2.1 Forces

Vector

A Vector has magnitude and direction

Scalar

A Scalar has just magnitude

Momentum

Momentum is vector

Energy

Energy is scalar

Time

Time is scalar

Acceleration

Acceleration is vector

Force

Force is vector

Mass

Mass is scalar

Speed

Speed is scalar

Velocity

Velocity is vector

Distance

Distance is scalar

Displacement

Displacement is vector

Non-Contact Forces

Forces between objects that are physically separated.

Electrostatic Force

The charges cause a force of attraction/repulsion.

Gravitational Attraction

The mass creates a force of attraction.

Contact Forces

Forces between objects that are physically touching.

Normal Contact Force

The force felt in the opposite direction to contact.

Friction

The surfaces and their roughness cause friction when moved in contact.

Weight

The force exerted on a mass by the gravitational field, in Newtons.

Weight Formula

weight = mass × gravitational field strength

Weight Measurement

Measured by a force meter (also known as calibrated spring-balance).

Gravitational Field Strength on Earth

On earth, g = 9.8

Acceleration in Free Fall

Acceleration in free fall is due to gravity, and is the same as g, i.e. 10 m/s².

Resultant Force

A single force representing the sum of all the forces acting on an object.

Free Body Diagrams

Show the forces (and their directions) acting on an object.

Resolving Forces

A force F at angle 𝜃 to the ground can be resolved parallel and perpendicular to the ground.

Pythagoras' Rule

Used to find the two components of a force resolved at an angle.

Work Done

Calculated as Force × Distance.

Work Done Formula

W = Fs, where W is in joules J, F is in newtons N, and s is in metres m.

Distance in Work

Distance is the distance moved along the line of action of the force.

Energy Transfer in Work

Work done is when energy is transferred from the object doing the work to another form.

One Joule Definition

One joule of work is done when a force of one newton causes a displacement of one metre.

Work Against Friction

Work done against frictional forces causes a rise in temperature of the object.

Deformation

Changing shape of an object.

Elastic Deformation

The object returns to its original shape when the load has been removed.

Plastic Deformation

The object does not return to its original shape when the load has been removed.

Hooke's Law

The extension of an elastic object is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.

Hooke's Law Formula

F = kx, where F is the force applied, k is the spring constant, and x is the extension.

Force/Extension Graph

A linear line indicates the elastic region following Hooke's Law.

Limit of Proportionality

The point at which the relationship between force and extension stops being linear.

Brittle Material

If the graph is just linear with no non-linear end section, the material is brittle, so snaps instead of stretches after the elastic limit.

Work Done on a Spring

When a force stretches/compresses a spring, the spring does work.

Work Done Formula for Spring

Work Done = 1/2 kx², where elastic potential energy is stored in the spring.

Moments and Rotation

For an object attached to a pivot point, if a force is applied along a line passing through the pivot, the object does not rotate.

Moment of a Force

Calculated as force × perpendicular distance from the pivot to the line of action of the force.

Moment Formula

M = Fd, where M is in newton-metres Nm, F is in newtons N, and d is the perpendicular distance in metres m.

Example of Moments

Bike Riding - pressing your foot down on the pedal causes a moment about the pivot, turning the pedal arms.

Equilibrium

Equilibrium is when: sum of anticlockwise moments = sum of clockwise moments

Gears

Gears can change speed, force or direction by rotation.

Smaller Gear

If connected to a gear with fewer teeth (i.e. a smaller gear), the second gear will turn faster but with less force and in opposite direction to first gear.

Larger Gear

If connected to a gear with more teeth (i.e. a larger gear), it turns slower, more force, and in opposite direction.

Power Supply

The second gear will always turn in the opposite direction.

Buoyancy Force

The buoyancy force is the upwards force that counteracts the weight of the floating object.

Pressure

Pressure, p = force/area = F/A.

Pressure Units

Where the pressure, p, is in pascals Pa, the force, F, in newtons N and the area, A, in metres squared, m².

Floating Condition

An object floats if its weight is less than the weight of the water it displaces.

