Studied by 14 peopleEngineers analyse forces when designing a great variety of machines and instruments, from road bridges and fairground rides to atomic force microscopes. Anything mechanical can be analysed in this way. Recent developments in artificial limbs use the analysis of forces to make movement possible.
WHAT DO SCALAR QUANTITIES HAVE?
Scalar quantities have magnitude (size) only.
WHAT DO VECTOR QUANTITIES HAVE? HOW CAN THEY BE REPRESENTED?
Vector quantities have magnitude and an associated direction.
A vector quantity may be represented by an arrow.
The length of the arrow represents the magnitude, and the direction of the arrow the direction of the vector quantity
COMPARE SCALAR AND VECTOR EXAMPLES.
WHAT IS A FORCE?
WHAT TYPE OF QUANTITY IS A FORCE?
A force is a push or pull that acts on an object due to the interaction with another object.
Force is a vector quantity.
WHAT ARE THE TWO TYPES OF FORCES
All forces between objects are either:
•Contact Forces – the objects are physically touching.
• Non-Contact Forces – the objects are physically separated.
Examples of contact forces include:
Friction (a force that opposes motion)
Air resistance.
Tension (a force that pulls two objects connected by a length, such as a string or rope. It occurs when a force is applied to the length).
Normal contact force (a force that pushes touching objects apart. It occurs when objects are supported by a surface).
Examples of non-contact forces are:
Gravitational force (the attractive force experiences by two objects with mass in a gravitational field. E.g the force between a planet and a comet).
Electrostatic force (a force experiences by charged objects which can be attractive or repulsive. For example, the attraction between a proton and an electron).
Magnetic force (a force experienced any magnetic material in a magnetic field. For example, the attraction between the North and South poles of magnets).
WHAT IS WEIGHT?
WHAT CAUSES THE FORCE OF GRAVITY CLOSE TO EARTH TO OCCUR?
WHAT DOES THE WEIGHT OF AN OBJECT DEPEND ON?
WHAT IS THE CENTRE OF MASS?
WHAT IS THE RELATIONSHIP BETWEEN WEIGHT AND MASS?
HOW IS WEIGHT MEASURED?
Weight is the force acting on an object due to gravity.
The force of gravity close to the Earth is due to the gravitational field around the Earth.
The weight of an object depends on the gravitational field strength at the point where the object is.
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.
Weight is measured using a calibrated spring-balance (a newtonmeter).
WHAT IS A FORCE PAIR?
HOW CAN THEY BE REPRESENTED?
When there is an interaction between two objects, a force is exerted on each object. This is known as a force pair.
Can be represented by arrows in vector diagrams.
WHAT IS A RESULTANT FORCE?
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 acting together.
This single force is called the resultant force.
Students should be able to calculate the resultant of two forces that act in a straight line.
(HT only) Students should be able to: • describe examples of the forces acting on an isolated object or system • (HT only) A single force can be resolved into two components acting at right angles to each other. The two component forces together have the same effect as the single force.
(HT only) Students should be able to use vector diagrams to illustrate resolution of forces, equilibrium situations and determine the resultant of two forces, to include both magnitude and direction (scale drawings only).
Resultant forces can be calculated by adding or subtracting all of the forces acting on the object. • forces working in opposite directions are subtracted. • forces working in the same direction are added together. • if the forces acting in opposite directions are equal in size, then there will be no resultant force – the forces are said to be balanced.
WHAT IS A FREE BODY DIAGRAM?
Models the forces acting on an object.
WHAT IS A VECTOR DIAGRAM?
RESOLVING FORCES
If a force acts at an angle, the force may be broken down or resolved. A single force can be resolved into two parts (components). • horizontal component • vertical component The magnitude of the horizontal and vertical components can be determined by drawing a vector diagram.
HOW DOES FORCE DO WORK ON AN OBJECT?
ONE JOULE =?
WHAT HAPPENS WHEN WORK IS DONE AGAINST FRICTIONAL FORCES?
When a force causes an object to move through a distance work is done on the object.
