Forces and Energy Exam Notes (copy)

Forces

• A force is a push, pull, or twist that can change the shape, size, or motion of an object.
• Forces are vectors, meaning they have both magnitude and direction.
• The units for force are Newtons (N).
• Forces are represented using arrows; the size of the arrow indicates the magnitude of the force.

Net Force (Resultant Force)

• The net force acting on an object is the sum of all forces acting on it.
• If the net force is zero, the object's motion does not change (it remains at rest or continues moving at a constant velocity).
• If there is a non-zero net force, the object will accelerate in the direction of the net force.

Newton’s 3 Laws of Motion

• Newton’s First Law (Law of Inertia): An object resists changes to its motion.
• Inertia is the resistance to a change in motion; the greater the mass, the greater the inertia.
• An object will remain at rest or move at a constant velocity unless acted upon by a net force.

*It's not just about objects staying still…

Newton’s Second Law

• If a non-zero net force acts on an object, it will accelerate.
• The relationship between net force, mass, and acceleration is given by the formula: F_{net} = ma
  • F = Force (N)
  • m = mass (kg)
  • a = acceleration (m/s²)
• Acceleration can be positive (speeding up) or negative (decelerating).
• Acceleration is also defined as the rate of change of velocity: a = \frac{v}{t}

Newton’s Third Law

• Every action force has an equal and opposite reaction force.
• Examples:
  • Jumping: A person applies a force downward; the Earth applies an equal and opposite force upward.
  • Rocket Launch: A rocket expels gas rearwards; the gas applies an equal and opposite force forward on the rocket.
  • Sitting on a Chair: Gravity pushes the chair down and the chair applies a reaction force upwards.
  • Standing on a Surface: Weight (force due to gravity) pulls us down, and the surface applies an equal and opposite reaction force upwards.
  • Buoyancy: Upward thrust from water on an object due to the weight of the object.
• Weight is a force measured in Newtons (N).

Friction

• Friction is the force between two surfaces moving or intending to move against each other.
• Friction is a contact force (requires physical contact).
• Friction always acts in the opposite direction to motion (or intended motion).
• Effects of Friction:
  • Slows down moving objects or makes it harder to start moving stationary objects.
  • Results in the objects heating up.

Resistance from Fluids (Drag)

• When an object moves through a fluid (gas or liquid), it experiences resistance due to friction from the particles in the fluid, termed "drag".
• Air resistance is drag due to an object moving through air (e.g., a car or airplane).
• Drag can be experienced in liquids like water or oil (e.g., a boat or ship).

Hooke's Law

• When a force is applied to an object, it may change shape or size (stretch, compress, bend, or twist).
• This requires more than one force acting on the object; otherwise, the object would simply move.
• If a spring is supported at the top and a weight is attached to the bottom, it stretches.
• Extension is the amount the object stretches.
• An elastic object returns to its original shape and length after the force is removed.
• An object that does not return to its original shape and length after the force is removed is permanently deformed.

Hooke's Law: Proportionality

• Load-extension graphs show how objects stretch.
• Load is the force or weight added to the end of the object.
• The first part of the graph is a straight line, indicating that extension and load are directly proportional.
• When the load gets large enough, the graph curves, indicating that load is no longer proportional to extension.
• The limit of proportionality (P) is the point where the graph starts to curve (load and extension stop being proportional).

Hooke's Law: Supplement

• The extension of a stretched spring (or certain other elastic solids) is directly proportional to the load or force applied: F \propto x
• This can be written as an equation: F = kx
  • F = force or load (N)
  • k = spring constant (N/cm or N/m)
  • x = extension (cm or m)
• k = \frac{F}{x}
• Ensure units match; if k is in N/m, extension must be in meters.
• The spring constant (k) is the force per unit extension, and depends on the material.
• A stiffer spring has a greater spring constant.
• The equation also works for compression, where x is the difference between the natural and compressed lengths.
• The proportion no longer applies if the load gets too great (beyond the limit of proportionality).

