Forces

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Scalar Quantity

A quantity that has a magnitude.

Magnitude

The size of a physical quantity.

Give some examples of scalar quantities.

• temperature (°C)

• mass (kg)

• energy (J)

• distance (m)

• speed (m/s)

• density (kg/m³)

How do you add scalar quantities?

• The sum of scalar quantities can be found by adding their values together.

• eg. Calculate the total mass of a 75 kg climber carrying a 15 kg backpack.

• 75 kg + 15 kg = 90 kg

How do you subtract scalar quantities?

• Scalar quantities can be subtracted by subtracting one value from another.

• A room is heated from 12°C to 21°C using a radiator. Calculate the increase in temperature.

• 21°C - 12°C = 9°C

Vector Quantity.

A quantity that has a magnitude and a direction.

Give some examples of Vector Quantities.

• force (N)

• displacement (km)

• velocity (m/s)

• acceleration (m/s²)

• momentum (kg m/s)

How can the direction of a vector be given?

• In a written description

• Drawn as an arrow (the length represents the magnitude/quantity)

Resultant Force

The single force that could replace all the forces acting on an object, found by adding these together. If all the forces are balanced, the resultant force is zero.

How do you calculate a resultant force with two forces in the same direction?

• Add the magnitudes of the two forces together

• Two forces, 3 newtons (N) and 2 N, act to the right. Calculate the resultant force.

• 3 N + 2 N = 5 N to the right

How do you calculate a resultant force with two forces in the opposite direction?

• Subtract the magnitude of the smaller force from the larger force

• A force of 5 N acts to the right, and a force of 3 N act to the left. Calculate the resultant force.

• 5 N - 3 N = 2 N to the right

What do vector diagrams do?

Vector diagrams are used to resolve (break down) a single force into two forces acting at right angles to each other.

Free Body Diagrams

A simplified drawing of an object or system showing the forces acting on it. The forces are shown acting away from the centre of a box or dot.

Do free body diagrams need to be drawn to scale?

No, but it helps if they are and you have to label each arrow with the force and magnitude it represents.

How would you draw and label a free body diagram of an accelerating speedboat?

Contact Forces

Force exerted between two objects when they are touching.

Give some examples of contact forces.

• Reaction Force (An object at rest on a surface)

• Tension (An object that is being stretched)

• Friction (When two objects slide past each other)

• Air Resistance (An object moving through the air)

What happens when an object experiences a contact force?

• Both objects experience the same size force, but in opposite directions

• This is Newton’s Third Law of Motion

Non-contact Forces

The push or pull acting between objects that are not physically touching when they interact.

Give some examples of non-contact forces.

• Magnetic Force (experienced by any magnetic material in a magnetic field) (two magnetic poles)

• Electrostatic Force (experienced by a charged particle in an electric field) (opposite charges)

• Gravitational Force (experienced by any mass in a gravitational field) (masses that attract)

• Weight (gravity exerts its force through a field, an object doesn’t need to touch earth to have a weight)

How can you find a resultant force?

• Adding two forces together

• Resolving a single force into two component forces at right angles to each other

How do you draw a vector diagram?

• Draw a right-angled triangle to scale, in which each side represents a force. Try to choose a simple scale, for example 1 cm = 1 N.

• Use the example for help.

Air Resistance

A force of friction produced when an object moves through the air.

Attract

Objects that tend to move together because of a force between them attract each other.

Charged Particles

Particles, usually ions or electrons, that carry electrical charges.

Electric Field

Area surrounding an electric charge that may influence other charged particles.

Electrostatic Force

A force of attraction between particles with opposite charges.

Friction

A force that opposes or prevents movement and converts kinetic energy into heat.

Magnetic

Able to be magnetised or attracted to a magnet.

Magnetic Field

Area surrounding a magnet that can exert a force on magnetic materials.

Mass

The amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g).

Reaction Force

Force exerted in the opposite direction to an action force.

Repel

Objects that tend to push apart because of a force between them repel each other.