So a force does work on an object when the force causes a displacement of the object.
The work done by a force on an object can be calculated using the equation: work done = force × distance moved along the line of act
One joule of work is done when a force of one newton causes a displacement of one metre.
1 joule = 1 newton-metre
Work done against the frictional forces acting on an object causes a rise in the temperature of the object.
WHICH FORCES ARE INVOLVED IN STRETCHING, BENDING, AND COMPRESSING?
In stretching the two forces are weight and tension.
In bending the two forces are weight and reaction force.
In compressing the two forces are weight and reaction force
HOW MANY FORCES NEED TO BE APPLIED TO CHANGE THE SHAPE OF A STATIONARY OBJECT AND WHY?
HOW CAN THEIR SHAPE CHANGE?
WHAT IS THE CHANGE OF SHAPE CALLED AND WHAT ARE THE TWO TYPES? AND WHEN DO THOSE OCCUR?
For stationary objects, more than one force has to be applied to change their shape.
Their shape can change by:
Stretching (forces in opposite directions away from the object).
Bending (forces that distort the object).
Compressing (forces in opposite directions towards the object).
A change of shape is called a deformation and can either be:
Elastic .
Inelastic.
Elastic deformation occurs when objects return to their original shape when the stretching force is removed.
Inelastic deformation occurs when objects remain stretched and do not return completely to their original shape even when the stretching force is removed
WHAT IS THE LIMIT OF PROPORTIONALITY?
The limit of proportionality is where if more force is added, the object may extend but will not return to its original shape when the force is removed (it will be inelastically deformed).
WHAT IS HOOKE’S LAW?
HOW IS IT REPRESENTED?
WHAT DOES IT MEAN WHEN AN OBJECT DOESN’T OBEY HOOKE’S LAW?
HOW IS IT REPRESENTED?
Hooke's Law states that: The extension of an elastic object is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
This relationship also applies to the compression of an elastic object, where ‘e’ would be the compression of the object.
A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring.
Provided the spring is not inelastically deformed, the work done on the spring = the Ee stored.
Hooke’s law is the linear relationship between force and extension.
This is represented by a straight line on a force-extension graph.
Materials that do not obey Hooke's law, i.e. they do not return to their original shape once the force has been removed, have a nonlinear relationship between force and extension.
This is represented by a curve on a force-extension graph. Any material beyond its limit of proportionality will h
FOrce extention graphs
HOW DO YOU CALCULATE THE SPRING CONSTANT?
The stiffer the spring, the greater the spring constant and vice versa This means that more force is required per metre of extension compared to a less stiff spring.
If the force is on the y axis and the extension on the x axis, the spring constant is the gradient of the straight line.
If the graph has a steep straight line, this means the material has a large spring constant.
If the graph has a shallow straight line, this means the material has a small spring constant.
If the force is on the x axis and the extension on the y axis, the spring constant is 1 ÷ gradient of the straight line.
If the graph has a steep straight line, this means the material has a small spring constant.
If the graph has a shallow straight line, this means the material has a large spring constant.
HOW IS WORK DONE ON A SPRING?
A force that stretches (or compresses) a spring does work and elastic potential energy is stored in the spring.
Provided the spring is not inelastically deformed, the work done on the spring and the elastic potential energy stored are equal (so the Ee equation is used to work it out).
Required practical activity 18: investigate the relationship between force and extension for a spring.
Force should be proportional to the extension - the spring obeys Hooke’s Law.
WHAT IS DISTANCE?
WHAT TYPE OF QUANTITY IS DISTANCE?
Distance is how far an object moves.
Distance is a scalar quantity. Distance does not involve direction.
WHAT IS DISPLACEMENT?
WHAT TYPE OF QUANTITY IS DISPLACEMENT?
(Green.)
Displacement includes both the distance an object moves, measured in a straight line from the start point to the finish point and the direction of that straight line.
Displacement is a vector quantity. Students should be able to express a displacement in terms of both the magnitude and direction.
WHAT IS SPEED?
WHAT TYPE OF QUANTITY IS SPEED?