Moments

• Forces acting around a fixed point (pivot) have turning effects called moments.
• Moments are used in everyday life (e.g., door handles, spanners).
• The moment of a force is a measure of its turning effect.
• The size of the moment is given by: moment = force × perpendicular distance from the pivot M = Fd
  • M = moment (Nm)
  • F = force (N)
  • d = perpendicular distance from the pivot (m)
• The perpendicular distance is the distance from the pivot that forms a right angle with the line of action of the force applied.

*Moments in a seesaw

• A Question of Balance - Are the Moments Equal?
• To get the maximum moment (or turning effect) you need to push at right angles (perpendicular) to the spanner.
• Pushing at any other angle means a smaller moment because the perpendicular distance between the line of action and the pivot is smaller.

Moments in a Seesaw

• The principle of moments states:
  • If an object is balanced, then total anticlockwise moments = total clockwise moments.
• Example:
  • A person weighs 300 N and sits 2.1 m from the pivot of a seesaw. If you weigh 700 N, where should you sit to balance the seesaw?
  • Total anticlockwise moments = total clockwise moments
  • 300 \times 2.1 = 700 \times y
  • Where should you sity = 0.90 m

Moments in a Seesaw Supplement

• In seesaws, the forces are acting downwards, but sometimes forces are acting upwards.
• If a light rod is supported at both ends, the upwards force provided by each support will not always be the same.
• If a heavy object is placed on the rod, the support closer to the object will provide a larger force.
• Example:
  • A 6 m long light rod is suspended horizontally by two cables (A and B) at its ends. A 900 N weight is placed 4 m from one end.
    
  • To work out the forces, start at one end and treat that end as a pivot.
  • Clockwise moment around B = anticlockwise moment around B
  • T_A \times 6 = 900 \times 4
  • T_A = \frac{3600}{6} = 600 N
  • Then work out the force in B knowing vertical forces balance:
  • 900 N = TA + TB
  • TB = 900 - TA = 900 - 600 = 300 N

Unequal Moments

• If the total anticlockwise moments do not equal the total clockwise moments, there will be a resultant moment, so the object will turn.
• There can be several forces acting on each side of a pivot.
• In this case, work out the moment created by the weight of each child and add them together to give you the total clockwise moment.

Moments and Equilibrium

• If an object's motion isn't changing in any way, and it isn't rotating either, it is in equilibrium.
• Two conditions must be met for an object to be in equilibrium:
  1. There is no resultant force on the object.
  2. There is no resultant moment (total clockwise moment = total anticlockwise moment about any pivot).
• A uniform beam balanced on a pivot will be in equilibrium if the center of gravity of the beam is exactly over the pivot so that the weight of the beam doesn't cause a moment.

The Moment of a Force

• The moment of a force is bigger if the force is bigger.
• The moment of a force is bigger if it acts further from the pivot.
• The moment of a force is greatest if it acts at 90° to the object it acts on.

Center of Gravity

• The entire mass of an object can be thought of as being concentrated at a point called its center of gravity.
• A freely suspended object will swing until its center of gravity is vertically below the point of suspension.

Centre of Gravity of Regular Shaped Objects

• For a symmetrical object of uniform density, the center of gravity is located at the point of symmetry.
• E.g., the center of gravity of a sphere is at the center.

Center of Gravity

• The line of action is the imaginary line from the center of gravity (weight) to the ground.
• If the weight force and contact force are in the same line of action, there will be NO RESULTANT FORCE.
• If the line of action of weight falls outside the base, there will be a RESULTANT FORCE, and the object will not be stable, so it will topple over.

Center of Gravity: Stability of Objects

• An object will be stable (harder to tip over) if it has a low center of gravity and a wide base area.
• The higher the center of gravity and the smaller the base area, the less stable the object will be.
• If you tilt an object such that its center of gravity is no longer directly over the point of contact with the ground (which acts as a pivot), there will be a turning effect or moment.
• A suspended object swings until its center of gravity is below the pivot.

