Mechanics Flashcards
Modelling a particle
Particle - Dimensions of the object are negligible.
• mass of the object is concentrated at a single point
• rotational forces and air resistance can be ignored
Modelling a rod
Rod - All dimensions but one are negligible, like a pole or a beam.
• mass is concentrated along a line
• no thickness
• rigid (does not bend or buckle)
Modelling a lamina
Lamina - Object with area but negligible thickness, like a sheet of paper.
• mass is distributed across a flat surface
Modelling a uniform body
Uniform body - Mass is distributed evenly.
• mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
Modelling a light object
Light object - Mass of the object is small compared to other masses, like a string or a pulley.
• mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass
• treat object as having zero mass
• tension the same at both ends of a light string
Modelling a inextensible string
Inextensible string - A string that does not stretch under load.
•acceleration is the same in objects connected by a taut inextensible string
Modelling a smooth surface
Smooth surface
• assume that there is no friction between the surface and any object on it
Modelling a rough surface
Rough surface - If a surface is not smooth, it is rough
• objects in contact with the surface experience a frictional force if they are moving or are acted on by a force
Modelling a wire
Wire - Rigid thin length of metal.
• treated as one-dimensional
Modelling a smooth and light pulley
Smooth and light pulley - all pulleys you consider will be smooth and light.
•pulley has no mass
• tension is the same on either side of the pulley
Modelling a bead
Bead - Particle with a hole in it for threading on a wire or string.
• moves freely along a wire or string
• tension is the same on either side of the bead
Modelling a peg
Peg - A support from which a body can be suspended or rested
• dimensionless and fixed
• can be rough or smooth as specified in question
Modelling air resistance
Air resistance - Resistance experienced as an object moves through the air.
• usually modelled as being negligible
Modelling gravity
Gravity - Force of attraction between all objects. Acceleration due to gravity is denoted by g. g = 9.8 m/s^2
• assume that all objects with mass are attracted towards the Earth
• Earth’s gravity is uniform and acts vertically downwards
• g is constant and is taken as 9.8 m 5-2, unless otherwise stated in the question
SI units
Mass = kilogram = kg
Length/displacement = metre = m
Time = seconds = s
The most common forces
• The weight (or gravitational force) of an object acts vertically downwards.
• The normal reaction is the force which acts perpendicular to a surface when an object is in contact with the surface.
• The friction is a force which opposes the
motion between two rough surfaces.
• If an object is being pulled along by a string, the force acting on the object is called the tension in the string.
• If an object is being pushed along using a light rod, the force acting on the object is called the thrust or compression in the rod.
• Buoyancy is the upward force on a body that allows it to float or rise when submerged in a liquid.
• Air resistance opposes motion.
Vector quantity
A vector is a quantity which has both magnitude and direction (displacement, velocity, acceleration, force/weight)
Can be positive or negative
Scalar quantity
A scalar quantity has magnitude only (distance, speed, time, mass)
Always positive
Vector using i,j notation
(i) = (x)
(j) (y)
displacement-time graph
Velocity is the rate of change of displacement.
On a displacement-time graph the gradient represents the velocity.
If the displacement-time graph is a straight line, then the velocity is constant.
Average velocity = displacement from starting point / time taken
Average speed = total distance travelled / time taken
velocity-time graph
Acceleration is the rate of change of velocity.
In a velocity-time graph the gradient represents the acceleration.
If the velocity-time graph is a straight line, then the acceleration is constant.
The area between a velocity-time graph and the horizontal axis represents the distance travelled.
For motion in a straight line with positive velocity, the area under the velocity-time graph up to a point t represents the displacement at time t.
suvat equations
• v = u + at
• S= ((u + v) / 2) x t
• v^2 = u^2+ 2as
• s = ut + 0.5at^2
• s = vt - 0.5at^2
Vertical motion under gravity
The force of gravity causes all objects to accelerate towards the earth. If you ignore the effects of air resistance, this acceleration is constant. It does not depend on the mass of the object.
An object moving vertically in a straight line can be modelled as a particle with a constant downward acceleration of g = 9.8 m/s^2
Newton’s first law of motion
states that an object at rest will stay at rest and that an object moving with constant velocity will continue to move with constant velocity unless an unbalanced force acts on the object.
The effect of a resultant force acting on an object
object will cause the object to accelerate in the same direction as the resultant force.
How to find the resultant force of two or more forces given as vectors
By adding the vectors
Newton’s second law of motion
states that the force needed to accelerate a particle is equal to the product of the mass of the particle and the acceleration produced: F = ma
W =
W = mg
Weight = mass x gravity
Solving problems involving connected particles
Consider the particles separately or, if they are moving in the same straight line, as a single particle.
Newton’s third law
states that for every action there is an equal and opposite reaction.