WHAT IS A PERSON’S SPEED WHILE WALKING/RUNNING/CYCLING AFFECTED BY?
WHAT ARE THE TYPICAL VALUES FOR THINGS IN THE PICTURE?
“IT IS NOT ONLY MOVING OBJECTS THAT HAVE VARYING SPEED,” SO WHAT ELSE IS THERE?
Speed does not involve direction.
Speed is a scalar quantity.
The speed of a moving object is rarely constant.
When people walk, run or travel in a car their speed is constantly changing.
The speed at which a person can walk, run or cycle depends on many factors including: age, terrain, fitness and distance travelled.
It is not only moving objects that have varying speed. The speed of sound and the speed of the wind also vary. A typical value for the speed of sound in air is 330 m/s.
WHAT IS NON-UNIFORM MOTION AND HOW DO YOU CALCULATE IT?
Non-uniform motion refers to motion that is changing.
Use the “average speed” formula to work it out.
WHAT IS VELOCITY?
WHAT TYPE OF QUANTITY IS VELOCITY?
The velocity of an object is its speed in a given direction.
Velocity is a vector quantity.
Students should be able to explain the vector–scalar distinction as it applies to displacement, distance, velocity and speed.
WHAT IS THE VELOCITY OF MOTION IN A CIRCLE?
Motion in a circle involves constant speed but changing velocity.
When an object travels along a circular path, its velocity is always changing.
The speed of the object moving in a circle might be constant - that is, it is travelling the same distance every second.
However, the direction of travel is always changing as the object moves along the circular path.
WHEN CAN A D-T GRAPH BE USED?
HOW CAN A D-T GRAPH BE USED TO CALCULATE SPEED?
HOW CAN THE SPEED ON ACCELERATING OBJECT BE CALCULATED?
WHAT DOES A STRAIGHT LINE REPRESENT?
WHAT DOES THE SLOPE OF THE STRAIGHT LINE REPRESENT?
If an object moves along a straight line, the distance travelled can be represented by a distance–time graph.
The speed of an object can be calculated from the gradient of its distance–time graph.
If an object is accelerating, its speed at any particular time can be determined by drawing a tangent and measuring the gradient of the distance–time graph at that time.
A straight line represents constant speed.
The slope of the straight line represents the magnitude of the speed.
WHAT IS ACCELERATION?
WHAT IS DECELERATION?
HOW CAN THE ACCELERATION OF AN OBJECT BE CALCULATED?
WHAT DOES A STRAIGHT LINE REPRESENT?
WHAT DOES A STEEP SLOPE REPRESENT?
WHAT DOES A FLAT LINE REPRESNT?
Acceleration is defined as the rate of change of velocity.
An object that slows down is decelerating.
The acceleration of an object can be positive or negative, depending on whether the object is speeding up or slowing down. • If an object is speeding up, its acceleration is positive
Students should be able to estimate the magnitude of everyday accelerations.
The acceleration of an object can be calculated from the gradient of a velocity–time graph.
A straight line represents constant acceleration (or deceleration). The slope of the line represents the magnitude of acceleration (or deceleration).
A steep slope means large acceleration (or deceleration).
A flat line means the acceleration is zero - i.e. the object is moving with a constant velocity.
HOW CAN THE DISTANCE/DISPLACEMENT OF AN OBJECT BE CALCULATED?
The distance travelled by an object (or displacement of an object) can be calculated from the area under a velocity–time graph.
NEAR THE EARTH’S SURFACE, WHAT IS THE ACCELERATION OF ANY FREE FALLING OBJECT?
WHY DOES AN OBJECT FALLING THROUGH A FLUID INITIALLY ACCELERATE?
Near the Earth’s surface any object falling freely under gravity has an acceleration of about 9.8 m/s2.
An object falling through a fluid initially accelerates due to the force of gravity. Eventually the resultant force will be zero and the object will move at its terminal velocity.
WHAT IS NEWTON’S FIRST LAW?
EXEMPLIFY THIS WITH A VEHICLE.
