Braking distance is the distance the car travels after the driver has applied the brakes.

The braking distance of a vehicle can be affected by adverse road and weather conditions and condition of the vehicle.

Braking depends on friction between the brakes and wheels. Friction always slow things down.

The faster a vehicle travels, the greater the braking force needed to stop it in a certain distance.

The greater the braking force the greater the deceleration of the vehicle. Large decelerations may lead to brakes overheating and there is a greater chance of skidding.

Reaction time varies from person to person, but a typical time is between 0.2 s and 0.9 s.

Reaction time can be affected by tiredness, drugs, alcohol or distractions.

Momentum

Momentum is just the product of the mass and velocity of an object.

Momentum is also a vector quantity, It has size and direction.

In a closed system, total momentum is conserved. Which means the total momentum is the same before and after an event such as a collision.

Momentum can be calculated using the following equation:

Momentum = Mass × Velocity

The units used in the equation above are as follows:

• Momentum is measured in kilogram metres per second, kg m/s

• Velocity is measured in metres per second, m/s

• Mass is measured in kilograms, kg

Conservation of momentum

In a closed system, the total momentum before an event and after the event is equal. The total momentum of a system remains constant.

Change in momentum

Forces cause a change in momentum. When a force acts on an object that is moving, or able to move, a change in momentum happens.

The rate of change of momentum is equal to the force causing the change.

A larger force means a faster change of momentum.