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Year 10 Forces & Motion
Learning Objectives
Students should understand the following:

Scalar quantities have magnitude only.

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.

The kinetic energy of a moving object can be calculated using the equation: kinetic energy = 0.5 × mass × speed^{2} E_{k} = 1/2mv^{2}

^{The amount of gravitational potential energy gained by an object raised above ground level can be calculated using the equation: g.p.e. = mass × gravitational field strength × height}

A force is a push or pull that acts on an object due to the interaction with another object.

All forces between objects are either:
contact forces – the objects are physically touching
noncontact forces – the objects are physically separated.

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

Examples of noncontact forces are gravitational force, electrostatic force and magnetic force.

Force is a vector quantity.

Students should be able to describe the interaction between pairs of objects which produce a force on each object. The forces to be represented as vectors.

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 can be calculated using the equation:
weight = mass × gravitational field strength

gravitational field strength, g, in newtons per kilogram, N/kg (In any calculation the value of the gravitational field strength (g) will be given.)

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 springbalance (a newtonmeter)

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.

Students should be able to:
 describe examples of the forces acting on an isolated object or system
 use free body diagrams to describe qualitatively examples where several forces lead to a resultant force on an object, including balanced forces when the resultant force is zero.

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.

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).

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 action of the force
(W = F s)

One joule of work is done when a force of one newton causes a displacement of one metre.

1 joule = 1 newtonmetre

Students should be able to describe the energy transfer involved when work is done.

Students should be able to convert between newtonmetres and joules.

Work done against the frictional forces acting on an object causes a rise in the temperature of the object.

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

Distance is a scalar quantity.

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.

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.

Typical values may be taken as:

walking ̴ 1.5 m/s

running ̴ 3 m/s

cycling ̴ 6 m/s.

Students should be able to recall typical values of speed for a person walking, running and cycling as well as the typical values of speed for different types of transportation systems.

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.

Students should be able to make measurements of distance and time and then calculate speeds of objects.

For an object moving at constant speed the distance travelled in a specific time can be calculated using the equation: distance travelled = speed × time (s = v t)

Students should be able to calculate average speed for nonuniform motion.

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.

Students should be able to explain qualitatively, with examples, that motion in a circle involves constant speed but changing velocity.

Students should be able to explain qualitatively how:
 for circular orbits, the force of gravity can lead to changing velocity but unchanged speed
 for a stable orbit, the radius must change if the speed changes.

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.

Students should be able to draw distance–time graphs from measurements and extract and interpret lines and slopes of distance–time graphs, translating information between graphical and numerical form.

Students should be able to determine speed from a distance–time graph.

The average acceleration of an object can be calculated using the equation:
Acceleration = change in velocity/time taken (a = Δ v/t)

An object that slows down is decelerating.

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.

The distance travelled by an object (or displacement of an object) can be calculated from the area under a velocity–time graph.

Students should be able to:

draw velocity–time graphs from measurements and interpret lines and slopes to determine acceleration

interpret enclosed areas in velocity–time graphs to determine distance travelled (or displacement)

measure, when appropriate, the area under a velocity–time graph by counting squares.

The following equation applies to uniform acceleration:
Final velocity^{2} − initial velocity^{2} = 2 × acceleration × distance
(v^{2} − u^{2} = 2 a s)

Near the Earth’s surface any object falling freely under gravity has an acceleration of about 9.8 m/s^{2}

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.

Students should be able to:

draw and interpret velocity–time graphs for objects that reach terminal velocity

interpret the changing motion in terms of the forces acting.

Newton’s First Law:

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.

Students should be able to apply Newton’s First Law to explain the motion of objects moving with a uniform velocity and objects where the speed and/or direction changes.

The tendency of objects to continue in their state of rest or of uniform motion is called inertia.

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.

As an equation: resultant force = mass × acceleration (F = m a)

Students should be able to explain that:
 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.

Students should be able to estimate the speed, accelerations and forces involved in large accelerations for everyday road transport.

Students should recognise and be able to use the symbol that indicates an approximate value or approximate answer, ~

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.

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.

Students should be able to estimate how the distance for a vehicle to make an emergency stop varies over a range of speeds typical for that vehicle.

Students will be required to interpret graphs relating speed to stopping distance for a range of vehicles.

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. Distractions may also affect a driver’s ability to react.

Students should be able to:
 explain methods used to measure human reaction times and recall typical results
 interpret and evaluate measurements from simple methods to measure the different reaction times of students
 evaluate the effect of various factors on thinking distance based on given data.

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

Adverse road conditions include wet or icy conditions. Poor condition of the vehicle is limited to the vehicle’s brakes or tyres.

Students should be able to:
 explain the factors which affect the distance required for road transport vehicles to come to rest in emergencies, and the implications for safety
 estimate how the distance required for road vehicles to stop in an emergency varies over a range of typical speeds.

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 be able to:
 explain the dangers caused by large decelerations
 estimate the forces involved in the deceleration of road vehicles in typical situations on a public road.

Momentum is defined by the equation:
momentum= mass × velocity (p = m v)

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
 complete calculations involving an event, such as the collision of two objects.

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

The equations F = m × a and a = v – u/t combine to give the equation F = m Δ v/Δ
where mΔv = change in momentum ie force equals the rate of change of momentum.

Students should be able to explain safety features such as: air bags, seat belts, gymnasium crash mats, cycle helmets and cushioned surfaces for playgrounds with reference to the concept of rate of change of momentum.

Students should be able to apply equations relating force, mass, velocity and acceleration to explain how the changes involved are interrelated.
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