# GCSE AQA Physics - Triple Higher - Forces and Motion

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• Created by: jeban02
• Created on: 17-05-20 20:09

## Scalar and Vector Quantities

• A scalar quantity is a measurement that has size (magnitude), and does not have a direction. An example of some scalar quantities are mass, temperature, speed, energy, distance and time.
• A vector quantity is a measurement that has size (magnitude), and a direction. An example of some vector quantities are displacement, momentum, weight, acceleration, force and velocity.
• Distance is a scalar quanitity. It tells us how far the destination is, but it does not give a direction. Distance is measured in metres of kilometres - giving the route.
• Displacement is a vector quantity. It is a distance in a specific direction. It is measured in metres and kilometres, but it also gives a direction, such as North, East etc. It is a straight line from A to B.
• To summarise:
Scalar quantities have size and no direction.
Vector quantities have size and direction.
Distance is a scalar quantity measured in m or km, and it describes the route taken without direction.
Displacement is a vector quantity measured in m or km, and it describes the direct distance from A to B with direction.
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## Contact and Non-Contant Forces

• A force is a push or a pull that acts on an object due to the interaction with another object.
• All forces are vector quantities, as they have both direction and size.
• The unit of force is Newtons (N)
• All forces can be divided into two categories:
• Contact Forces physically touch to exert the force:
• Tension, Friction, Air resistance and Normal Contact force are all examples of contact forces.
• Non-Contact Forces do not need to touch physically in order to exert a force:
• Gravitational force, Electrostatic Force, Magnetic Forces are all examples of non-contact forces.
• For example, when a skydiver falls, he experiences air resistance, as when the air particles collide with the parachute, he begins to decelerate, as the force of the air resistance causes the resultant force to act upwards. This is a contant force.
• For example, when a person jumps, they will fall back to the ground, due to the gravitational pull of the earth. This is a non-contact force.
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## Gravity and Weight

• Gravity is a vector quantity. It attracts object to each other. It has both size and magnitude. It is measured in (N/kg)
• Mass is how much matter an object has. It is a scalar quantity. It is measured in (kg)
• Weight is the force on acting on an object's mass, due to gravity. It is measured in (N), as it is a force.
• We can measure the weight of an object by using a Newton-metre, which is a callibrated spring balance.

• At the surface of the Earth, the gravitational force is 9.8 N/kg.
• The gravitational field strength is a measure of the force of gravity in a particular location.
• The weight of an object is directly proportional to the mass of the object.
The weight of an object (the force due to gravity, can be considered to act at a single point, and that is called the centre of mass

• We can calculate the weight of an object by using this equation:
• Weight (N) = Mass (kg) x Gravitational Field Strength (N/kg)
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## Resultant Forces and Free-Body Diagrams

• A resultant force is a single force that has the same effect as all the original forces acting together when they are combined
• To find the resultant force, add all the forces together.
• Resultant forces can be displayed on a free-body diagram.
• The length of the arrow represents the size of the force.
• The direction of the arrowhead represents the direction of the force.

• If a plane is flying at a constant altitude, at a constant velocity, then the arrows will be same in size, both vertically and horizontally, to show us that the plane is not accelerating or decelerating, flying higher, or lower.

• If a car is accelerating to move to the motorway, we will display the arrow that represents the thrust of the driving force as larger than the one that represents the resistive forces of friction with ground and air, to show that the car is speeding up, (non-constant velocity). However, the vertical arrows will be equal to show that the car is at a constant altitude. (Cars cannot fly!)
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## Work Done and Energy Transfer

• Work measures energy transfer. Whenever a force is used to move an object, the energy is transferred, and we call this work. Work done can be measured in (Nm) or (J)
• For example, a man pushing a box along the floor is using his chemical store in his muscles to increase the kinetic store of the box. He is doing work.
• The equation for work is:
• Work done (J) = Force (N) x Distance (m)
• The distance must be in the line of action of the force.
• For example, if a man is walking up the stairs, and he has travelled 20 m vertically (remember, that we only account for the distance in the line of action, weight is exerted downwards), and weighs 60 N (remember, that weight is a force, as he walks upstairs, he is exerting the force of his weight onto the stairs), calculate the work done:

20 M x 60 N = 1200 Nm or J

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## Forces and Elasticity

• To stretch an object - more than one force is always required. If one force acted on an object, it would simply be moving.
• Elastic deformation is when deforming forces are applied to an elastic object, that will change its size and shape, but when the deforming forces are removed, it will return to its original size and shape.
• Plastic deformation or inelastic deformation is when the deforming forces are applied to an elastic object, but the deforming forces exceed the limit of proportionality for that elastic object, therefore, the object cannot return to its original size and shape.
• We can calculate the force needed to stretch an elastic object by using this equation:
• Force (N) = Spring Constant (N/m) x Extension (m)
• Calculate the force needed to extend a spring by 4cm, if the spring constant is 200 N/m.

4cm = 0.04 m
0.04 m x 200 = 8 N force required to extend the spring by 4cm.

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## Required Practical - Stretching a Spring

Equipment Needed:

Clamp stand, heavy weight, two bosses, ruler, horizontal pointer, spring, 1 N weights.

Method:

• Set up the apparatus as two bosses around one clamp stand with a heavy weight to stop it from falling over, and tighten a ruler vertically around one boss, and one to hang the spring from. Place a wooden splinter at the end of the spring horizontally for accurate readings.
• Hang the spring in line with the zero point of the ruler, and measure the position of the spring - that is the unstretched, original length you will be subtracting with to find the extension.
• Add on a 1 N weight, and record the new length. To find the extension, subtract original length from the new length. Remember to keep the pointer horizontal and ruler vertical. Repeat for several readings.
• Plot the extension against the weight - you will get a straight line graph that goes through the origin of direct proportinality - a linear relationship. This tells us that weight is directly proportional to extension. To find the spring constant - find the gradient.
• If we add too many weights, the L.O.P. will be exceeded - the graph will curve upwards.
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## Moments

• The turning effect of a force is called the moment of the force.
• We can calculate the moment of a force by using this equation:
• Moment (Nm) = Force (N) x Distance (m)

• When calculating the moment, the distance has to be perpendicular from the line of action of the force to the pivot (the middle of the object being turned).
• A balanced moment means that the anti clockwise and clockwise moments are equal around the pivot. In other words, the force multiplied by the distance in the clockwise direction, equals the force multiplied by the distance in the anti-clockwise direction.
• For example:
• Person B applies a force of 350 N and is 0.76 m away from the pivot. Person A applies a force of 500 N. Calculate the distance person A must be away from the pivot in order to balance the moments and keep the seesaw balanced.

350 N x 0.76 m = 266 Nm
266 Nm ÷ 500 N = 0.532 m away from the pivot.

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## Levers and Gears

Levers are force multipliers, as it increase the distance between the pivot and the force of the line of action (where the force is being exerted), therefore the force is multiplied. This means that the same moment can be created by extending the distance, and requires less force - less effort.

Gears transmit the rotiational effects of forces:

• They are interlocked cogs with different radii.
• A force transimitted to a large gear (bigger radius), will cause a bigger moment, as the distance from the pivot is greater with the same force.
• A larger gear turns slower than a smaller gear.
• The force that is transmitted by the smaller gear to the bigger gear will always be the same as forces are always equal and opposite. This means that the large gear will turn more slowly.
• For example:
A cog with radius 2cm is driving a 10cm cog. The moment about the small cog is 6Nm. What is the moment around the 10 cog?
• General Formula: Moment Cog A ÷ Moment Cog B = Radius Cog A ÷ Radius Cog B =
• 30 Nm (Use ratios and common sense!)
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## Speed and Velocity

• Speed is how fast an object travels. it is a scalar quantity.
• The equation for speed is:
• Speed (m/s) = Distance (m) ÷ Time (s)

