# Mechanics

Mechanics

Velocity = speed in given direction. Units = ms-1.

Acceleration = Rate of change in velocity. Units = ms-2.

Acceleration due to gravity = 9.8m/s/s and this figure is used in problems when objects are thrown upward or dropped.

When motion is in a straight line use formulae page 50 & 51. 1st half of each page.

You must derive equations of motion (see main notes.)

Time is measured on a sulfur track by using the mains electricity. The mains cycles every 50th of a second. So a line and a gap on the sulfur track is equal to 0.02 of a second.

Vector quantity has magnitude and direction (velocity). Scalar quantity has magnitude only(time).

Formulae for vectors and scalars to be found tables page

Resultant of two vector forces in lab. Use three spring balances tied together. The resultant of any two is the reading on the third balance.

Force is anything that causes the velocity of an object to change. Unit = Newton.

Weight of a body is the force that the earths gravity puts on it. Weight is a force so unit = Newton.

Momentum of a body is its mass multiplied by its velocity. Unit = kgms-1.

Conservation of momentum = When two bodies collide their momentum is the same after the collision as it was before the collision.

Laws of motion.

1. everybody will stay at rest or keep moving unless an unbalanced force acts on it.

2. If unbalanced force acts on the body the body's rate of momentum change will be proportional to the force and takes place in the direction of the force.

3. For every action there is an equal and opposite reaction.

Density of a substance is its mass per unit volume. Unit = kgm-3.

Archimedes principle = when object is partially or totally immersed in water it will feel an upthrust that is equal in magnitude to the weight of the water it displaces.

Law of flotation = The weight of a floating body is equal to the weight of fluid it displaces.

Pressure in a liquid increases with depth, is perpendicular to all surfaces and is equal in all direction

Boyle's law states that at constant temperature the volume of a fixed mass of gas is inversely proportional to pressure. Page 57 tables.

Newton's gravitational law = The force between 2 masses is proportional to the product of the masses and inversely proportional to the square of the distance between them. Page 56 tables.

Explanation of inverse square law = If the distance between the objects is doubled the force becomes 4 times weaker. If the distance is trebled the force becomes 9 times weaker.

Derive formula for weight.

w=mg w= Gmm/R 2.

mg=GMm/R2. Canceling m's we get g= GM/R 2.

An object is said to be in equilibrium if the sum of all the vector forces acting on it is zero. It hyas zero acceleration. It is not moving.

Couple = 2 parallel forces with the same magnitude acting in the same direction.

Lever = rigid body free to rotate around a fixed point called a fulcrum.

Principle of conservation of energy = Energy cannot be created or destroyed just changed from one from to another. Energy unit = Joule.

Kinetic energy = E due to motion. Potential energy = E due to position. Tables page 55.

Remember that Ek and Ep values can usually be interchanged in questions depending on info given.

Renewable energy = An energy source that doesn't get used up.

Power = rate at which work is done. Unit = watt = joules/sec. Tables page 55.

All formulae for circular motion page 51.

Relationship between linear speed and angular velocity. Derivation of v = rw.

Θ = s/r. Divide both sides by t. θ/t = s/t X 1/r. But θ/t = w and s/t = v. So w=v/r. So v = rw.

Relationship between the period of an orbit and its radius. Derivation of T2 = 4п2R3 /GM

V2 = GM/R and T = 2пR/v. Squaring T gives T2 = 4п2R2/v2. Sub in V2 . And get T2 = 4п2R3 /GM

Angular velocity = The rate of change of an angle with respect to time. Unit = radian.

Centripetal force = The force towards the centre of a circle which keeps a body moving in a circle.

Centripetal acceleration = acceleration the rotating body has towards the centre of the circle.

Period of an orbit is the time taken for one revolution.

Geostationary / parking orbit =Orbit which leaves the orbiting body at the same point above equator

Gravity is the centripetal force which keeps satellites in orbit.

Hooke's law = The restoring force is directly proportional to displacement for a stretched body.

A body is in simple harmonic motion if, its acceleration is directly proportional to a fixed point on its path and if its acceleration is always towards that point.

One cycle per second = one Hertz.

Formulae for simple harmonic motion = page 54 tables.