# 5.1-Contact and Non-Contact Forces

Vectors have magnitude and direction

• Force is a vector quantity-vector quantities have a magnitude and a direction

• Lots of physical quantities are vector quantities: force, velocity, displacement, acceleration, momentum,etc

• Some physical quantities only have magnitude and no direction, these are called scalar quantities:speed, distance, mass, temperature, time, etc

• Vectors are usually represented by an arrow-the length of the arrow shows the magnitude and the direction of the arrow shows the direction of the quantity

• Velocity is a vector, but speed is a scalar quantity.

• Both bikes are travelling at the same speed, but they have different velocities because they are travelling in different directions

Forces can be contact or non-contact

• A force is a push or a pull on an object that is caused by it interacting with something

• All forces are either contact or non-contact forces

• When two objects have to be touching for a force to act, that force is called a contact force

• If the objects do not need to be touching for the force to act, the force is a non-contact force

• When two objects interact, there is a force produced on both objects.

• An interaction pair is a pair of forces that are equal and opposite and act on two interacting objects(basically Newtons third law)

Examples:

• The sun and the earth are attracted to each other by the gravitational force.

• This is a non-contact force.

• An equal but opposite force of attraction is felt by both the sun and earth.

• A chair exerts a force on the ground, whilst the ground pushes back at the chair with the same force.

• Equal but opposite forces are felt by both the chair and the ground

# 5.2-Weight, Mass and Gravity

Gravitational force is the force of attraction between masses

• Gravity attracts all masses, but you only notice it when one of the masses is really big, like a planet

• This has two important effects:

• On the surface of a planet, it makes all things fall towards the ground

• It gives everything a weight

Weight and mass are not the same

• Mass is just the amount of stuff in an object.

• For any given object this will have the same value anywhere in the universe

• Weight is the force acting on an object due to gravity, the pull of gravitational force on the object.

• Close to Earth, this force is caused by the gravitational field around the Earth

• Gravitational field strength varies with location.

• It’s stronger the closer you are to the mass causing the field, and stronger for larger masses

• The weight of an object depends on the strength of the gravitational field at the location of the object.

• This means that the weight of an object changes with its location

• For example, an object has the same mass whether it’s on Earth or on the Moon-but its weight will be different. A 1kg mass will weigh less on the Moon, because the gravitational field strength is less

• Weight is a force measured in newton

• Weight is measured using a calibrated spring balance

• Mass is not a force, and is measured in kilograms with a mass balance

Mass and weight are directly proportional

• You can calculate the weight of an object if you know its mass and the strength of the gravitational field:

Weight(N)=Mass(kg) x Gravitational Field Strength(N/kg)

• For Earth, g=9.8N/kg and for the moon its around 1.6N/kg.

• Increasing the mass of an object increases its weight.

• If you double the mass, the weight doubles meaning they are directly proportional(W=M)

# 5.3-Resultant Forces and Work Done

Free body diagrams show all the forces acting on an object

• Size of the line shows the relative magnitudes

• Need to be able to describe all forces happening on something

A resultant force is the overall force on a point or object

• In most situations there are at least 2 forces acting on an object

• If you have a number of forces acting at a single point, you can replace them with a single force

• This single force is called the resultant force

• If the forces all act along the same line, the overall effects is found by adding those going in the same direction and subtracting any going in the opposite direction

If a resultant force moves an object, work is done

• To make something move a force must be applied

• The thing applying the force needs a source of energy

• The force does work to move the object and energy is transferred from one store to another

• Whether energy is transferred usefully or is wasted you can still say that work is done

• You can find out how much work has been done using: W=Fs

• One joule of work is done when a force of one newton causes an object to move a distance of one metre. You need to be able to convert joules to newton metres:1J=1Nm

# 5.4-Calculating Forces

Use scale drawings to find resultant forces

• Draw all the forces acting on an object, to scale, ‘tip-to-tail

• Then draw a straight line from the start of the first force to the end of the last force-this is the resultant force

• Measure the length of the resultant force on the diagram to find the magnitude and the angle to find the direction of the force

An object is in equilibrium if the forces on it are balanced

• If all of the forces acting on an object combine to give a resultant force of zero, the object is in equilibrium

• On a scale diagram, this means that the tip of the last force you draw should end where the tail of the first force you draw begins

• You might be given forces acting on an object and told to find a missing force, given that the object is in equilibrium.

• To do this, draw out the forces you do know, join the end of the last force to the start of the first force.