• A few typical speeds are:
• Walking - 1.5 m/s
• Running - 3 m/s
• Cycling - 6 m/s
• Speed of sound - 330 - 345 m/s (Sound travels faster on warmer days)
• Car - 13 m/s
• Train - 50 m/s
• Aeroplane - 250 m/s
• Velocity is the speed of an object in a given direction. It is a vector quantity
• There is a special case of velocity, for objects moving in a circle:
• If a car moves around a circular roundabout at a constant speed, then its speed is constant, but its velocity is not, as velocity is speed in a given direction, and the direction is changing constantly because a circle has infinite corners.
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## Distance-Time Graphs

• If an object travels in a straight line, then the distance travelled can be represented by this graph. Remeber, it is a scalar quantity, which is only one direction - straight.
• The gradient of the distance time graph tells us the speed othe object.
• When the line in the distance time graph CURVES OR SLOPES, it tells us that the object is CONSTANTLY INCREASING / DECREASING IN SPEED, otherwise, accelerating or decelerating constantly.
• If we asked in the exam, to work out the speed of an object at a certain time, we need to draw a tangent to work out the gradient. This is only if the object is accelerating (the line is curved). If the line is straight to show constant speed, then we can read across as usual.
• Here are a few questions for you to try:
• Draw a D-T graph, with constant positive acceleration that is increasing in distance (moving forward more quickly).
• Draw a D-T graph, with constant negative acceleration (deceleration) that is increasing in distance (moving forward more slowly).
• Draw a D-T graph, with a constant positive acceleration, that is decreasing in distance (moving backwards more quickly).
• Draw a D-T graph, with a constant negative acceleration (deceleration), that is decreasing in distance (moving backwards more slowly)
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## Velocity-Time Graphs

Acceleration of an object is the change of velocity over a given time. (Velocity y-axis).

• The gradient of a V-T graph shows us the acceleration of an object.
• If the line slopes upwards and is straight, it is a constant acceleration. (constant = uniform)
• If the line slopes downwards and it is straight, it is a constant deceleration.
• A curve implies changing acceleration. If the graph is curved, use a tangent to find the acceleration.
• If the line is straight and horizontal, velocity is constant.
• If unsure, check the axis.
• The area under the graph is the displacement.

You can find the average acceleration using this equation:

• Acceleration (m/s^2) = Change in velocity (m/s) ÷ Time (s)

You can use this equation for constant acceleration: (constant = uniform).

• V^2 - U^2 = 2as
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## Newton's First and Second Law of Motion

• If the resultant force acting on a stationary object is zero, then the object will remain stationary, and if the resultant force of a moving object is zero, it will continue moving in the same direction with the same speed (with the same velocity). - First Law

There will be no change, as long as the resultant forces do not become unbalanced.

• The acceleration of an object is proportional to the (resultant) force acting on the object and is inversely proportional to the mass of the object. - Second Law
• The equation for this is:
• Force (N) = Mass (kg) x Acceleration (m/s^2)
• The Inertial Mass of an object is how difficult it is to change the velocity of an object, from rest, or from its current velocity.
• Inertia is the property or tendency of an object to remain stationary or at a constant velocity, until the resultant force is more than 0 (First Law)
• It is the ratio of the force needed to accelerate an object over the acceleration produced.
• An object with a larger inertial mass will require a large force to produce a given acceleration than an object with a smaller inertial mass.
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## Newton's Third Law of Motion

Whenever two objects interact, the forces they exert on each other are equal and opposite. This is Newton's Third Law.

Each action has an equal and opposite reaction.

For example:

• When we are rowing a boat, the paddle exerts a force on the water, and the water exerts a force on the paddle, they are equal in size and opposite in direction.
• When a lamp is on a table, the lamp exerts a force on the table, due to its weight due to gravity. The table pushes on the lamp with the same and opposite force - normal reaction force which keeps the lamp on the table.

Try to give examples of your own.

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## Forces Acting on Skydiver

(Refer to notes for detailed explanation and graph).