Tension

Pulling force exerted by each end of an object such as a string or rope.

All objects with ____ produce a _______ _____. The more mass an object has the ________ its _________ ______ will be.

Mass, Gravitational Field, Greater, Gravitational Field

What is Gravitational Field Strength measured in?

• g is measured in N/kg

• 9.8 N/kg on Earth

• 1.6 N/kg on the Moon

What is the equation for Weight, W?

• mass x gravitational field strength

• m x g

The weight of an object and its mass are ____ _____________.

directly proportional

Weight

The force acting on an object due to the pull of gravity from a massive object like a planet. The force acts towards the centre of the planet and is measured in newtons (N).

Centre of Mass

The point representing the mean position of the matter in a body.

Component Force

One of two forces, at right angles to each other, that can be added together to form a resultant force.

Work

Energy transferred by a force. Work done = force × distance moved in the direction of the force.

Work Done

• The amount of energy it takes to do a task. Measured in joules (J)

• One joule of work is done when a force of 1 N causes a movement of 1 m so it can also be measured in Newton-metres (Nm)

What is the equation for Work Done, W?

• force x distance

• F x s

Compression

A shortening in length, for example, as a result of being squeezed.

Deformation

Changing shape and/or size as a result of forces being applied.

Elastic

Elastic materials return to their original shape and size after being stretched or squashed.

Elastic Potential Energy

Energy stored in squashed, stretched or twisted materials.

Extension

Increase in length, for example, as a result of being pulled.

Inelastic

• Inelastic materials do not return to their original shape and size after being stretched or squashed.

• The relationship between force and extension becomes non-linear

Limit of Proportionality

The point beyond which Hooke's law is no longer true when stretching a material.

Proportional

When two quantities have the same ratio or relative size. For example, current is proportional to voltage if the current doubles when the voltage is doubled.

What is Hooke’s Law?

A law stating that the strain in a solid is proportional to the applied stress within the elastic limit of that solid.

What is the equation for Hooke’s Law?

• Force = spring constant x extension

• F = k x e

• N = N/m x m

The higher the _____ _______ the _______ the spring

Spring constant, stiffer

Elastic Limit

The furthest point a material can be stretched or deformed while being able to return to its previous shape

Force-extension graphs

• Linear extension and elastic deformation can be seen below the limit of proportionality.

• Non-linear extension and inelastic deformation is above the limit of proportionality/elastic limit. The gradient of a force-extension graph before the limit of proportionality is equal to the spring constant.

______ is done when a spring is extended or compressed.

Work is done when a spring is extended or compressed

What is the equation for elastic potential energy?

• elastic potential energy = 0.5 × spring constant × (extension)²

• ^{Ee = 0.5 x k x e²}

• ^{J = 0.5 x N/m x m²}

Required Practical: how forces affect the extension of a spring

1. Secure a clamp stand to the bench using a G-clamp or a large mass on the base.

2. Use bosses to attach two clamps to the clamp stand.

3. Attach the spring to the top clamp, and a ruler to the bottom clamp.

4. Adjust the ruler so that it is vertical, and with its zero level with the top of the spring.

5. Measure and record the unloaded length of the spring.

6. Hang a 100 g slotted mass carrier - weight 0.98 newtons (N) - from the spring. Measure and record the new length of the spring.

7. Add a 100 g slotted mass to the carrier. Measure and record the new length of the spring.

8. Repeat step 7 until you have added a total of 1,000 g.

Required Practical: Results: how forces affect the extension of a spring

1. For each result, calculate the extension: extension = length - unloaded length

2. Plot a line graph with extension on the vertical axis, and force on the horizontal axis. Draw a suitable line or curve of best fit.

3. Identify the range of force over which the extension of the spring is directly proportional to the weight hanging from it.

Required Practical: Hazards: how forces affect the extension of a spring

• Equipment falling off the table → bruises from heavy objects → use a G-clamp to secure the equipment

• Sharp end of the spring recoiling if broken → damage to eyes + cuts → wear eye protection

• Masses falling → bruises from heavy objects → carefully add each mass onto spring

Axle

A bar, rod or shaft which passes through a wheel or gear. The wheel or gear will rotate around the axle.