• This line is the missing force so you can measure its size and direction

You can split a force into components

• Not all forces act horizontally or vertically-some act at awkward angles

• To make these easier to deal with, they can be split into two components at right angles to each other

• Acting together, these components have the same effect as the single force

• You can resolve a force by drawing it on a scale grid. Draw the force to scale, and then add it horizontal and vertical components along the grid lines.

• Then you can just measure them

# 5.5-Forces and Elasticity

Stretching, compressing or bending transfers energy

• When you apply a force to an object you may cause it to stretch, compress or bend

• To do this, you need more than one force acting on the object, otherwise the object would simply move in the direction of the applied force instead of changing shape

• An object has been elastically deformed if it can go back to its original shape and length after the force has been removed

• Objects than can be elastically deformed are called elastic objects

• An object has been inelastically deformed if it doesn’t return to its original shape and length after the force has been removed

• Work is done when a force stretches or compresses an object and causes energy to be transferred to the elastic potential energy store of the object.

• If it is elastically deformed.

• ALL this energy is transferred to the object’s elastic potential energy store

Extension is directly proportional to force

If a spring is supported at the top and then a weight is attached to the bottom, it stretches

• The extension of a stretched spring is directly proportional to the load of force applied

• F=ke

• The spring constant depends on the material that you are stretching-a stiffer spring has a greater spring constant

• The equation also works for compression

But this stops working when the force is great enough

• There’s a limit to the amount of force you can apply to an object for the extension to keep on increasing proportionally

• The graph shows force against extension for an elastic object

• There is a maximum force above which the graph curves, showing that extension is no longer proportional to force.

• This is known as limit of proportionality and is shown on the graph at the point marked P

• You might see graphs with these axis the other way round-extension force graphs.

• The graph still starts with a straight part, but starts to curve upwards once you go past the limit of proportionality, instead of downwards

# 5.6-Investigating Springs

You can investigate the link between force and extension

• Set up the apparatus and make sure you can extra masses, then measure the mass of each and calculate the weight using W=mg

• Measure the natural length of the spring with a millimetre ruler clamped to the stand.

• Make sure you take the reading at eye level and add a marker to the bottom of the spring to make the reading more accurate

• Add a mass to the spring and allow it to come to rest.

• Record the mass and measure the new length of the spring.

• The extension is the change in length

• Repeat this process until you have enough measurements, no fewer than 6

• Plot a force-extension graph of your results.

• It will only start to curve if you exceed the limit of proportionality.

You can work out energy stored for linear relationships

• As long as a spring is not stretched past its limit of proportionality, the work done in stretching a spring can be found using: Ee=1/2ke2

• For elastic deformation, this formula can be used to calculate the energy stored in a spring’s elastic potential energy store. It’s also the energy transferred to the spring as it’s deformed

# 5.7-Moments

A moment is the turning effect of a force

• A force, or several forces, can cause an object to rotate.

• The turning effect of a force is called its moment.

• The size of the moment of the force is given by:

M=Fd, Moment of a force=force x distance

• The force on the spanner causes a turning effect or moment on the nut.

• A larger force or a longer distance would mean a larger moment

• To get the maximum moment you need to push at right angles to the spanner.

• Pushing at any other angle means a smaller distance, and so a smaller moment

Levers make it easier for us to do work

• Levers increase the distance from the pivot at which the force is applied. Since M=Fd this means less force is needed to get the same moment.

• This means levers make it easier to do work

Gears transmit rotational effects

• Gears are circular discs with ‘teeth’ around their edges

• Their teeth interlock so that turning one causes another to turn, in the opposite direction

• They are used to transmit the rotational effect of a force from one place to another

• Different sized gears can be used to change the moment of the force.

• A force transmitted to a larger gear will cause a bigger moment, as the distance to pivot is greater

• The larger gear will turn slower than the smaller gear

# 5.8-Fluid Pressure

Pressure is the force per unit area

• Fluids are substances than can flow because their particles are able to move around

• As these particles move around, they collide with surfaces and other particles

• Particles are light, but they still have a mass and exert a force on the object they collide with.

• Pressure is force per unit area, so this means the particles exert a pressure

• The pressure of a fluid means a force is exerted normal, at right angles, to any surface in contact with the fluid

• You can calculate the pressure at the surface of a fluid by using:

p=F/A

Pressure in a liquid depends on depth and density

• Density is a measure of the compactness of a substance. For a given liquid, the density is uniform and it doesn’t vary with shape or size.