Energy Stores and Energy Transfers

• Energy exists in energy stores and can be transferred between them.
• Seven energy stores:
  1. Kinetic: Energy of anything moving.
  2. Gravitational Potential: Energy of anything that will fall (or would if it were not supported).
  3. Chemical: Energy that can be released by chemical reactions (e.g., food, fuels).
  4. Elastic (Strain): Energy stored in anything stretched (e.g., springs, rubber bands).
  5. Nuclear: Energy released from atomic nuclei in nuclear reactions.
  6. Electrostatic: Energy between two charges that attract/repel each other.
  7. Internal (Thermal): Energy of any object (the hotter it is, the more energy it has).

Ways Energy can be Transferred

• Between objects and from one energy store to another.
• Four main ways:
  1. Mechanically: Work is done by a force acting on an object (e.g., pushing, pulling, stretching, squashing).
  2. By Waves: Energy being transferred by waves (e.g., light, electromagnetic waves, sound).
  3. Electrically: Work is done by an electric current flowing.
  4. By Heating: Energy being transferred from a hotter object to a colder object.

The Principle of Conservation of Energy

• Energy can be stored, transferred from one store to another, or dissipated, but it can never be created or destroyed.
• Dissipated means energy is spread out and lost to the surroundings.
• When an energy transfer takes place, the same amount of energy comes out as was put in.
• Not all energy is transferred usefully; some energy is wasted (often transferred to the internal energy stores of objects and surroundings).

Efficiency

• Devices transfer energy, but only some of that energy goes to useful energy stores.
• Some input energy is wasted by being transferred to an energy store that isn't useful, usually internal energy stores.
• The less energy that is wasted, the more efficient the device or process is.
• Efficiency is the proportion of input energy that is transferred usefully.
• Efficiencies are usually stated as percentages.
• Due to conservation of energy, total input energy always equals total output energy.
• If a device is 75% efficient, this means it transfers 75% of its input energy usefully and wastes 25% of its input energy.
• No real device or process is 100% efficient.

Calculate Efficiency

• Efficiency = (useful energy output / total energy input) × 100%
• Efficiency = (useful power output / total power input) × 100%

Kinetic and Gravitational Potential Energy Stores

• Anything that is moving has energy in its kinetic energy store.
• The amount of energy depends on the object's mass and speed.
• Kinetic Energy: E_k = \frac{1}{2}mv^2

*A car with a mass of 2500 kg is traveling at 20 m/s
What is the amount of energy in its kinetic energy storeE_k = \frac{1}{2} \times 2500 \times 20^2 = 500000 J

Gravitational Potential Energy Stores

• Lifting an object in a gravitational field transfers energy to its gravitational potential energy store.
• The energy depends on the object's mass, its height, and the strength of the gravitational field.
• Change in Gravitational Potential Energy: \Delta E_p = mg \Delta h
  • \Delta E_p = Change in gravitational potential energy (J)
  • m = mass (kg)
  • g = gravitational field strength (N/kg, approximately 9.8 N/kg on Earth)
  • \Delta h = Change in height (m)
• When an object falls from a height, it's accelerated by gravity, and some of the energy in the object's gravitational potential energy store is transferred to its kinetic energy store.
• If there is no air resistance, then:
  • Energy lost from the gravitational potential energy store = Energy gained in the kinetic energy store.
• In real life with air resistance, some of the energy is transferred to other energy stores, e.g., the internal energy stores of the object and the surroundings.

Energy Resources

• Energy resources are either renewable or non-renewable resources.

Non-Renewable Energy Resources

• Non-renewable energy resources cannot be made at the same rate as they are used and will one day run out.
• Fossil fuels (coal, oil, natural gas) and nuclear fuels (e.g., uranium, plutonium).

