# Forces

## Forces

Forced act in pairs. When 2 forces interact they are equal and opposite in direction e.g. a person exerts a force on the chair but the chair applies an equal force upwards on the person, a reaction force.

Weight

Weight is also a force measured in newtons. **Don’t confuse** mass and weight as mass is actually the amount of ‘stuff’ that makes up an object measured in kilograms. This is calculated by:

Weight (N) = Mass (kg) x Gravitational field strength (N/kg)

## Resultant Force

The gravitational field strength on Earth is taken as 10N/kg.

A resultant force is the sum of forces acting on an object.

--> Resultant force = 2N + 4N = 6N to the right

--> Resultant force = 4N - 2N = 2N to the right

Balanced forces occur when an object is stationary or moving at a constant speed. The faster an object is moving the bigger the frictional forces acting on it.

Resultant Force (N) = Mass (kg) x Acceleration (m/s^{2})

## Distance-time and velocity-time graphs

Distance-time graphs tell you how an objects distance is changing over time. If there is a smooth slope on your graph then the object is moving at a constant speed. If there is a flat line then there is no movement. A steeper slope means a faster speed. If the slope is downwards the object is returning to the starting position. If there is an upwards curve on a distance time graph then the object is accelerating, a downward curve it means it is decelerating.

In order to work out the speed from the slope you choose a section of the slope and determine what size it is relative to the axis. Since speed is distance ÷ time you then use those values from the slope. So in this case --> Speed = 4m ÷ 4s = 1m/s

Speed is how fast you are travelling and velocity is your speed in a given direction.

Velocity-time graphs tell you how an objects velocity is changing over time. If there is a smooth slope on your graph then the object is accelerating. If there is a flat line then the object is moving at a constant speed. A steeper slope means a larger acceleration. If there is a downwards slope then the object is decelerating. The area under the velocity time graphs tells you the distance travelled. To work out the acceleration from a section of the slope you use the same method as above for the distance-time graph. A velocity-time graph tells you how an objects velocity changes over a certain time.

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## Distance-time and velocity-time graphs (cont)

Final velocity (m/s) - Initial velocity (m/s)

Acceleration (m/s^{2}) ------------------------------------------------------------------------------

Time taken (s)

## Cars and braking forces

How quickly a car can come to a stop depends on the car and the driver. The stopping distance is the thinking distance (which depends on the drivers reactions) and the braking distance (which depends on the car and road conditions).

Stopping distance = thinking distance + braking distance

The thinking distance will be increased if the driver is tired, been drinking alcohol, been on drugs etc. The braking distance will depend on the road surface, weather conditions and how well the car responds e.g. condition of brakes.

## Hooke’s Law

When a weight (force) is applied to a spring it extends. The amount it extends is proportional to the force added. It is governed by the equation:

Force (N) = spring constant (N/m) x extension (m)

(F = k x e )

The spring constant can be determined from the gradient (slope of the line) on a force extension graph.

## Force and energy

When a force acts upon an object causing it to move a through a distance energy is transferred and work is done. The amount of work done is equal to the amount of energy transferred. The amount of work done is calculated by:

Work done (Joules, J) = Force applied (N) x distance moved (m)

If you try to do work against a surface with friction then most of the energy gets transformed into heat. Power is the amount of work done (energy transferred) every second and is calculated using the following equation:

Energy transformed (J)

Power (W) = -------------------------------------------

Time (s)

Work can also be done on other objects. If you change the shape of an object then the energy gets stored in the object, e.g. an elastic band. This is elastic potential energy. Remember, potential energy is stored energy that is ‘waiting’ to be used, kinetic energy is movement energy.

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## Force and energy (cont)

Gravitational potential energy is the amount of energy an object has when it is held above the ground. It is calculated using the following equation:

Gravitational potential energy (J) = mass (kg) x gravitational field (N/kg) x height (m)

Example: A book of mass 0.5kg is on a shelf 2 metres off the ground. What is its gravitational potential energy if the gravitational field strength is 10N/kg.

Answer: GPE = m x g x h

GPE = 0.5 x 10 x 2 = 10J

To work out the kinetic energy a body has you need to know it’s mass and it’s velocity;

Kinetic energy (J) = 1/2 x mass (kg x velocity^{2} (m/s) ^{2}

## Momentum

Momentum (has the symbol p) describes how much motion an object has. It is measured in kilogram metre per second (kg m/s). Like velocity, momentum has magnitude acting in a certain direction.

Momentum (kg m/s) = Mass (kg) x Velocity (m/s)

e.g. football Mass = 0.1kg it moves to the right Velocity = 50m/s. What is the momentum of the ball?

Momentum = 0.1kg x 50m/s = 5kg m/s

In all situations, momentum is conserved, providing there are no external forces acting. For collisions, the momentum before the collision is equal to the momentum after the collision.

Another example is cannon before being fired and after being fired. Before the cannon is fired the momentum is zero, after it is fired the cannon ball moves forward and the cannon moves back. The momentum of the cannon ball is the same as the momentum of the cannon moving backwards. In this sort of example you should choose one direction to be positive and the other direction to be negative.

## Static electricity

In static electricity when two objects are rubbed together the electrons move from one object to another. This causes one object to have an overall positive charge and the other object to have an overall negative charge. Like charges repel, unlike charges attract, Neutral objects are attracted to both positively and negatively charged objects.

If an object becomes highly charged then the potential difference between then object and the ground increases and the objects will discharge. When a charged object discharges (goes to ground) then a spark might occur. This is the electrons jumping from the object to the earthed conductor.

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