# Mechanics-Work.Power&Energy

At the end of this section you should be able to: a. b. c. d. e. f. describe potential energy as energy due to position and derive potential energy as mgh describe kinetic energy as energy due to motion and derive kinetic energy as mv2/2 state conservation of energy laws and solve problems where energy is conserved define power as rate of energy transfer define couple, torque and calculate work done by variable force or torque solve problems where energy is lost due to friction

Table of contents: 3 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 3.4 3.5 3.6 3.6.1 3.6.2 3.6.3 Work, Power and Energy......................................................................................................................................1 Work done by a constant force .............................................................................................................................2 Work done by a variable force..............................................................................................................................3 Energy ..................................................................................................................................................................3 Potential Energy..........................................................................................................................................4 Formulae for gravitational potential energy................................................................................................4 Kinetic energy.............................................................................................................................................5 Formulae for kinetic energy........................................................................................................................5 Kinetic energy and work done ....................................................................................................................6 Conservation of energy.........................................................................................................................................7 Power....................................................................................................................................................................8 Moment, couple and torque ................................................................................................................................11 Work done by a constant torque................................................................................................................12 Power transmitted by a constant torque ....................................................................................................13 Work done by a variable torque ................................................................................................................15

Page numbers on the same topic in, Applied Mechanics, 3rd Edition, Hannah & Hillier Secti notes All of Section 3 Section in Hannah & Hillier Chapter 10 Excluding sections 10.4, 10.9, 10.11, 10.16, 1.17 Page No. in Hanna & Hiller 180 - 210

Fundamentals of Mechanics – Kinetics: Section 3 - Work, Powers and Energy

1

3.1

Work done by a constant force

When the point at which a force acts moves, the force is said to have done work. When the force is constant, the work done is defined as the product of the force and distance moved.

work done = force × distance moved in direction of force

Consider the example in Figure 3.1, a force F acting at the angle θ moves a body from point A to point B.

F

sθ s co

A

θ s

B

Figure 3.1: Notation for work done by a force The distance moved in the direction of the force is given by

Distance in direction of force = s cosθ

So the work done by the force F is

Work done = F s cosθ

Equation 3.1 If the body moves in the same direction as the force the angle is 0.0 so Work done = Fs When the...

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