• The density of a gas can vary though

• The more dense a given liquid is, the more particles it has in a certain space.

• This means there are more particles that are able to collide so the pressure is higher

• As the depth of the liquid increases, the number of particles above that point increases.

• The weight of these particles adds to the pressure felt at that point, so liquid pressure increases with depth

• You can calculate the pressure at a certain depth due to the column of liquid above using:

• P=HPG, pressure x height of column in liquid x density of liquid x gravitational field strength

• You could write the answer in standard form so its easier to read

# 5.9-Upthrust and Atmospheric Pressure

Objects in fluids experience upthrust

• When an object is submerged in a fluid, the pressure of the fluid exerts a force on it from every direction

• Pressure increases with depth, so the force exerted on the bottom of the object is larger than the force acting on the top of the object

• This causes a resultant force upwards, known as upthrust

• The upthrust is equal to the weight of fluid that has been displaced by the object

An object floats if its weight=upthrust

• If the upthrust on an object is equal to the object’s weight, then the forces balance and the object floats

• If an object’s weight is more than the upthrust, the object sinks

• Whether or not an object will float depends on its density

• An object that is less dense than the fluid it is placed in weighs less than the equivalent volume of fluid.

• This means it displaces a volume of fluid that is equal to its weight before it is completely submerged

• At this point, the object’s weight is equal to the upthrust, so the object floats

• An object that is denser than the fluid it is placed in is unable to displace enough fluid to equal its weight.

• This means that its weight is always larger than the upthrust, so it sinks

Atmospheric pressure decreases with height

• The atmosphere is a layer of air that surrounds Earth.

• It is thin compared to the size of the Earth

• Atmospheric pressure is created on a surface by air molecules colliding with the surface

• As the altitude increases, atmospheric pressure decreases

• This is because as the altitude increases, the atmosphere gets less dense, so there are fewer air molecules that are able to collide with the surface

• There are also fewer air molecules above a surface as the height increases.

• This means that the weight of the air above it, which contributes to atmospheric pressure, decreases with altitude

# 5.10-Distance, Displacement, Speed and Velocity

Distance is Scalar, Displacement is a Vector

• Distance is just how far an object has moved. It’s a scalar quantity, so it doesn’t involve direction.

• Displacement is a vector quantity.

• It measures the distance and direction in a straight line from an object’s starting point to its finishing point.

• The direction could be relative to a point, then 5m south, your displacement is 0m but the distance travelled is 10m

• If you walk 5m north, then 5m south, your displacement is 0m but the distance travelled is 10m

Speed and velocity are both how fast you’re going

• Speed and velocity both measure how fast you’re going, but speed is a scalar and velocity is a vector

Speed is just how fast you’re going with no regard to the direction.

• Velocity is speed in a given direction

• This means you can have objects travelling at a constant speed with a changing velocity.

• This happens when the object is changing direction whilst staying at the same speed.

• An object moving in a circle at a constant speed has a constantly changing velocity, as the direction is always changing

• If you want to measure the speed of an object that’s moving with a constant speed, you should time how long it tales the object to travel a certain distance.

• You can then calculate the object’s speed from your measurements using this formula:

• distance travelled= speed x time

• Objects rarely travel at a constant speed. For these cases, the formula above gives the average speed during that time

You need to know some typical everyday speeds

• Whilst every person, train, car is different, there is usually a typical speed that each object travels at.

• Remember these typical speeds for everyday objects

• Lots of different things can affect the speed something travels at.

• For example, the speed at which a person can walk, run or cycle depends on their fitness, their age, the distance travelled and the terrain as well as many other factors

• It’s not only the speed of objects that varies.

• The speed of sound changes depending on what the sound waves are travelling through, and the speed of wind is affected by many factors

• Wind speed can be affected by things like temperature, atmospheric pressure and if there are any large buildings or structures nearby

# 5.11-Acceleration

Acceleration is how quickly you’re speeding up

• Acceleration is definitely not the same as velocity or speed

• Acceleration is the change in velocity in a certain amount of time

• You can find the average acceleration of an object using:

• Acceleration=Change in velocity / time

• Deceleration is just negative acceleration

You need to be able to estimate acceleration

• You might have to estimate the acceleration of an object.

• To do this, you need the typical speeds from the previous page:

• First, give a sensible speed for the car to be travelling at

• Next, give it a time

• Put these numbers into the acceleration equation

• The question asked for the deceleration so you can lose the minus sign

Uniform acceleration means a constant acceleration

• Constant acceleration is sometimes called uniform acceleration

• Acceleration due to gravity is uniform for objects in free fall.

