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Work power and energy - Grade: dwdwdwdwd
Dynamics Of Rigid Bodies (CE 002)
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Work, Energy and Power In this section of the Transport unit, we will look at the energy changes that take place when a force acts upon an object. Energy be created or destroyed, it can only be changed from one type into another type. We call this rule conservation of energy. Work Work and energy are the same thing. When a force moves something along any distance we say that work has been done and energy has been transformed (energy has been changed from one type to another type). The different kinds of energy that you will have met before are Kinetic Potential Light Sound Nuclear Heat Electrical Chemical For example, if a box is pushed across the floor, work has to be done to overcome the force of friction between the floor and the bottom of the box that is opposing the movement. How do we calculate the work done? Energy transformed work done applied force x distance We write this equation as WD F x d Example: A crate of mass 50kg is pushed along a floor with a force of 20N for a distance of 5m. Calculate the work done. Solution: Use WD Fxd 20N x 5m WD 100Nm But energy transformed work done Energy is measured in Joules (J) so Nm must be the same unit as J. This means we can say that WD 100J Note that the mass of the crate is not required to answer the question. The mass would be required if we needed to calculate the work done lifting the crate but not pushing it. Example: How far must a 5N force pull a 50g toy car if 30J of energy are transferred? Solution: Use WD F x d Rearrange to get so ! WD 30 F 5 d 6m Now we can use WD F x d to calculate the stored energy. WD F x d (mg) x d (mg) x h so WD mgh This tells us that the energy needed to lift something (E) is given E mass x gravitational field strength x height In other words, the potential energy stored in the object raising it up is given Ep mgh Example: A football of mass 2 is lifted up to the top of a cliff that is 180m high. How much potential energy does the football gain? Solution: Use Ep mgh 2 x 10 x 180 so Ep 4500J Power Power is the way we mearure how quickly energy is being changed. When we look at the power of a moving object, we are really looking at how fast work is happening. We define power as work done time taken Power and using symbols, we write this as ! (F x d) t Power is measured in Watts. ! Example: A person of mass 70kg runs up a flight of stairs with a vertical height of 5m. If the trip takes 7s to complete, calculate the power. Solution: WD Ep mgh 70 x 10 x 5 3500J Power work done 3500 time 7 so ! Power 500W Kinetic Energy Any moving object has Kinetic Energy (Ek). The kinetic energy of an object will increase if mass increases. The kinetic energy will increase if speed increases. We can calculate kinetic energy using the equation 1 Ek mv2 2 where m is the mass of the object and v is the speed. ! Notice that the speed is squared in the equation. This means that if speed is doubled, energy x 4 if speed is trebled, energy x 9 Example: How much kinetic energy has a 160g cricket ball when it is thrown at a speed of Solution: use 1 Ek mv2 2 x 0 x (22)2 ! 0 x 0 x 484 so Ek 38 Example: How fast is a trolley moving if it has 180 of kinetic energy? Solution: 1 Ek mv2 2 rearrange to get ! 2Ek so ! ! v2 2Ek m 2Ek 2x180 m 4 391 4 90 so v ! Potential and Kinetic Energy often appear in the same problems. Imagine a brick falling from a wall. The brick originally has only potential energy. As the brick falls, it loses potential energy but gains kinetic energy as it accelerates towards the ground. The total energy of the brick at any point in time is given the sum of the potential and kinetic energies and is always equal to the initial potential energy. This is due to the conservation of energy.
Work power and energy - Grade: dwdwdwdwd
Course: Dynamics Of Rigid Bodies (CE 002)
University: Technological Institute of the Philippines
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