Forces and motion

distance definition

total length between 2 points/

how much ground an object has covered during its motion

speed definition

total distance travelled per unit of time

displacement definition

the overall change in an objects position/

how far an object has travelled from its starting position in certain direction

velocity

rate of change of displacement of an object

acceleration

rate of change of velocity of an object

What is instantaneous speed/ velocity

Speed/ velocity of an object at any given point in time

What does curved line of s / t graph

accelerating - chaning v

How to find instantaneous velocity from distance- time graph:

• Draw tangent at required time

• Find grad

Displacement-Time graph characteristics:

• Grad = velocity

• Y-intercept = initial displacement

• Diagonal straight line = constant v

• Curved line = acceleration

Velocity- time graph characteristics:

• Slope = acceleration

• Y-intercept = initial velocity

• Straight line = uniform acceleration

• Curved line= non-uniform acceleration

• Area under curve = displacement/ distance travelled

Acceleration-time graph:

• Slope = meaningless

• Horizontal line = constant acceleration

• Area under curve = change in velocity

Acceleration of free fall, g, is defined as:

The acceleration of any object in response to the gravitational attraction between the earth and the object

Stopping distance consists of two parts:

• Thinking distance

• Braking distance

The stopping distance increases considerably with the ____ of a car

speed

The thinking distance ________ _______ with speed

increases proportionally

The braking distance increases at an even ____ rate with speed

faster

Thinking distance is defined as

The distance travelled by the vehicle from when the driver sees a problem and the brakes are applied

How to calculate thinking distance

Thinking distance = Initial speed × Reaction time

Braking distance is defined as:

The distance travelled by the vehicle after the driver has applied the brake

What is the braking distance of the vehicle is proportional to?

square of the initial speed of the car, u²

vehicle’s kinetic energy (½ mv²) must be dissipated by the brakes in order to come to a stop

Work done by brakes:

Work Done = Braking Force × Braking Distance = ½ mv²

Time of flight:

how long the projectile is in the air

Maximum height attained:

the height at which the projectile is momentarily at rest

Range:

the horizontal distance travelled by the projectile

when asked to calculate horizontal range of an oblique projectile vertical displacement is usually 0m

The only force acting on the projectile, after it has been released, is ____

gravity

If the resultant force is at an angle, it will change the ______ of the body

direction

SI units for Newtons

kg m s^–2

What is free fall?

An object in free fall is falling solely under the influence of gravity

In the absence of air resistance, all bodies near the Earth fall with ___ ____ _______ regardless of their mass

the same acceleration

Weight is a _____

Mass is a _____

vector

scalar

Tension definition

The force experienced by a cable, rope, or string when pulled, hung, rotated or supported

Normal Contact Force/reation force:

The force arising when an object rests against another object acting at a 90° angle to the plane of contact

normally labelled as _ or _ on free body diagrams

N or R

What was normal force arise because of

newton’s 3rd law

What is upthrust:

+equation

The upward buoyancy force acting on an object when it is submerged or partially submerged object experiences in a fluid

Upthrust= (h2- h1)pgA

What is friction:

The force that arises when two surfaces are in contact with each other/ FORCE THAT OPPOSES MOTION

The magnitude of the drag force depends on several factors, including:

• The speed of the object

• The object’s shape and texture

• The density of the fluid

what is terminal velocity?

• The drag force will increase until it is equal in magnitude to the weight of the object

• This leads to the object reaching a steady speed, known as its terminal velocity

• Opposing drag forces reduce the net force acting on an object and as a result, reduce the magnitude of the acceleration

What is it called when the drag force is equal to the gravitational pull on the body, and the body will no longer accelerate and will fall at a constant velocity

terminal velocity

V -T graph of parachutist

What is a moment?

turning effect of a force

/ force multiplied by the perpendicular distance between the line of action of the force and the turning point

Moment equation (given)

 Moment (N m) = Force (N) × perpendicular distance from the pivot (m)

Principle of moments:

For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)

Uniform beam

weight will act as its centre of gravity

Moments diagrams

What is a couple

pair of equal and opposite coplanar forces (act on same plane) that acts to produce rotation only

A couple consists of a pair of forces that are:

• Equal in magnitude

• Opposite in direction

• Perpendicular to the distance between them

What is the resultant force of couples and what does this mean

zero

according to newton’s 2nd law, object does not accelerate

Unlike moments of a single force, the moment of a couple doesn’t depend on a _____

pivot

The moment of a couple is equal to:

Force × Perpendicular distance between the lines of action of the forces

What is torque

moment of a couple

/ sum of the moments produced by each of the forces in a couple

Units of torque equation (given)

T=Fd

• τ = torque (N m)