If the resultant force acting on an object is zero and:
• the object is stationary, the object remains stationary
• the object is moving, the object continues to move at the same speed and in the same direction. So the object continues to move at the same velocity.
So, when a vehicle travels at a steady speed the resistive forces balance the driving force. So, the velocity (speed and/or direction) of an object will only change if a resultant force is acting on the object.
WHAT IS 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.
An object will accelerate (change its velocity) in response to a resultant force.
The bigger this resultant force, the larger the acceleration.
• For a given force, the greater the object's mass, the smaller the acceleration experienced
WHAT IS INERTIA?
WHAT IS INERTIAL MASS?
WHAT IS INERTIAL MASS DEFINED AS?
The tendency of objects to continue in their state of rest or of uniform motion is called inertia.
Inertial mass is a measure of how difficult it is to change the velocity of an object
Inertial mass is defined as the ratio of force over acceleration.
Required practical activity 19: investigate the effect of varying the force on the acceleration of an object of constant mass, and the effect of varying the mass of an object on the acceleration produced by a constant force.
WHAT IS NEWTON’S THIRD LAW?
WHERE CAN IT BE APPLIED?
Newton’s Third Law: Whenever two objects interact, the forces they exert on each other are equal and opposite.
Students should be able to apply Newton’s Third Law to examples of equilibrium situations.
All forces arise in pairs - if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
WHAT IS STOPPING DISTANCE?
HOW DO BRAKING FORCE AND STOPPING DISTANCE LINK?
The stopping distance of a vehicle is the sum of the distance the vehicle travels during the driver’s reaction time (thinking distance) and the distance it travels under the braking force (braking distance).
For a given braking force the greater the speed of the vehicle, the greater the stopping distance.
WHAT ARE TYPICAL VALUES OF REACTION TIME?
WHAT CAN AFFECT A DRIVER’S REACTION TIME?
Reaction times vary from person to person.
Typical values range from 0.2 s to 0.9 s.
A driver’s reaction time can be affected by tiredness, drugs and alcohol.
WHAT ARE THE FACTORS THAT CAN AFFECT BRAKING DISTANCE?
WHICH FACTORS AFFECT THE BRAKING DISTANCE?
The braking distance of a vehicle can be affected by:
Adverse road and weather conditions (includes wet or icy conditions).
Poor condition of the vehicle ( limited to the vehicle's brakes or tyres).
WHAT HAPPENS WHEN A FORCE IS APPLIED TO THE BREAKS OF A VEHICLE?
HOW DOES SPEED AFFECT BRAKING DISTANCE?
WHAT ARE THE DANGERS OF LARGE DECELERATIONS?
When a force is applied to the brakes of a vehicle, work done by the friction force between the brakes and the wheel reduces the kinetic energy of the vehicle and the temperature of the brakes increases.
The greater the speed of a vehicle the greater the braking force needed to stop the vehicle in a certain distance.
The greater the braking force the greater the deceleration of the vehicle.
Large decelerations may lead to brakes overheating and/or loss of control.
Students should estimate the forces involved in the deceleration of road vehicles in typical situations on a public road.
WHAT IS MOMENTUM?
WHAT DOES THE MOMENTUM OF AN OBJECT DEPEND ON AND WHY?
WHAT DOES THIS MEAN?
WHEN COULD AN OBJECT’S MOMENTUM CHANGE?
Momentum is a property of moving objects
Velocity is a vector this means that the momentum of an object also depends on its direction of travel.
This means that momentum can be either positive or negative. If an object travelling to the right has positive momentum, an object travelling in the opposite direction (to the left) will have negative momentum.
Therefore the momentum of an object will change if:
• The object accelerates (speeds up) or decelerates (slows down).
• Changes direction.
• Its mass changes.
WHAT IS THE CONSERVATION OF MOMENTUM?
In a closed system, the total momentum before an event is equal to the total momentum after the event. This is called conservation of momentum.
Students should be able to use the concept of momentum as a model to describe and explain examples of momentum in an event, such as a collision.
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