Chapter+3+-+WORK,+ENERGY,+POWER

Chapter 3 - WORK ENERGY POWER

=WORK= If an object is on the move the work done is force x distance moved in the direction of the force. If someone applies a force that's not in the direction of motion then components must be calculated.

W.D = F x S;
ONE joule, ONE newton, ONE meter. (It may take more force to move it)

A Prickly Situation...... Bill And Ben are transporting their cactus, but are having a disagreement about where it should go. Bill wants the cactus at the top of the slope, whereas Ben wants it at the bottom of the slope. Unfortunately for Ben, it appears Bill is stronger and is managing to overcome gravity as well!! The coefficient of friction between the plant pot and the slope is 0.8, the force applied by Bill down the slope is 200N, and the total driving force is 6/5 times the forces acting down the slope. Find the work done by the driving force, and the work done against friction. The cactus weighs 50Kg and the angle of incline is 30 degrees and it moves 10m.

(Bill can do it 10 times over on a ryvita) Solutions: Resolving Perpendicular: R = 50gcos30 = 424 N Resolving Parallel: 200 + 0.9R + 50gsin30 = 5x/6 Therefore x = 992 N W.D by driving force = 992.3 * 10 = 9923 Interestingly 9923 J are equivalent to 2.4 kcal (a tenth of a Ryvita!)

=CONSERVATION OF ENERGY= There are three forms of mechanical energy: Kinetic, Gravitational Potential (both as covered above), and Elastic Potential (but this isnt in M2)

The Principle of the Conservation of Mechanical Energy = The total mechanical energy can only change if..........1) A force other than gravity acts on the system such that work is done .....or..2) There is a sudden change in motion ie jerk in the string, or parts of the system collide

The Work-Energy Principle: Total Work Done = Change in Mechanical Energy

or expressed differently: Energy at the start = Energy at the end + Work Done

Example: A ball of mass 2kg is rolled along a straight road where the frictional force is of constant magnitude 2N. Its initial speed is 4ms-1. Find the speed after the particle has travelled 3m. NB This could be done using Newton's second law, F=ma, but for the purposes of M2 we will use the work energy principle

Energy at the start = Energy at the end + Work done 4^2 = v^2 + (2x3) Therefore....v^2 = 10 So, v = rt10 ms-1

=POWER= Power is the rate of doing work and is given by: Power = Driving force x Velocity

Example: Fortunate unfortunately drops the cake, soon after she works out its centre of mass. (see chapter on centre of mass for prequel) The only force acting on the cake is its weight, and its mass is 1.5kg. Assuming the cake remains in one piece on its descent, find its velocity at the moment when the power is 50W. Using Newtons Second Law, F=ma F = 1.5 x 9.8 = 14.7 N Power = Fv 50 = 14.7 x v Therefore v = 3.4ms-1