Renewable Energy Resources

• Renewable energy resources can be made at the same rate (or faster) than they are used, so they will never run out.
• Solar, wind, water waves, hydroelectricity, biofuels, tides, geothermal.

Generating Electricity from Fuels

• One common method of generating electricity is using one of the three fossil fuels in big power stations. The power stations that use each fuel are all very similar. The typical features of a fossil fuel power station show below.
  *Note Turbine
  **Make sure you really understand that bit about how turning a turbine ends up generating electricity including energy transfers involved. With that memorized, you're halfway to telling the examiner how we get energy from fossil fuels, nuclear, biofuels, wind, geothermal, tides and hydroelectric the only exception is solar power. Read on for more on these energy resources.

Reliable and Available Non-Renewables

• Fossil fuels and nuclear fuel are readily available energy resources — there are enough fossil and nuclear fuels to meet current demand. This means power stations always have fuel in stock and can generate a reliable electricity supply. This also means that the power stations can respond quickly to changes in electricity demand.
• They also take up relatively little space per unit of power produced. This means they can produce energy on a very large scale, with one power station alone producing large amounts of energy.

Environmental Problems Created by Non-Renewables

• Coal, oil, and gas release carbon dioxide (CO2) into the atmosphere when they are burned. This CO2 adds to the greenhouse effect and contributes to global warming.
• Burning coal and oil also releases sulfur dioxide, which causes acid rain., which can be harmful to trees and soils and can have far-reaching effects in ecosystems.
• Although generating electricity using nuclear fuel produces very little of the pollutants produced by fossil fuel power stations, the nuclear waste it produces is very dangerous and difficult to dispose of.
• Nuclear power stations always carry a risk of a major catastrophe, like the Fukushima disaster in Japan.

Solar Power

• The Sun isn't just good for making our days bright and warm. It can be a powerful renewable energy resource for heating and generating electricity, thanks to some useful bits of technology.
  All the Energy on Earth starts at the Sun

Solar Cells — Expensive but Not Much Environmental Damage

• Solar cells generate electric currents directly from sunlight often Solar cells are attached together to form a solar panel.
• The only place this isn't true is on the equator, where days
  are always 12 hours long.

Wave Power - Lots of Little Wave-Powered Turbines

• There is no pollution. The main problems
  are disturbing the seabed and the
  habitats of marine animals, spoiling the
  view and being a hazard to boats.
• Wave power is never likely to provide energy on
  a large scale, but it can be very useful on small islands.

Tidal Barrages - Using the Sun and Moon's Gravity

• Tides are used in lots of ways to generate electricity.
  turbines
  They also don't work when the water
  level is the same either side of the barrage this happens four times a day because of the tides.

Biofuels and Wind Power

• Biofuels are a renewable energy resource created from plant products or animal dung.
  They have Pros…
  1) Generating electricity using biofuels is theoretically carbon neutral

Wind Power-Lots of Wind Turbines

• There's no pollution (except for a bit when they're manufactured)…
  There's no permanent damage to the landscape - if you remove
  the turbines, you remove the noise and the view returns to normal.

Geothermal and Hydroelectric Power

Geothermal Power - Energy from Underground

Electricity - very few environmental problems - release some CO , from underground but it much less than fossil fuel power station

Hydroelectric Power Uses Falling Water

• Hydroelectric power generates electricity from the energy in the kinetic energy stores of falling water.
  Flooding of the valley

Work

• Work (like a lot of things) means something slightly different in physics to what it means in everyday life…

'Work Done' is Just 'Energy Transferred'

• Whether the force is friction or weight or tension in a rope, it's the same equation.

Power

• Power is a measure of how quickly work is being done, i.e., how much energy transferred per second.

• The unit of power is the watt (W), where 1 W = 1 J of energy transferred per second (J/s).

• to Calculate Power you Divide Energy by Time and energy transferred is equal to work done
  Power = \frac{Energy \, transferred}{Time \,taken}

• P =$\frac{\Delta E}{t}$