Pressure in a Liquid

Pressure in a liquid varies with depth and density, leading to an upwards force on a partially submerged object.

Weight of Displaced Fluid

This is equal to the weight of the fluid displaced by the object.

Ping Pong Ball

A ping pong ball floats on water as its density is less than the density of the water.

Pressure Increase with Depth

Increasing the depth increases the weight of the water above you, resulting in greater pressure felt.

Upthrust

Upthrust is the resultant force upwards experienced by a partially (or totally) submerged object due to greater pressure on the bottom surface than on the top surface.

Earth's Atmosphere

Earth's Atmosphere is a thin layer of air around the Earth that gets less dense with increasing altitude.

Atmospheric Pressure

The weight of the air is the force which causes the pressure; fewer air molecules at higher elevations result in less pressure.

Idealised Assumptions of Atmosphere

Isothermal, transparent to solar radiation, opaque to terrestrial radiation.

Momentum of Gears

To increase the power, a larger gear is used for the secondary (red) gear, as the force on the red gear is a further distance from its pivot.

Pressure Formula

p = hρg, where pressure p is in pascals Pa, height h in metres m, density ρ in kilograms per metre cubed kg/m³, and gravitational field strength g in newtons per kilogram N/kg.

Pressure Direction

Pressure produces a net force at right angles to any surface.

Weight of Boat

A 1000kg boat will sink into the water until it has displaced 1000kg of water, providing it doesn't completely submerge before displacing this amount.

Typical Speeds of Wind

5 − 7 m/s

Typical Speeds of Sound

330 m/s

Typical Speeds of Walking

~ 1.5 m/s

Typical Speeds of Running

~ 3 m/s

Typical Speeds of Cycling

~ 6 m/s

Typical Speeds of Bus

14 km/h

Typical Speeds of Train

125 miles/h

Typical Speeds of Plane

900 km/h

Speed Formula

speed = distance / time (v = d / t)

Average Speed Formula

average speed = total distance / total time

Displacement-Time Graph

Gradient is velocity; sharper gradient means faster speed.

Velocity-Time Graph

Gradient is acceleration; sharper gradient means greater acceleration.

Terminal Velocity

The constant speed that a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.

Newton's First Law

An object has a constant velocity unless acted on by a resultant force.

Inertia

The tendency for objects to continue in uniform velocity (or stay at rest).

Newton's Second Law

The acceleration of an object is proportional to the resultant force acting on the object, and inversely proportional to the mass of the object.

Kinetic Energy Formula

Kinetic Energy = 1/2 mv²

Force Formula

𝐹 = 𝑚𝑎 where F is the force in newtons N, m is the mass in kg and a is the acceleration in m/s².

Newton's Third Law

Whenever two objects interact, the forces they exert on each other are equal and opposite.

Rocket Taking Off

The rocket exerts a force on the gases being ejected. The gases apply a force equal in magnitude but in opposite direction on the rocket, which lifts it off the surface.

Book on a Table

The weight of the book (from the Earth) = the pull of the book on the Earth.

Vehicle Stopping Distances

Stopping distance = thinking distance + braking distance.

Thinking Distance

The distance traveled before a driver reacts after seeing a hazard.

Braking Distance

The distance over which a vehicle slows down and stops after the brakes are applied.

Factors Affecting Braking Distance

Speed, poor road conditions (icy, wet), bald tires (low friction), worn brake pads, weight (more passengers).

Factors Affecting Reaction Time

Speed, affected by reaction time, concentration, tiredness, distractions, influence of drugs/alcohol.

Speed and Braking Distance

Greater the speed, the greater distance traveled during the same time (reaction time).

Typical Stopping Distances

Measured by the 'ruler drop' method.

Reaction Times

Vary 0.2 − 0.9 seconds for each person.

Ruler Drop Method

Drop a ruler through the person's open hand, the time it takes to catch it can be determined by s = ut + 1/2 at² where u = 0, a = g, s = distance.

Work Done by Brakes

Work is done by the brakes (by friction) onto the wheel, reducing the vehicle's kinetic energy.

Braking Force and Speed

Greater the speed = greater braking force needed to stop the car (over the same distance).