Scalars and Vectors
SCALAR: has only size, no direction; just an amount of something
VECTOR: has both magnitude and direction
Adding Vectors involves the use of Pythagoras and Triginometry:
Use PYTHAGORAS to find the magnitude of the resultant vector -> a2 + b 2 = c2
Use TRIGONOMETRY to find the bearing (direction) of the resultant vector from the horizontal -> SOH CAH TOA
Resolving Vectors into horizintal and vertical components
Use SOH CAH TOA to find the horizontal and vertical components.
Motion with Uniform Acceleration
NB: Uniform acceleration = Constant acceleration
Remember that acceleration can mean a change in speed or direction, or both
There are 3 Equations of Motion involving a constant acceleration:
v = u + at
s = ut + 1/2at2
v2 = u2 + 2as
Remember when doing a question to write out everything from SUVAT that you know. Thi helps you find the right equation to use.
Free Fall and Projectile Motion
Free Fall is when there's only gravity - and nothing else
acceleration due to gravity (g) = 9.81ms-2
When calculating a value from SUVAT of an object in free fall, just replace a with g in the Equations of motion.
A step by step guide for projectiles:
1) Draw the Picture
2) Resolve into horizontal and vertical components if it hasn't been done already.
3) Use the vertical motion to work out the time. Multiply by two if the object both rises and falls. Take this same time for the horizontal motion.
4) Use the horizontal velocity and the equation speed = distance/time to find the distance or range of the object.
(a) - the body is stationary. It is not moving, therefore the displacement remains constant.
(b) - the body is moving at a constant velocity. Velocity can be found from the gradient.
(c) - the body is accelerating, shown by a constant change in gradient. The steeper the curve, the bigger the acceleration. A curve with increasing gradient means acceleration, while a cureve with decreasing gradient means deceleration. You can find the velocity at a given point draw a tangent at that point and find the velocity using the gradient at that point.
The only thing not below is non-uniform acceleration, which is a curve on a V-T graph. A curve with an increasing gradient means increasing acceleration, and vice versa.
Mass, Weight and Centre of Gravity
Weight = mass x gravitational field stregth or W = mg
Density = mass / volume or ρ = m/v
Centre of gravity: assume all the mass is in one place:
You can calculate the centre of gravity of a regular object by finding the objects centre.
The lower the centre of gravity the more stable it is. The most stable objects will have a wide base area combined with a low centre of gravity.
Free body force diagrams are used to show all the forces acting on a single object.
The arrows should show the size and the direction of the force.
If the body's in equilibrium, the forces acting on it will be balanced.
Forces are vectors, meaning they can be resolved and also the resultant force found from two initial components. Do this in the same way you would any vector, using Trigonometry and Pythagoras.
Newton's Laws of Motion
NEWTON'S FIRST LAW: If all the forces acting on an object are balanced, the object will remain at a constant speed.
It follows that a resultant force is needed for an object to accelerate.
NEWTON'S SECOND LAW: if there is a resultant force on the body, it will accelerate proportionally to the force and inversely proportional to the mass of the object.
This can be summarised in the relationship:
F=ma Remember that F indicates a resultant force
NEWTONS'S THIRD LAW: if body A exerts a force on body B, B will then exet a force on A that is equal in size and type, but opposite in direction.
This just means forces come in pairs. These pairs are:
equal in size and type
opposite in direction and acting on different bodies
Mechanics in the Real World
Stopping Distance of Cars
Thinking Distance + Braking Distance = stopping distance
Thinking Distance = speed x reaction time reaction time can be affected by tiredness, alcohol, drugs, illness and distraction. Braking Distance depends on braking force, friction, mass and speed. Braking force is reduced by worn or badly adjusted brakes. Friction is reduced by wet or icy road conditions.
Car Safety Features are designed to gradually slow you down
- Seatbelts - keep you in your selt, and also give way a little to bring you to a stop over a longer period of time.
- Airbags - inflate during a collision and deflate a little when the user slams into them, slowing the stopping time.
- Crumple zones - at the front and back of car. Give way more easily, absorbing some of the impact energy.
- Saftey Cages - help prevent the area around the car occupants from being crushed in.
Forces Act on Sports people - you'll often be asked to draw free body force diagrams.
Power and Work
WORK DONE is the amount of energy transferred:
Work done = Force x Distance ∆W = F x ∆s
sometimes the force given isn't in the direction of the motion. Use SOH CAH TOA to find the component of the force that is in the direction of the motion, and use that to find work done.
KINETIC ENERGY is the energy an object has due to its motion:
Kinetic Energy = 1/2 x Mass x Velocity2 Ek = 1/2mv2
GRAVITATIONAL POTENTIAL ENERGY is the energy something gains or loses due to it's change in height:
G.P.E = mass x strength of gravitational field x height ∆Egrav = mg∆h
POWER is the rate of energy transferral
Power = Energy / Time OR Power = Work Done / Time P = E/T
So: Power also = (Force x Distance) / Time ∴ = force x velocity (because s/t = v)
Conservation of Energy
The Principle: Energy cannot be created or destroyed. Energy can be transferred on from one form into another, but the total amount of energy in a closed system will not change.
Total energy in = total energy out Efficiency = useful Power Output / Power input
When an object gains height, it has GPE. When it's falling, it gains Kinetic energy. You can use these facts to convert between the two in questions. Take the pendulem for an example below: