Mechanics

What must always be true when using the SUVAT equations of motion?

The acceleration must be uniform - if the acceleration is changing, the equations are not valid.

What does the gradient of a distance-time graph represent?

Speed

What does the gradient of a displacement-time graph represent?

Velocity

What does the gradient of a velocity-time graph represent?

Acceleration

Describe the shape of a velocity-time graph for an object travelling with uniform acceleration.

If acceleration is constant, the gradient of the velocity-time graph will be constant and so it will form a straight line graph.

If acceleration is not constant, the gradient of the velocity-time graph will change and so it will form a curve.

Compare the velocity-time graphs for a uniformly accelerating and a uniformly decelerating object.

- For an accelerating object, the gradient will be positive

- For a decelerating object, the gradient will be negative.

What is a scalar quantity?

A scalar quantity is one that has a magnitude but not a fixed direction.

What is a vector quantity?

A vector quantity is one that has a magnitude and a fixed direction

Give five examples of scalar quantities

1. Distance

2. Speed

3. Mass

4. Energy

5. Temperature

Give five examples of vector quantities

1. Displacement

2. Velocity

3. Acceleration

4. Momentum

5. Force

How is a vector quantity represented on a diagram?

- As an arrow

- The direction of the arrow represents the direction of the quantity

- The length of the arrow represents the magnitude of the quantity

What does resolving a vector involve?

Splitting the vector into two perpendicular components (horizontal and vertical)

Define the horizontal component of the below vector in terms of V and 0`

X = Vcos0`

Define the vertical component of the vector below in terms of V and 0`

Y = Vsin0`

Describe the relationship between the perpendicular components of a vector.

The perpendicular components are independent of each other.

How should the components of a projectile be handled when carrying out calculations?

- The horizontal and vertical components are independent of each other and so should be treated separately

- SUVAT should be used separately for each component.

If a projectile is moving freely under gravity under gravity, what can be said about the vertical acceleration?

The vertical acceleration will be the acceleration due to gravity and so will have a magnitude of 9.81m/s

State Newton's first law of motion in words

An object at rest will remain at rest, and an object moving with a given velocity will continue moving with that same velocity, unless acted on by an external resultant force.

State Newton's second law of motion in words

The acceleration of an object is directly proportional to the resultant forces acting on it and inversely proportional to its mass

State the defining equation for Newton's Second Law of motion

Resultant force (N) = Mass (kg) x Acceleration (m/s-2)

F = ma

Can an object travelling with constant speed change direction, without an external force acting?

For an object to change direction, its velocity must change. This means there must be an acceleration. An acceleration cannot occur without an external resultant force acting.

Describe the forces acting on an object travelling at terminal velocity.

● The forces are balanced in both the vertical and horizontal components of its motion

● There is no resultant force, and therefore no acceleration

What is meant by terminal velocity?

For a given set of conditions, the terminal velocity is the maximum speed of the object. An object has zero acceleration at terminal velocity.

State the equation used to calculate the weight of an object.

W = mg

Weight = mass x gravitational field strength

What is the unit of weight?

Newton, N

State Newton's third law of motion in words

Every action has an equal and opposite reaction. This means that there is always a pair of forces acting on interacting objects, equal in magnitude, but in opposite directions.

State the equation for momentum

p = mv

momentum = mass x velocity

What is the unit of momentum?

kgms^-1

What is the consequence of the linear conservation of momentum?

The total momentum of a system before an event is always equal to the total momentum of the system after the event.

What is a moment?

A moment is the turning effect of a force.

State the equation used to calculate the moment of a force.

moment of a force (Nm) = force (N) x distance (m)

What distance must be used when calculating a moment?

The perpendicular distance between the line of action of the force and the axis of rotation

What is the unit of a moment?

Nm

What is the principle of moments?

For an object to be in equilibrium, the sum of the clockwise moments about a point must be equal to the sum of the anticlockwise moments

What is an object's centre of gravity?

The single point through which the object's entire weight can be said to act.

What will occur if the line of action an object's centre of gravity lies outside its base?

The object's weight will produce a resultant moment and so if is unsupported, the object may topple.