• The sky diver accelerates to begin with, because the only force acting is weight, so the resultant force acts downwards.
• As the sky diver accelerates downwards, the air resistance increases. However, the weight is still greater than the air resistance, so she continues to accelerate downwards, due to the resultant force being downwards.
• As the skydiver's velocity increases, the air resistance increases due to the third law.
• At a certain point, the air resistance balances her weight, so there is no resultant force and the velocity stays constant - now she must open the parachute to increase air resistance for a safer landing.
• The parachute opens, and a large surface area causes the air resistance to increase, so the resultant force acts upwards causing deceleration
• Because the velocity decreases, the air resistance also decreases.
• At some point, the air resistance will balance the weight of the sky diver, bringing her to a safer terminal velocity, and the resultant force is zero - with a constant velocity that is safe to land with.
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## Required Practical - Acceleration

Variables:

• Force is being changed so it is the independent variable.
• Mass is kept constant by distributing masses.
• Acceleration is being found out, so it is the dependent variable.

Equipment:

• Ramp, Trolley, Masses, Mass holder, String, Books for leverage, Interrupt card, Ruler, Light gates, Data logger, Computer.

Method:

• Attach a string to the front of the trolley, and at the end, add a mass holder.
• Put the trolley on a slightly lifted ramp, setting up two light gates.
• Put a small card to act as an interrupt between the light gates on the trolley.
• Place a certain amount of masses to be distributed between the trolley and the force, on the trolley.
• Let go of the string, and let the data logger record the data, while you add masses to the force each time. Collect the results.
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## Required Practical - Effects of force and mass on

The previous experiment changed the force and kept the mass constant, however if we want to dicover the effect of mass on acceleration, we can keep the force constant, and keep adding masses the trolley, while keeping a fixed force on the weights at the end of the string.

• The lifted ramp allows us to have a more accurate data, because it cancels out the friction.
• The light gates use s = d ÷ t, to calculate the velocities at each light gate at a given time, therefore the acceleration, We input the difference between them on the computer, and the size of the interrupt. It record the time, to work out the speed therefore velocity, and then the difference in them divided by the time gives us the accceleration. It cancels out error.
• We need to make sure that the masses are constant, by distrubuting them amongst the trolley and the force, to keeop the same mass within the system.
• One person needs to hold the string to make sure the masses don't drop.
• When we increase the force and decrease the mass on the trolley, the acceleration increases, meaning that acceleration is directly proportional to the force being increased, giving us a straight line through the origin - a linear relationship, if we plot acceleration against force.
• This means that when the force is kept constant, the increasing masses will slow down the acceleration, meaning that acceleration is inversely propotional to mass.
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## Vehicle Stopping Distances

• The stopping distance is the total distance travelled when the driver first spots the obstruction, to when the car stops.
• It can be divided into two parts:
• Thinking distance: The distance travelled by the car during the reaction time. The reaction time is the time taken for the driver to spot the obstruction, make a decision and press the brakes.
• The reaction time varies from 0.2 - 0.9 s.
• The reaction time depends on tiredness, drugs and alcohol and distractions in the car.
• Braking Distance: The distance the car travels from when the driver applies the break, to when the car stops.
• This depends on poor road conditions and weather, that will decrease friction, such as rain, sleet, snow, poor vehicle conditions, such as worn brakes and tires, and an increased mass in the vehicle, which will require a bigger distance to remove all the kinetic energy.
• Thinking Distance + Braking Distance = Stopping Distance
• The greater the speed of the vehicle, the greater the stopping distance.
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## Forces when Braking

When brakes are applied:

• Kinetic energy store of the car goes to the thermal energy store of the brakes.

When we brake the car, there is friction between the brake and the tyre, which reduces the kinetic energy, and goes to the thermal energy of the brakes, as the friction causes increase of temperature. This thermal energy is dissipated into the surroundings.

The car slows down to the loss of kinetic energy, and the energy goes to the thermal energy of the tyres, as the friction causes an increase of temperature - remember, energy is always conserved.

If the braking force is too big, the brakes and tyres can overheat, or the driver may lose control of the vehicle.

Refer to notes for an example of a question.

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