Topic A - Mechanics

List SUVAT

S - displacement/distance - m 

U - initial speed/velocity - ms^-1

V - final speed/velocity - ms^-1

A - acceleration - ms^-2

T - time - s

Distance

How far in total an object has travelled

Displacement

How far an object has travelled from the start to finish in a straight line (with direction).

Speed

Total distance travelled per unit second

Velocity

Rate of change of displacement

Acceleration

Rate of change of velocity

What is the gradient on a displacement time graph?

The velocity

How do you measure the instantaneous velocity on a displacement time graph? 

Take the gradient of the tangent line of the point you are measuring.

What is the gradient on a velocity time graph?

The acceleration

What is the area under on a velocity time graph?

The displacement

What is the area under on a acceleration time graph?

The change in velocity

List the 5 SUVAT equations.

s = (u + v / 2)*t

v = u + at

s = ut + ½ at²

v² = u² + 2as

s = vt - 1/2at²

Define Projectile Motion

The motion of an object thrown into the air.

What is the only force that will be acting on a object after the initial force and if air resistance is negligible ?

Weight Force - 9.8ms^-2

What is the principle when air resistance isn’t negligible?

It is proportional to the square of the velocity.

• F = ½ ρAv²

State the air resistance formula

F = ½ ρ A v²

How does the path a projectile takes change when Air resistance is increased? (List 3 things)

• It reaches a lower vertical height

• It travels less far horizontally

• The path become asymmetrical with the section before the peak as it is longer than the section afterwards

What are the 4 main ways energy can be transferred?

Mechanically - an object moving due to a force acting on it

Electrically - a charge moving through a p.d

Heating - energy transferred from a hotter object to a colder object

Radiation - energy transferred by e.g. light/sound

Work

Amount of energy transferred from one stores to another.

State the mechanical work formula

W = Fscosθ

What is the difference if work done is negative or positive?

If the work done is positive then work has been done on the object, if it is negative then work has been done by the object.

What is the formula for GPE?

ΔE_p = mgΔh

What is the formula for EPE?

ΔE_H = ½ k (Δx)²

• Any object being deformed.

What is the formula for KE?

½ mv²

(½ mv² - ½ mu²)

• Any object in motion.

What does the area under a Force Displacement graph represent?

The work done.

State the law of conservation of energy

In any closed system energy cannot be created or destroyed it can only be transferred from one store to another.

•  ΔE_t = 0

• It is a law of physics and empirical.

Empirical 

Based on observations or experiments.

Theoretical

Based on theories or hypotheses.

Power

The rate of work done.

Define efficiency

The ratio of how much useful energy was put in, to how much useful energy was put out.

What are the 2 formulas for efficiency?

η = useful work out / total work in

η = useful power out / total power in

What is a Sankey diagram and what do they show?

A Sankey diagram is a visual representation of energy transferred in applications/scenarios.

What can a resultant force on an object change?

The objects shape (compresses, extend, deform) and the objects velocity (speed and or direction).

Tension

The force exerted by a string, rope, cable, spring etc.

It is the same along all points

What law must all elastic objects obey?

They must all obey Hooke’s Law, where force is proportional to extension.

What is weight force?

Mass x gravitational field strength.

What is Normal reaction force?

When one body tries to pass through another there is a force of reaction that opposes the applied force.

It is always perpendicular to the surface.

Friction

Opposes the motion of the applied force when one body tries to slide along another.

Always parallel to the surface.

Static friction

The friction acting on an object when there is an applied force and it stays stationary. It increases linearly until a maximum value. F_f <= μ_sF_N

Dynamic Friction

Friction force rapidly decreases to a constant value when the object is in constant motion. F_f = μ_sF_N

Buoyancy Forces

F_B = ρVg (ρ being the density of the fluid and v being the volume displaced of fluid - the volume of the object)

Objects which are less dense than the fluid float and the opposite for those that sink.

It arises due to differences in presssure between the top and bottom of a floating object.

Viscous drag

The frictional force between an object and a fluid which opposes the motion between the object and the fluid.

Viscous drag for a sphere is calculated using Stokes Law

Fd = 6πηrv (η being the coefficient of viscosity)

Newtons 1st Law

An object continues to move at a constant velocity or remain stationary unless acted upon by a resultant force.

ΣF = 0

Newtons 2nd Law

The resultant force on a body is equal to its rate of change in momentum.

ΣF = change in p / change in t

ΣF = ma

Newtons 3rd Law

For every action force there is always an equal and opposite reaction force.

These forces will act on two different bodies.

Linear momentum formula

p = mv

Define impulse and what is its formula?

Impulse is the change in momentum measured in joules.

J = Δp = mv-mu

J =FΔt

What is the area under a force time graph?

Impulse

Conservation of momentum

In a closed system, the total momentum of the system (collisions or explosions) remain constant.

This is possible beacuse momentum is a vector quantity

Closed system

The total mass of the system remains constant, and the net external force is zero.

Elastic collision

The total kinetic energy of the system before and after are the same.

Inelastic collision

The total kinetic energy of the system before and after is not the same.

What type of colision is it when the objects stick together?

The collision is said to be completely inelastic, because it reduces internal kinetic energy more than any other type of collision.

Time period

Time taken for 1 revolution

Frequency

Number of revolutions that happen per second.

How do you convert from rpm?

Divide by 60.

How do you calculate the number of radians in an angle?

θ = arc length / radius = s/r

How do you find the velocity of an object in circular motion?

v = 2πrf or v = ωr

What is Angular velocity and its formula?

Angle passed through per second.

ω = angle(rad)/time = 2πf or θf

For objects moving in circular motion what is the direction of the centripetal acceleration and the velocity?

The velocity is always tangent to the circle and the centripetal acceleration points towards the centre of the circle.

What are the formulas for a_c?

a_c = v²/r

a_c = ω²r

a_c = 4π²r/T²

What is centripetal force?

A label given to the resultant force pointing towards the centre.

What are the formulas for centripetal force?

F = mv²/r

F = mω²r

F = m4π²r/T²

What is the work done by the centripetal force?

There is no work done by the centripetal force as:

W = Fscosθ

W = Fscos90

W = 0J therefore no work is done or enrgy transferred by the centripetal force because force is perpendicular to motion.

Why isn’t a car going over a hill or a bung on the end of a string undergoing uniform circular motion?

Because the resultant force (centripetal force) isn’t always pointing towards the centre.

How do you convert from linear to rotational/angular motion?

Divide by the radius.

What is the moment of inertia?

Also known as angular mass, it is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.

Conservation of angular momentum

The total angular momentum of a closed system remains constant providing no external torque acts on the system.

When rolling an object on a flat surface what does the total energy equal?

E_T = E_k (linear) + E_k (rotational)

When rolling an object down a sloped surface what does the total energy equal?

At the start: E_t = mgh

When released E_t = ½ mv² + ½Iω²

What is torque?

The twisting effect of a force acting on object around a specific pivot point or axis

Couples

A pair of equal and opposite forces that do not act in the same straight line. This combination of forces produces a torque that causes an object to undergo angular acceleration but not translational acceleration (the object stays in place but will rotate on the spot).

When an object is not in equilibrium and is undergoing rotational motion what can be said about its angular speed, angular acceleration and torque?

• The angular speed is changing

• The angular acceleration is not 0

• 𝜏 = Iα

When an object is equilibrium and is undergoing rotational motion what can be said about its angular speed, angular acceleration and torque?

• The angular speed is constant

• The angular acceleration is 0.

• 𝜏 = 0