# Work and Energy

- Created by: Jenna k
- Created on: 08-04-14 08:35

## Work and the conservation of energy

**Work >** The product of a force and the distance moved in the direction of that force. Also referd too as the converstion of energy form one form to another, measured in joules.

**Joule >** Unit of energy 1J is the work done when a force of 1N moves its point of application 1m in the direction of the force.

Work can be calaculated by **W=Fx** and **W=Fxcos(0)** is the force is at an angle.

**Conservation of energy: ** **In any closed system energy may be converted from one form into another, but cannot be created or destroyed.**

Interms of sankey diagrams, which simulates a closed system, one can see where the energy is used and converted.

Work done is equal to the treansefer of energy. One would need to use this to solve problems.

## Kenetic energy and potential energy

Potential energy:

One needs to remember using the formular F=ma. One then needs to Weight=massx gravity. This is ten used in addition to W=Fx. So one would expect to find. **F=mgh (Force + Mass x gravity x distance)** This equation whould give one a method to work out the gravitational potential energy of an object near the Earths surface.

Kenetic energy:

Kenetic energies apply to moving bodies which equales the work it can do as a result of its motion. For one to calculate the kenetic energy of an object one would use **k.e = 1/2 mv^2.** Kenetic energy is the energy that is needed to get the oboject to the velocity it is going. Not the maintaing of the velocity.

One will be asked about the convertion os gravitational energy to kenetic energy when an object is falling and visa versa. When an object is at a height and is dropped it has no kenetic energy to start will. Hoever there is it maximum potential energy. Once moving downwards the GPE decrease and KE increases. This is proof for conservation of the energy in the potential to fall and the speed that height creats.

## Power and Efficiency

**Power > The rate at which work is done.**

**Watt > unit of power. (1W = 1Js^-1)**

Once has a choice of power related equations to choose form but the recomended eqaution is Power = Work done / time taken.

**Efficiency**

One must know that efficiency is worked out in per centage and out of 100%. However you will never find an appliance that is 100% effiient becasue everything looses heat, which is a convertion of energy.

The eqaution that dinfines efficiency is; **(Useful energy out / total energy in ) x100%** This can be done with power too; **(Useful power out / total power in ) x100%**

**One will need to be able to apply this to sanky diagrams.** One will need to understand and draw one, so you need to know this well.

## Deformation os materials.

Everything moves and changes shaped when a force is applied to it. It's a question of whether it returns to its orgional shape (elastic) or stays is it deformed state (plastic).

**Tensile forces >** when objects are stretched. When two equal and opersite forces are applied to stretch the object.

**compressive forces >** when a objects is squeezed. When two equal and oppersite force are applied to compres the object.

**An experiment to measure the elastic limit of a wire.** Clamp a wire at one end of the table and guid it over a pull at the other end of the table. Place a ruller under neath it and a marker on the wire. Place masses on the end of the wire by the pully and record the movement of the marker each time a mass is added. Draw a graph from this. It should show you that there is a point at which the graoh stops increaseing and starts to platoe. This is when it reaches its elastic limmit and becomes plastic.

## Hooks law

What I discribed on the previous page was an experiment that Hook used to find his force constant. He suggested that: **The extention of an elastic body is proportional to the force that causes it.**

In equation form this becomes F=Kx where F is the force causing extention, K is the force contant and x is the distance it extended by.

This can be shown by plotin a graph of extention and tention. The area under the line would be the work doen by the force on the wire. So work done can be found by 1/2Fx. In addition with F=Kx the new eqution is Work done = 1/2 x Kx^2 This is also used to find the **elastic potential energy.**

## Youngs modulus; stress and strain

**Stress >** The force per unit cross-sectioal area measured in pascals.

**Strain >** Extention per unit length

**Young modulus >** The ratio between stress and strain measured in pascals.

**Ultimate tensile strength >**The maximum stress that can be applied to and object before it brakes.

Y = stress/strain = (force/area)/(extention/length) = Force x length / extention x area.

**An experiment to measure young mondulus.**

Clamp a wire at one end of the table and guid it over a pully at the other end of the table. Place a ruller under neath it and a marker on the wire. Place masses on the end of the wire by the pully and record the movement of the marker each time a mass is added. You also need to meausre the origional length of the wire and the cross-sectional area of the wire. You then plot a graph of force by extention. The straight line part is the young modulus. Here you fnd the gradient. You must then work out the cross sectional area and extention of the wire. The gradient woul be equal to F/x so F/x x L/A would eqaul the young modulus measured in pascals.

## Categories of materials ; Ductile

Ductile > Materials that have a large plastic region.

When put under pressure the material will increase in length and decrease its cross sectional area. This is becasue when you but material under tention the atoms rearage themsleves so they can stretch more. So a cross-section of 4 atoms then becomes 2 and one and then it brakes.

Look at the graph below. In terms of Stress and strain ductile materials have a large plastic region (OL). However the graph shows that at E there is a maxiums stress applied. This is known as **untimate tensile stress.** The area underneath the graph decreases showing that there is an increase in stress applied. In between Y and B is the plastic region. And at B the wire snaps.

## Categories of materials: Brittle

**Brittle > ** A material that distrots very little even when subject to a large stress and soes not echinit and plastic deformation. (Concrete)

This graph shows a small area under neath the graph which indecated that the **elastic potentail energy** has been stored in the material. This material will maintian under high stress but will eventually just snap. It does not reach a plastic region only and elastic region.

## Categories of materials; Polymeric

**Polymeric materials >** A material made of many smaller molecules bonded together, often making tangled long chains. These materials often exhibit very large strains. (Rubber) When a strain is applide to the polymeric material it's chains bcome straight and dont brake.

Like this graph below shows there is little stress and a lot of strain which tell us that the the materials bend and have a tensile ablity. However we know that such materials can also be compressed and they still have a low amount of stress and strain. The the end point the material will brake completly however there is a period of elastic postential and a nearly plastic period.

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