WORK AND SIMPLE MACHINES

WORK Work is said to be done when a force acting on a body moves the body a certain distance in the direction of the force when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (motion in the direction of the force).

FORMULA FOR WORK The formula for calculating work is: Work = F × Δ D × Cosine(θ) In this equation F is the force, ΔD is basically the distance the object travelled and the θ is the one between the force and the direction of motion. If the object is traveling in a straight path the angle is 0 o and the Cosine(0) = 1 The unit for work is Joules (J)

SAMPLE PROBLEMS FOR CALCULATING WORK Work = F × Δ D × Cosine(θ) W=100N x 5meters x Cosine(0) W = 100Nx5metersx1 W = 500 J

SAMPLE PROBLEMS FOR CALCULATING WORK Work = F × Δ D × Cosine(θ) For this problem we know the distance and the angle but not the force The force in this case has to be calculated using the formula F=ma We are given the mass of 15kg since it’s moving towards the ground the acceleration is gravity 9.8 m/sec2 F = 15kg(9.8 m/sec2) F = 147N W= 147Nx5mxcosine (0) W = 735J 15kg A block of 15kg moves a distance of 5 meters at constant speed towards the ground.

EFFICIENCY Anything that does "Work" is transforming energy from one form to another. An example of this would be a motor transforming electrical energy to kinetic energy. In every situation there will be some energy lost, in the example of the motor some energy will be lost as sound and heat. This lead to the term efficiency. Efficiency tells us how much useful energy we can get from something given the energy we supply. Efficiency is expressed in terms of a percentage It shows us how many joules of useful energy we get for every 100J we supply

SIMPLE MACHINES Simple machines make work easier for us by allowing us to push or pull over increased distances. simple machines create a greater output force than the input force the ratio of these forces is the mechanical advantage of the machine. There are six simple machines that have been used for thousands of years, and the physics behind several of them were quantified by Archimedes.Archimedes These machines can be used together to create even greater mechanical advantage, as in the case of a bicycle.

MECHANICAL ADVANTAGE This takes a look at the ratio of the forces you put into moving something MA = F (output) / F (input) The F input is usually whatever is pushing or pulling the F output is usually the weight of the object

MECHANICAL ADVANTAGE If you push down on the piece of wood with a force of 30lbs to lift the 90lb weight from the floor the mechanical advantage of the lever is : MA = F(output)/F(input) MA = 90/30 MA = 3

SIMPLE MACHINES

SEE A REAL ONE IN ACTION

CALCULATING EFFICIENCY The most difficult part of these type of problems is determining the forces Keep in mind that for the most part the input is going to be done by a person on the machine In this diagram the boy does the input work on the lever

INPUT WORK We said that work was W= FΔ D × Cosine(θ) The Work Input by the boy pushing down = 120N (1meter) (cosine 0) = 120J

OUTPUT WORK For the output work (how much the crate moved with the force of the kid and the help of the lever) We said that work was W= FΔ D × Cosine(θ) The output work = 400N (.2meter) (cosine 0) = 80J

EFFICIENCY If we are asked to calculate the efficiency E = (Work output / Work input) x 100% E = (80/120) x 100 % E= 67%

FINALLY One last thing to point out since this can get confusing Mechanical Advantage is the number of times a machine increases the input force. Efficiency is the ratio of output work to input work. Remember that work only happens when an object is moved