• It’s roughly equal to 9.8m/s2 near the Earth’s surface and has the same value as gravitational field strength

• You can use this equation for uniform acceleration

• v2-u2=2as, Final velocity-initial velocity = 2 acceleration x distance

# 5.12-Distance-Time and Velocity-Time Graphs

You can show journeys on distance-time graphs

• If an object moves in a straight line, its distance travelled can be plotted on a distance-time graph

• Gradient=speed. This is because speed = distance / time

• Flat sections are where it’s stationary, it’s stopped

• Straight uphill sections mean it is travelling at a steady speed

• Curves represent acceleration or deceleration

• A steepening curve means it’s speeding up(increasing gradient)

• A levelling off curve means it’s slowing down

• If the object is changing speed you can find its speed at a point by finding the gradient of the tangent to the curve at that point

You can also show them on a velocity-time graph

• How an object’s velocity changes as it travels can be plotted on a velocity-time graph

• Gradient = acceleration, since acceleration is change in velocity / time

• Flat sections represents travelling at a steady speed

• The steeper the graph, the greater the acceleration or deceleration

• Uphill sections are acceleration

• Downhill sections are deceleration

• A curve means changing acceleration

• The area under any section of the graph is equal to the distance travelled in that time interval

• If the section under the graph is irregular, it’s easier to find the area by counting the squares under the line and multiplying the number by the value of one square

# 5.13-Terminal Velocity

Friction is always there to slow things down

• If an object has no forces propelling it along it will always slow down and stop because of friction

• Friction always acts in the opposite direction to movement

• To travel at a steady speed, the driving force needs to balance the frictional forces

• You get friction between two surfaces in contact, or when an object passes through a fluid

Drag increases as speed increases

• Drag is the resistance you get in a fluid. Air resistance is a type of drag.

• The most important factor by far in reducing drag is keeping the shape of the object streamlined.

• This is where the object is designed to allow fluid to flow easily across it, reducing drag.

• Parachutes work in the opposite way-they want as much drag as they can get

• Frictional forces from fluids always increase with speed.

• A car has much more friction to work against when travelling at 70mph compared to 30mph.

• So at 70mph the engine has to work much harder just to maintain a steady speed.

Objects falling through fluids reach a terminal velocity

• When a falling object first sets off, the force of gravity is much more than the frictional force slowing it down, so it accelerates.

• As the speed increases the friction builds up.

• This gradually reduces the acceleration until eventually the frictional force is equal to the accelerating force.

• It will have reached its maximum speed or terminal velocity and will fall at a steady speed

Terminal velocity depends on shape and area

• The accelerating force acting on all falling objects is gravity and it would make them all fall at the same rate if it wasn’t for air resistance.

• This means that on the Moon, where there’s no air, hamsters and feathers dropped simultaneously will hit the ground together.

• However, on Earth, air resistance causes things to fall at different speed, and the terminal velocity of any object is determined by its drag in comparison to its weight.

• The frictional force depends on its shape and area.

• The most important example is the human skydiver.

• Without his parachute open he has quite a small area and a force of W=mg pulling him down.

# 5.14-Newton’s First and Second Laws

A force is needed to change motion

Newton’s first law says that a resultant force is needed to make something start moving, speed up or slow down

• If the resultant force on a stationary object is zero, the object will remain stationary.

• If the resultant force on a moving object is zero, it’ll just carry on moving at the same velocity

• So when a train or car or bus or anything else is moving at a constant velocity, the resistive and driving forces on it must all be balanced.

• The velocity will only change if there’s a non-zero resultant force actin on the object.

• A non-zero resultant force will always produce acceleration in the direction of the force

• This acceleration can take five different forms: starting, stopping, speeding up, slowing down and changing direction

• On a free diagram, the arrows will be unequal

Acceleration is proportional to the resultant force

• The larger the resultant force acting on an object, the more the object accelerates-the force and the acceleration are directly proportional.

• You can write this as F=a

• Acceleration is also inversely proportional to the mass of the object-so an object with a larger mass will accelerate less than one with a smaller mass

• There’s a formula that describes Newton’s second law:

F=ma, Resultant force, mass x acceleration

• You can use this to get an idea of the forces involved in everyday transport, large forces are needed to produce large acceleration

# 5.15-Inertia and Newton’s Third Law

Inertia is the tendency for motion to remain unchanged

• Until acted upon by a resultant force, objects at rest stay at rest and objects moving at a steady speed will stay moving at that speed.

