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Mechanics : Chapter �Work, Energy and Power

�(www.dilanmaths.com)

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What do we understand by Work?

If an object has energy => it can do work.

Work transfers energy from one place or form to another.

Work is done by a force when it moves an object.

 

Directions must be consistent (if not, use components)

 

A horizontal force of 8N moves a box 5m across a horizontal floor. Calculate the work done by the force.

 

?

Units:�If force is in Newtons (N) and distance in meters (m)�=> Work is in Joules (J)

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What do we understand by Work?

 

 

 

 

 

 

 

 

 

 

 

Both (always) give the same answer

Note: Work done by Y = Work done against friction + Work done against gravity + Kinetic energy gained.

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An Example

 

 

Solution to a)

 

 

 

 

 

No change in kinetic energy

 

Diagram?

 

 

Solution to b)

 

Solution to c)

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Exercise 4A

Pearson Mechanics 2

Pages 101-102

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Energy

 

 

 

 

 

 

Units: Energy, like work, is measured in Joules (J).

 

 

 

 

Let: F=ma and distance = s

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Quickfire Kinetic Energy

Mass

Velocity

Kinetic Energy

10 kg

5 m/s

125 J

2 tonnes

​

9000 J or 9 KJ

4 kg

​

50 J

20 kg

​

1690J

?

?

?

?

Fill in the gaps in the table below

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An Example

 

 

10m

 

3

4

5

 

Note: The answer to part a was given to 3 S.F.(176)

Answers given to more than 3.S.F. claim ‘unjustifiable accuracy’ (as g = 9.8 which is only accurate to 2 S.F). This looses marks in the exam.�Give final answer to 2 or 3 significant figures.

However the full figure (176.4) was used as an input to the working in part b – this ensures answers to subsequent parts are as accurate as possible.�Use unrounded values in working.

Solution to b)

(a)

Solution to a)

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Test Your Understanding

?

Edexcel M2 Jan 2005 Q3 (modified)

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Exercise 4B

Pearson Mechanics 2

Pages 105-106

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The law of Conservation of Energy

  • Initial Energy = Final Energy
  • Work in + Initial K.E. + Initial G.P.E. = Final K.E. + Final G.P.E. + Work out

 

The law of Conservation of Energy: the total energy of an isolated system remains constant

Some of the initial energy might have been stored in an engine or battery that then does work, transferring this energy to another form.

Some of the energy may be ‘lost’ if the object did work against a resistive force which transfers some energy into heat (and perhaps sound etc.)

Using the formulae we get:

The idea underlying this formula is the ‘work energy principle’

  1. In chapter 3 we will also add Elastic Potential Energy (the energy stored in a spring) to each side of this equations

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An Example

 

 

Solution (1st part)

 

 

 

0

8

 

 

 

There is no driving force: The particle is given initial kinetic energy but is not ‘powered’ or ‘driven’ up the slope after the initial ‘projection’

Define the starting position as G.P.E. =0

The particle comes to instantaneous rest => Final K.E. = 0

Driving force?

Initial G.P.E?

Final K.E?

Diagram?

 

 

 

 

Solution (remainder)

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Another Example

 

 

?

Note: It is not that common for skiers to ‘do work’. They mostly rely on their G.P.E. to slide downhill.

In this question the skier does do work and may look more like the skier in the bottom of the two pictures on the right.

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Test Your Understanding

Edexcel M2 June 2007 Q4

 

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Test Your Understanding

Edexcel M2 June 2007 Q4

 

 

a?

 

b?

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Exercise 4C

Pearson Mechanics 2

Pages 109-110

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Power

 

Directions must be consistent (if not, use components that do have consistent directions)

 

 

 

 

?

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An Example

 

T

600

6

a

 

 

T’ used instead of T as the force has changed

b?

Diagram?

a?

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Test Your Understanding

Edexcel M2 June 2003 Q6

?

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Exercise 4D

Pearson Mechanics 2

Pages 114-115