• F = one of the forces (N)

• d = perpendicular distance between the forces (m)

The forces given might not always be perpendicular to the distance between them

find the component of the force vector that is perpendicular by resolving the force vector.The forces that make up a couple cannot share the same line of action which is the line through the point at which the force is applied.

centre of mass of an object is

point at which the weight of the object may be considered to act

For symmetrical objects with uniform density, the centre of mass is located at the ___ ___ _____

point of symmetry

An object is stable when its centre of mass lies above its _____

base

stability

• The wider base an object has, the lower its centre of mass and it is more stable

• The narrower base an object has, the higher its centre of mass and the object is more likely to topple over if pushed

A system is in equilibrium when all the forces are balanced. This means:

• There is no resultant force

• There is no resultant torque

Coplanar forces can be represented by ____ ______

vector triangles

In equilibrium, coplanar forces are represented by ____ vector triangles

closed

equilibrium represented in diagram

1 Pa is the same as ___

1 N/m²

units of equation of hydrostatic pressure P=hpg

P= Pressure (pa)

h=change in height (m)

p= density (kgm-3)

g=acceleration due to gravity (ms-2)

Archimedes’ principle states:

+WHY

An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid displaced by the object

Upthrust= (h2-h1)pgA= Vpg = mg= W

The object sinks until

the weight of the fluid displaced is equal to its own weight

object floats when the magnitude of the upthrust equals the _____ of the object

weight

magnitude of upthrust can be calculated by(learn):

F=pgV

F= upthrust/ buoyancy force (N)

p=density of a fluid (kgm-3)

g=acceleration due to gravity (ms-2)

V= volume displaced (m3)

how is that equation devised

Since m = ρV, upthrust is equal to F = mg which is the weight of the fluid displaced by the object

total pressure=

atmospheric pressure + hydrostatic pressure

Atmospheric pressure (also known as barometric pressure) is equal to ______

101 325 Pa

Work is defined as

The amount of energy transferred when an external force causes an object to move over a certain distance

If the force is _____ to the direction of the object's displacement, the work done can be calculated using the equation: W = Fx

parallel

What units mean in W = Fx

• W = work done (J)

• F = average force applied (N)

• x = displacement (m)

SI unit for energy

kg m² s^–2

1 Joule definition

The energy transferred to (or work done on) an object when a force of 1 N acts on that object parallel to its motion through a distance of 1 m

energy equations to learn

Transfer of energy = Work Done

Thermal (heat) is the work done on or by a system to transfer heat

E = mcΔT

• m = mass (kg)

• c = specific heat capacity (J kg^-1 K^-1)

• ΔT = change in temperature (K or °C)

Elastic potential energy is the work done in stretching or compressing an object

E = ½ Fx = ½kx²

• F = stretching or compressing force (N)

• x = extension (or compression) (m)

• k = force constant (N m^-1)

Nuclear is the work done by nuclei during the processes of fusion and fission

E = Δmc²

• Δm = mass defect (kg)

• c = speed of light

derivation of KE equation

derivation of GPE equation

power of a machine is

rate at which it transfers energy or the work done per unit time

units of P=Fv (given)

P= power (W)

F= force (N)

v= velocity (ms-2)

When to use P=Fv

• constant force moves a body at constant velocity. Power is required in order to produce an acceleration

• The force must be applied in the same direction as the velocity

deriving P=Fv

Newton's First Law states:

A body will remain at rest or move with constant velocity unless acted on by a resultant force

Newton's Second Law states:

The resultant force is equal to the rate of change in momentum. The change in momentum is in the same direction as the resultant force

What can newton’s 2nd law also be rewritten as:

F=ma (learn)

How if F=ma derived from the definition of momentum

Newton's Third Law states:

If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction

• Newton’s Third Law force pairs must act on two ___ objects

• Newton’s Third Law force pairs must also be of the ____ ___e.g. gravitational or frictional

• different

• same type

Linear momentum (p) is defined as the product of mass and velocity: P=mv (given)

P= Momentum (kg ms-1)

m= mass (kg)

v= velocity (ms-1)

momentum is a _____

vector

Force is defined as

rate of change of momentum (final momentum minus the initial momentum) on a body

F= ▵p/▵t (given)

F= Force (N)

▵p= change in momentum (kg ms-1)

▵t= change in time (s)

How to find ▵p

▵p= pf -pb

change in momentum= final p - before p

what can average force be worked out from?

F=▵p/▵t

F=resultant force

How to find impulse equation:

force and momentum equation can be rearranged to find the impulse. cuz impulse, I, is equal to the change in momentum: 

I = FΔt = Δp = mv – mu

unit for impulse

Ns