WORK

=Work= [image:https://i.imgur.com/8zZpqMT.png] ===Work is defined as a force moving through a displacement '''d''' where the displacement and force are in the same direction.=== ===Work is also equal to the '''Change in Energy''' of an object. Therefore the unit for work is the same as for any form of energy = Joules (J).=== ===The formula for work can also be put into a triangle to be rearranged.=== [image:http://i.imgur.com/CmprGmM.png?1] For instance, if it takes 100J to push an object 2.0m in the same direction as the force, the force applied can be calculated as follows. F = W ÷ d F = 100 ÷ 2 = 50 N Because energy is conserved, it takes the same amount of energy to lift a box as it does to push it up a ramp to the same position (ignoring any friction). In both cases the object gains the same amount of Gravitational Potential Energy. [image:http://i.imgur.com/lMJzqGK.png] The force is acting down towards the centre of the Earth and the displacement in the vertical direction (the height) is the same in both cases. While both methods require the same amount of energy, the force needed and the distance through which the force must be applied vary. Lifting the box requires greater force, but it is applied through a shorter distance. Pushing it up the ramp takes less force, but it must be applied through a greater distance. This is how many simple machines such as ramps, pulleys, levers and gears work. They trade-off the force required for the distance through which it is applied (or vice versa). ==Examples== ===Lifting the box:=== For instance, if the box has a mass of 10 kg and is lifted 2m the work done can be calculated as follows: [image:http://i.imgur.com/dsiSgXO.png?1] We must first calculate the Force required to lift the box. This is simply the weight force (force due to gravity) and can be calculated as follows. We can then calculate the work done. You'll notice that if you work out the Gravitational Potential Energy gained (Ep = m g h) you will get the same result. ===Pushing the box up a ramp:=== If the box is pushed 4m up a ramp, but reaches the same position, the work done must still be 200J (ignoring friction). The force required to push the box up the ramp can be calculated as follows: ===[image:http://i.imgur.com/v9qsuOS.png?2]=== If you look carefully at the two different methods you will notice that while they both require the same amount of energy, pushing the box up the ramp takes half the force, but twice the distance. In reality pushing the box may require slightly more energy because some energy is lost as heat due to friction between the box and the surface of the ramp. ===An object Changing Speed=== If a 2.0kg mass changes speed from 1.0ms^-1^ to 3.0ms^-1^ then its Kinetic Energy has been changed by: (Ek = 1/2 x 2.0 x 1.0^2^ = ) 1.0J to (Ek = 1/2 x 2.0 x 3.0^2^ = ) 9.0J Therefore the Work Done = Change in Energy = '''8.0J''' Now if the Work was done over a displacement of 2.0m, How big was the force applied in this direction? === W = F.d === === F = W ÷ d === === F = 8.0 ÷ 2.0 === ===F = 4.0N===