Force

Force used to move a load over a distance.

Force Multiplier

Something that increases the effect of a force.

Gear

A toothed wheel used with other gears to turn axles at different speeds.

Lever

A simple machine consisting of a pivot, effort and load.

Load

The overall force that is exerted, usually by a mass or object, on a surface.

Moment

A turning effect of a force.

Pivot

A point around which something can rotate or turn.

Equation of a moment

• moment of a force = force × distance

• M = F x d

• Nm = N x m

If an object is _____ the total ______ _____ about a pivot is ____ to the total ________ _____ about that pivot

balanced, clockwise moment, equal, anti-clockwise moment

For a balanced object you can calculate:

• The size of a force

• The perpendicular distance of a force from the pivot

Give some examples of the different types of lever.

Arrangement of compoents	Examples
effort - pivot - load	see-saw, crowbar, scissors
pivot - load - effort	wheelbarrow, nutcracker
pivot - effort - load	tweezers, cooking tongs

How do simple levers work?

A simple lever could be a solid beam laid across a pivot. As effort is applied to rotate one end about the pivot. The opposite end is also rotated about the pivot in the same direction. This has the effect of rotating or lifting the load.

How do forces and moments act on gears?

• The forces acting on the teeth are identical for both gears, but their moments are different:

• If the driven gear is made larger is will rotate more slowly but with a greater moment. For example, a low gear ratio on a bike or car.

• If the driven gear is made smaller it will rotate more quickly but with a smaller moment. For example, a high gear ratio on a bike or car.

How do gears rotate?

As one gear turns, the other gear must also turn. Where the gears meet, the teeth must both move in the same direction. In the diagram, the teeth of both gears move upwards. This means that the gears rotate in opposite directions.

Altitude

A measure of an area’s height above sea-level

Atmosphere

The layers of gases that surround the Earth. The important gases in the atmosphere are nitrogen, oxygen and carbon dioxide.

Fluid

A substance that can flow, such as a liquid or a gas

Normal

Acting at an angle of 90° to a surface or boundary

Pressure

Force exerted over an area. The greater the pressure, the greater the force exerted over the same area. It determines the effect of force on a surface.

Up-thrust

Upwards force exerted by a liquid or gas on an object floating in it.

What is the equation for pressure?

• pressure = force ÷ area

• p = F ÷ A

• Pa = N ÷ m²

Pressure _______ as _____ increases in a ________

increases, depth, liquid

Equation for pressure in a liquid

• pressure = height of column (water) x density x gravitational field strength

• p = h x ρ x g

• Pa = m x kg/m³ x N/kg

Give two key features of the atmosphere.

• it is thin compared to the size of the Earth

• it becomes less dense (atmospheric pressure decreases) as the altitude increases

What is the atmospheric pressure at sea-level?

101,000Pa

What happens when altitude increases?

• the number of air molecules decreases

• the weight of the air decreases

• there is less air above a surface

Acceleration

The rate of change in velocity is measured in m/s²

Equation for Acceleration.

• Acceleration = change of velocity ÷ time taken.

• α= Δv ÷ t

• m/s² = Δm/s ÷ s

• or

• a = (v² - u²) ÷ 2s

Deceleration

Slowing down or negative acceleration

Displacement

Quantity describing the distance from the start of the journey to the end in a straight line with a described direction

Distance

Numerical description of how far apart two things are.

Gradient

Another word for steepness. On a graph, the gradient is defined as being the change in the 'y' value divided by the change in the 'x' value.

Rate of change

The amount of change in the size of a quantity each second.

Speed

The distance travelled in a fixed time period, usually one second.

Tangent

A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the tangent.

Velocity

The speed of an object in a particular direction.

What can the speed of a person walking depend on?

• age

• terrain

• fitness

• distance travelled