Simple Machines

Definition of work Work carries a specific meaning in physics 4/23/2008 Definition of work Work carries a specific meaning in physics Simple form: work = force  distance W = F x d Work is a measure of energy used You get tired doing work Spring 2008 2 Lecture 9 2

Doing work Work done = Force x distance moved (in direction of the force) In this case the effort move the same distance as the load The effort force is equal to the load force (weight of load) Load Effort

Making doing work easier Apply less force over larger distance for same work Machines were invented to make work easy (ramps, levers, etc. are simple machines)

4/23/2008 Ramps A ramp is a simple machine. A smaller force over a larger distance to achieve the same amount of work done (height raised) Same amount of work done in lifting the object Larger Force Small Force Short Distance Long Distance 5 Lecture 9 5

4/23/2008 Ramp Example How much work is needed to lift a 200 Kg mass vertically by 2 metres? The force needed is 200 x 9.81 (gravitational field strength) 1962 Newtons The work done is 1962 x 2 (metres) = 3924 Joules 2 m 6 Lecture 9 6

Ramp Example The work done pushing the block up a 10 metre ramp is also 3924 Joules (ignoring friction) The force needed is therefore 3924 ÷ 10 = 392. 4Newtons Which is 5 times less the lifting the block up vertically 2 m

4/23/2008 Work Examples How much work does it take to lift a 22 kg suitcase onto the table, 2meter high? (g =9.8 m/s2) How much work is done in pushing a crate 15 m across a floor with a force of 400N? Spring 2008 8 Lecture 9 8

Work Examples - Answers 4/23/2008 Work Examples - Answers How much work does it take to lift a 22 kg suitcase onto the table, 2 meter high? W = (22 kg)  (9.81 m/s2)  (2 m) = 431.6 J Pushing a crate 15 m across a floor with a force of 400 N requires 6,000 J (6 kJ) of work Spring 2008 9 Lecture 9 9

Force multipliers Simple Machines Work done = Force x distance moved (in direction of the force) Work done by effort = work done on load F x d (effort)= F x d (Load) The further the distance moved by the effort force compared to the distance moved by the load means that a smaller effort force can move a larger load force

Simple Machines Effort Load In the case of a lever the effort force moves further than the load so the less effort can lift a larger load

Simple Machines Diameter 400mm Diameter 200mm Driven pulley Driver pulley 20 RPM Driven pulley 10 RPM

Simple Machines A wheel and axle assembly used as a hoist the effort force again moves further than the load force Load Effort 100mm 400mm

Work is Exchange of Energy 4/23/2008 Work is Exchange of Energy There are two main categories of energy Useful energy and Potential energy (stored) Spring 2008 14 Lecture 9 14

Stored energy (Potential Energy) Gravitational potential energy (due to height) Mechanical potential energy (like in compressed spring) Chemical potential energy (stored in bonds) Nuclear potential energy (in nuclear bonds)

There are 4 types of useful energy Sound Light Heat Movement (kinetic)

Heat energy (specific heat capacity) Heat is not the same as temperature Specific heat capacity is defined as how much heat is required to raise the temperature of 1 Kg of a material through 1o C For example , it takes 4200 joules of energy to raise 1 Kg of water by 1 degree. The specific heat capacity of water Is 4,200 J/KgCo

Linear coefficient of expansion Heating a material such as a metal cause it to expand If a 10,000 meter steel railroad track with a coefficient of linear expansion of 12 x 10-6 per degree Celsius changes temperature from 18°C to 38°C. it will expand by 2.4 metres

Linear coefficient of expansion The coefficient of linear expansion (α) defines how much a material will increase in length when heated α= ∆L/Lo x ∆T ∆L = change in length Lo = original length ∆T = change in temperature ∆L = α x Lo x ∆T

Coefficient of friction This allows us to calculate the force needed to move one material over another μ = Force needed to move the object ÷ the weight of the object (in Newtons)

Coefficient of friction F = μ x wt ) Example Find the force required to move a 25 kg crate South across the floor (µ = 0.45) at a uniform speed.

Coefficient of friction F = μ x wt 25Kg = 245.25 newtons F =0.45 x 245.25 =110.37newtons

Power is the rate of using energy in joules per second Power, defined Power is the rate of using energy in joules per second 1 watt = 1j/s