• This tendency to continue in the same state of motion is called inertia

• An object’s inertial mass measures how difficult it is to change the velocity of an object

• Inertial mass can be found using Newton’s Second Law of F=ma.

• Rearranging this gives m=F/a, so inertial mass is just the ratio of force over acceleration

Newton’s third law: equal and opposite forces act on interacting objects

• When two objects interact, the forces they exert on each other are equal and opposite

• If you push something, say a shopping trolley, the trolley will push back against you, just as hard

• And as soon as you stop pushing, so does the trolley

• The important thing to remember is that the two forces are acting on different objects

• It can be easy to get confused with Newton’s third law when an object is in equilibrium.

• A book resting on the ground is in equilibrium.

• The weight of the book is equal to the normal contact force.

• But this is NOT Newton’s third law because the two forces are different types, and both acting on the book

# 5.16-Investigating Motion

You can investigate the link between force and extension

• Set up the apparatus and make sure you can extra masses, then measure the mass of each and calculate the weight using W=mg

• Measure the natural length of the spring with a millimetre ruler clamped to the stand.

• Make sure you take the reading at eye level and add a marker to the bottom of the spring to make the reading more accurate

• Add a mass to the spring and allow it to come to rest.

• Record the mass and measure the new length of the spring.

• The extension is the change in length

• Repeat this process until you have enough measurements, no fewer than 6

• Plot a force-extension graph of your results.

• It will only start to curve if you exceed the limit of proportionality.

You can work out energy stored for linear relationships

• As long as a spring is not stretched past its limit of proportionality, the work done in stretching a spring can be found using: Ee=1/2ke2

• For elastic deformation, this formula can be sued to calculate the energy stored in a spring’s elastic potential energy store. It’s also the energy transferred to the spring as it’s deformed

# 5.17-Stopping Distances

Many factors affect your total stopping distance

• In an emergency, a driver may perform an emergency stop.

• This is where maximum force is applied by the brakes in order to stop the car in the shortest possible distance.

• The longer it takes to perform an emergency stop, the higher the risk of crashing into whatever’s in front.

• The distance it takes to stop a car in an emergency is found by:

Stopping distance = Thinking Distance + Braking Distance

• Where the THINKING DISTANCE is how fast the car travels during the driver’s reaction time.

• And the BRAKING DISTANCE is the distance taken to stop under the braking force.

• Typical car barking distances are: 14m at 30mph, 55mm at 60mph and 75m at 70mph

• Thinking distance is affected by:

• Your SPEED-the faster you’re going the further you’ll travel during the time you take to react

Braking distance is affected by:

• Your Speed-for a given braking force, the faster a vehicle travels, the longer it takes to stop

• The WEATHER or ROAD SURFACE-if it is wet or icy, or there are leaves or oil on the road, there is less grip, and so less friction, between a vehicles tyres an the road, which can cause tyres to skid

• The CONDITION of your TYRES-if the tyres of a vehicle are bald, then they cannot get rid of water in wet conditions. This leads to them skidding on top of the water.

• How good your BRAKES are-if brakes are worn or faulty, they won’t be able to apply as much force as well-maintained brakes, which could be dangerous when you need to brake hard

• You need to be able to describe the factors affecting stopping distance and how this affects safety=especially in an emergency

• Speed limits are really important because speed affects the stopping distance

Braking relies on friction between the brakes and wheels

• When the brake pedal is pushed, this causes brake pads to be pressed onto the wheels.

• This contact causes friction, which causes work to be done,

• The work done between the brakes and the wheels transfers energy from the kinetic energy stores of the wheels to the thermal energy stores of the brakes.

• The brakes increase in temperature

• The faster a vehicle is going, the more energy it has in its kinetic stores, s the more work needs to done to stop it.

• This means that a greater braking force is needed to make it stop within a certain distance

• A larger braking force means a larger deceleration.

• Very large decelerations can be dangerous because they may cause brakes to overheat or could cause the vehicle to skid

• You can estimate the forces involved in accelerations of vehicles using typical values:

• Assume the deceleration is uniform, and rearrange v2-u2-2as to find the deceleration

• Then use F=ma with m=1000kg

# 5.18-Reaction Times

Reaction times vary from person to person

Everyone’s reaction time is different, but a typical reaction time is between 0.2 and 0.9 s. This can be affected by tiredness, drugs or alcohol. Distractions can also affect your ability to react

You can measure reaction times with the ruler drop test

You can do simple experiments to investigate your reaction time, but as reaction time are so short, you haven’t got a chance of measuring one with a stopwatch

One way of measuring reaction times is to use a computer-based test. Another is the ruler drop test:

• Sit with your arm resting on the edge of a table.