State the equation used to calculate the work done by a force.

W = FΔs

Work Done = Force x Change in Distance

What force is used when calculating the work done by a force over a distance?

The component of the force that is in the direction of the object's motion.

What is the unit of work?

Joules, J

What is the work done by the force,F when it moves the object by a distance of x?

Work done = Fcos0`x

What form o energy do all moving object have?

All moving objects have kinetic energy.

State the equation used to calculate the kinetic energy of an object.

Kinetic Energy = 1/2 x Mass x Velocity^2

E = 1/2mv^2

What form of energy does a raised object have?

Gravitational Potential Energy

State the equation used to calculate gravitational potential energy.

GPE = Mass x Gravitational Field Strength x Height

E = mgh

What is the conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed - it can only be transferred between different forms.

What is power?

The rate at which energy or work is done.

State two equations used to calculate power.

P = E/t

P = W/t

What is the unit of power?

Watt, W

What is the waste energy of an electrical appliance?

The waste energy is the energy that is not used for the appliance's intended purpose.

State the equation relating energy and efficiency.

Efficiency = useful energy output/total energy input

State the equation relating power and efficiency

Efficiency = useful power output / total power input

What is the unit of efficiency?

Efficiency is a ratio and so doesn't have an associated unit.

Scalar quantities are ones which only have a magnitude:

- Mass

- Time

- Energy

- Work

- Length

- Speed

Vector quantities are ones which have a magnitude and direction:

- Displacement

- Force

- Acceleration

- Velocity

- Momentum

Vectors have both a magnitude and direction, compared to scalar quantities which only have a magnitude. Vectors can be shown with arrow drawings.

Vector triangles can be used to determine resultant vectors.

If vector drawings are drawn to scale, they can be physically measured; if not then calculations must be used.

Resolving a vector means splitting it up into its horizontal and vertical components.

Because these components meet at right angles,they can be calculated using trigonometry. However, they can also be drawn to scale and found using the parallelogram method. The key to resolving vectors s putting the vectors head to tail.

The moment of a force about a point is the product of the force and the distance from the line of action of the force to the point.

Moment(Nm) = Force(N) x Perpendicular Distance(m)

When an object is in equilibrium, the moments on it about a point are balanced. For example, around a car's wheel axle. You can use this to work out forces and distances.

Total Clockwise Moment = Total Anti-clockwise Moment

A couple is a pair of equal and opposite parallel forces that both act on the same body and do not act in the same line.

Moment of a couple = force x perpendicular distance between lines of action

The centre of mass is where the mass of an object can be considered to be concentrated. The line of action acts from the centre of mass and shows how gravity is acting upon the object.

The centre of mass can be found by suspending an object by a pin and then using a plum line to draw on the line of action- where they cross is the centre of mass.

S = Displacement

U = Initial velocity

V = Final velocity

A = Acceleration

T = Time

In projectile motion, the horizontal and the vertical components are treated separately. Acceleration is due to gravity, hence only affects the vertical component and is positive if acting with the object and negative if against it.

Friction

A force that opposes the motion of a object.

Drag

A force that opposes motion in a fluid. It usually increases with speed.

Lift

An upward force created on an object as it moves through a fluid due to its shape.

Terminal Velocity

This happens when frictional forces equal the driving force, causing a resultant force of 0N and zero acceleration.

Terminal velocity in a falling object

1. Initially the weight > air resistance, so there is a resultant downwards force and the object accelerates

2. As velocity increases, air resistance increases.

3. When air resistance = weight, there is no resultant force and so the object travels at terminal velocity.

Energy is transferred when a force is applied across a distance, this is known as the work done.

Energy is measured in joules and power is measured in watts, where one watt is equal to one joule per second.

In elastic collisions, the kinetic energy of the system is not conserved and some kinetic energy is dissipated by being transferred to other forms - to work out the quantity of energy transferred to other forms you can compare the initial and final KE values

Change in K.E = K.E final - K.e initial

Impulse can be described as the change of momentum of an object. It is equal to the area under a Force-Time graph.

The force an object experiences is equal to the rate of change of momentum.