Physics 1 - Mechanics (AS)

Scalar - A quantity that has a magnitude but no direction. e.g. mass, time, temperature, length & speed

Vector - A quantity that has both magnitude and direction e.g. displacement, force, velocity, acceleration, momentum

Resultant vectors

1) Draw the vectors as arrows from tip to tail

2) if the vectors are at right angles, use Pythagoras or trig to find the resultant vector. If they are not at right angles, draw a scale diagram

Horizontal and vertical components

Horizontal component (Vh): Vh = vcos(x)

Vertical component (Vv): Vv = vsin(x)

Speed, displacement, velocity & acceleration

Definitions

Speed - How far something is moving. Does not take into account direction.

Displacement - How far something has travelled from its starting position.

Velocity - The rate of change of an object's displacement

Acceleration - The rate of change of an object's velocity

Equations

Speed = Distance / time

Velocity = change in displacement/change in time

Acceleration = Change in velocity/change in time

SUVAT equations

S - Displacement, U - Initial velocity, V - Final velocity, A - Acceleration, T - Time

v = u + at (S)

s = vt - 1/2at^2 (U)

s = ut + 1/2at^2 (V)

s = ((u+v)t/2 (A)

v^2 = u^2 + 2as (T)

Each SUVAT equation has one missing letter.

When approaching a question, write out the SUVAT values that you know and want. Once you have 4 of these, choose an equation removing the quanitity you do not need. Under projectile questions, acceleration is usually gravity (On earth = 9.81ms-1)

Acceleration

If an object is accelerating, its displacement-time graph will be curved (3). If the object is accelerating at a uniform rate, its graph will show a linear relationship (2). When the graph is flat, this shows that the object is stationary (1)

Features

The gradient on a displacement-time graph will tell you an object's velocity. This is the same when the graph is curved, you will just need to take a tangent at the point you are measuring. Different accelerations will have different gradients. A bigger acceleration will have a steeper gradient than a smaller acceleration. A deceleration will flatten out.

Features

Gradient - Calculates the acceleration of the object. Uniform acceleration is shown as a straight line and the steeper the gradient, the steeper the acceleration. The gradient can be negative (slopes down) which shows the object is decelerating.

Area under - Calculates the displacement of the object during this time. Areas in the negative parts of the graph shows that the object is moving back to the starting point.

Features

Height - Shows the object's acceleration at that particular time.

Area under the graph - Shows an object's change in velocity.

If a = 0, the object is accelerating with a constant velocity.

If the graph is negative, the object would be decelerating.

Newton's 1st law - An object will remain at rest or at a constant velocity unless an external force is acted upon it.

Newton's 2nd law - The acceleration of an object is proportional to the force applied to it. This rule gives rise to the equation Resultant Force (N) = Mass (kg) * Acceleration (ms-2) (F=ma)

Newton's 3rd law - Every action has an equal and opposite reaction.

If an object A exerts a force on B, then object B exerts an equal and opposite force on A. For example, if you punch a wall, you will recieve a force equal to the force you punched the wall with.

The momentum of an object is dependent on two things: the mass and its velocity. This gives the equation:

Momentum (kgms-1) = Mass (kg) * velocity (ms-1)

p = mv

Conservation of momentum

As long as no external forces act on the object, the momentum is always conserved. This is useful in collisions as you can work out the momentum since the total momentum before is equal to the total momentum after.

Work done

Work done (J) = Force (N) * Distance (m)

W = Fd

This equation gives you the definition of a Joule: One joule is the work done when 1 newton moves an object through a distance of 1 metre.

Power

Power = Work done every second

Power (P) = Energy transferred (E) / time (t) (P = E/t)

Power (P) = Work done (W) / time (t) (P = W/t)

Power is given in Watts (symbol W) and is defined as the rate of energy transfer equal to 1 Joule per second. (Js-1)

Kinetic energy

Ek = 1/2mv² Where m = mass of the object (kg) and v = velocity of the object (ms-1)

Gravitational potential energy

Egrav = mgh where m = mass of the object (kg), g = acceleration due to gravity, h = height of the object (m)

Conservation of energy

Principle of conservation of energy - Energy cannot be created or destroyed but can only be transferred from one from to the other.

E.g. when an object is dropped, gravitational potential energy will become kinetic energy. Energy transfers involves loss because some energy will be lost as heat or sound. The measure of how much useful energy is transferred is the efficiency and is given by the equation:

Efficiency = Useful energy output/total energy input

Weight

The weight of an object is the force experienced by a mass due to the gravitational field it is in.

Weight = Mass * Gravitational field strength (W = mg)

Because of this, an object will feel like it has less weight if it is on a body with a lesser gravitational field then that of Earth, eg. the moon

Centre of gravity

The centre of gravity is the single point where you can think an object's weight acts through. In a perfect sphere with evenly distributed weight, the centre of gravity will be in the middle.

The centre of gravity for an object can be found by symmetry or by experimental methods.

An object's stability is determined by how high its centre of gravity is. An object is stable if it has a low centre of gravity and a wide base. An object will topple over if a vertical line drawn downwards falls outside of its base area. The object's weight is now causing a turning force around a pivot.

A moment is the turning effect of a force and is defined by the equation:

Moment of a force (Nm) = Force (N) * Perpendicular distance from the pivot (m)

Sometimes an object will be at an angle to its pivot. In this case, you will need to resolve forces to calculate the moments.

Equilibrium

If an object is in equilibrium, the sum of the clockwise moments will be equal to the sum of the anticlockwise moments. Think of a seesaw which is not rotating in either direction.