• Get someone else to hold a ruler so it hangs between your thumb and forefinger, lined up with zero.

• You may need a third person to be at eye level with the ruler to check it’s lined up

• Without giving any warning, the person holding the ruler should drop it.

• Close your thumb and finger to try to catch the ruler as quickly as possible

• The measurement on the ruler at the point where it is caught is how far the ruler dropped in the time it takes you to react

• The longer the distance, the longer the reaction time

• You can calculate how long the ruler falls for because acceleration due to gravity is constant, roughly 9.8m/s

• It’s pretty hard to de this experiment accurately

• Make sure it’s a fair test-use the same ruler and same person

• You could try to investigate some factors affecting reaction time

• Do lots of repeats and calculate mean reaction time with distractions, which you can compare to the mean reaction time without distractions

# 5.19-More on Stopping Distances

Leave enough space to stop

• The figure below for typical stopping distance are from the Highway Code

• To avoid an accident, drivers need to leave enough space between their car and the one in front so that if they had to stop suddenly they would have time to do so safely.

• ‘Enough space’ means the stopping distance for whatever speed they’re going at

• Speed limits are really important because speed affects the stopping distance so much

Speed affects braking distance more than thinking distance

• As a car speeds up, the thinking distance increases at the same rate as speed.

• The graph is linear

• This is because the thinking time stays pretty high constant-but the higher the speed, the more distance you cover in that same time

• Braking distance, however, increases faster the more you speed up,.

• The work done to stop the car is equal to the energy in the car’s kinetic energy store.

• So as speed doubles, the kinetic energy increase 4-fold, and so the work done to stop the car increases 4-fold. Since W=Fs and the braking force is constant the braking distance increases 4-fold.

• Stopping distance is a combination of these two distances so the graph of speed against stopping distance for a car looks like this:

• You need to be able to interpret graphs like this for a range of vehicles-they’re all a similar shape

# 5.20-Momentum

Momentum=Mass x Velocity

Momentum is mainly about how much ‘oomph’ an object has. It’s a property that all moving objects have

• The greater the mass of an object, or the greater its velocity, the more momentum the object has

• You can work out the momentum of an object using:

• p=mv momentum = mass x velocity

Momentum before = momentum after

• In a closed system, the total momentum before an event is the same as after the event.

• This is called conservation of momentum

• In snooker, balls of the same size and mass collide with each other.

• Each collision is an events where the momentum of each ball changes, but the overall momentum stays the same

• Before: The red ball is stationary, so it has zero momentum.

• The white ball is moving with a velocity so has a momentum of p=mv

• After: The white ball hits the red ball, causing it to move.

• The red ball now has momentum.

• The white continues moving, but at a much smaller velocity.

• The combined momentum of the red and white ball is equal to the original momentum of the white ball, mv

• If the momentum before an event is zero, then the momentum after is zero

# 5.21-Changes in Momentum

You can use conservation of momentum to calculate velocities or masses

• Momentum is conserved in a closed system.

• You can use this to help you calculate things like velocity or mass of objects in an events

Example question:

1. Calculate the momentum of the pellet

2. The momentum before the gun is fired is zero.

3. This is equal to the total momentum after the collision

4. The momentum of the gun is 1.5 x v

5. Rearrange the equation to find the velocity of the gun.

6. The minus sign shows the gun is travelling in the opposite direction to the bullet

Forces cause a change in momentum

• You know that when a non-zero resultant force acts on a moving object it causes its velocity to change. This means that there is a change in momentum

• You also know that F=ma and that a= change in velocity / change in time

• So F=m x v-u/t which can also be written as: F = mchangeinv/changeint

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

• A larger force means a faster change of momentum

• Likewise, if someone’s momentum changes very quickly the forces on the body will be very large, and more likely to causes injury

• This is why cars are designed to slow people down over a longer time when they have a crash- the longer it takes for a change in momentum, the smaller the rate if change in momentum, and so the smaller the force.

• Smaller forces means the injuries are likely to be less severe

Cars have many safety features, such as:

• Crumple zones crumple on impact, increasing the time taken for the car to stop

• Seat belts stretch slightly, increasing the time taken for the wearer to stop

• Air bags inflate