Ch.5 Energy Energy comes in various forms:

When you apply a Force to an object and it moves a displacement (x), then you get done. i.e.(Weight is now w, not W) where: is the displacement, is the component of Force that is in the same direction as the displacement. is a scalar quantity with units of  

Work can be if the Force applied is in the to the displacement. i.e. the Work done by. ( removes from a system) e.g. Applying the brakes to stop a car. W = (θ = ) W is because Cos( o ) =

E.g. Calculate the Work done by pushing a 20kg shopping cart that’s at rest,15m with a 120N Force at 30 o below the horizontal. How fast will the cart be going after the 15m assuming a frictionless floor. m = 20kg x = 15m F = 120N θ = 30 o W = ? v f = ? 

When you push an object on a frictionless surface causing it to accelerate, you do to achieve this. When you release the object of, it moves with a constant. The object now has Energy of Motion known as: and is calculated by: (measured in Joules) So, the Net Work done is the change in the object’s Kinetic Energy.

E.g. A 250g ball at the top of a frictionless incline is pushed with an initial velocity of 2m/s. When it reaches the bottom of the 5m incline, it’s speed is now 10m/s. What Force (by Gravity) was needed to achieve this?

Gravitational Potential Energy (P E ) - is the Energy of an object due to its - It is stored energy that can be used to do e.g. holding a ball above the ground. The ball has the “potential” to fall to the ground. The higher the ball, the greater the potential. Remember:& so (in x direction) Now switch to y direction: Substitute and, and we get:

W g = Work done by gravity on an object. (please note that it is Initial – Final because the Force of Gravity points downward.) So, if an object falls, the work done by gravity is +ve.

When an external Force is increasing the height of an object, e.g. lifting something, then this is considered Working Gravity. And so Work is required to increase the object’s Potential Energy. Therefore: The Reference Level is arbitarily set. We usually choose the as the reference position for. This is not essential because we are only interested in

Reference Level At pt.A, the reference level is the At pt.B, the reference level is the At pt.C, the reference level is the They all have a value of zero for Potential Energy. (P E = 0)

N.B. that Work, PE & KE are. As stated before, we are interested in the difference between height and height, no matter what the path is. The is the same in each case because (y i – y f ) is 3m, even though they each came down a different way.

Conservation of Mechanical Energy When an object is in motion, it can possess both. Energy in a system can transfer from to, and vicey versi, with no loss of Energy from the system. i.e. Total Energy (E) (Assuming Conservative Forces only) So, E= Or we can say Total Energy before = Total Energy after. E i = E f

The Diver At the top, the diver only has Energy due to his position (height). As he falls, his is being converted into and so he gains speed. At the bottom, all his has been converted to. During the whole time, Total Energy has remained. E T =

Example: Using the Conservation of E: a.) Calculate the diver’s speed when he reaches the 5m mark. b.) Calculate the diver’s speed when he hits the water. (Is it twice as fast as in part a?) c.) Calculate the diver’s speed when he hits the water, but this time using a Kinematic equation.

The Pendulum A 50g pendulum bob hangs on the end of a string 1.5m long. It is then lifted such that the bob & string make a 60 o angle to the vertical. Calculate: a.) the change in it’s Potential Energy, and b.) the bob’s velocity at its lowest point.

Conservative Forces: A Force is considered conservative if the Work done by that Force is of the path it takes. i.e. only interested in the initial & final positions. E.g. is a conservative Force because the Work done by is independent of the path.

Non Conservative Forces A Force is considered Non Conservative if the Work done by that Force depend on the path it takes. e.g.

Conservation of Energy “Violated” Recap that W Nett =  KE = ½ mv f 2 – ½ mv i 2 Factoring in a Non Conservative Force like friction, then W Nett = W c + W nc where W c = -  PE (Work done by Gravity) so Realise that will be a –ve number reflecting that Energy has been removed from the system.

Example

Power Remember: Work is a Force applied over a distance. does not matter. e.g. If a 10N Force is applied over 5m, then the Work done is 50J. Whether it was done in or, the Work is still the same for both situations. To distinguish the difference between these 2 situations, we introduce the term. is defined as the rate at which Work is done.

i.e. Units: J/s = Watts (W) Substitute so or & for the Petrol Heads! 1 horsepower (hp) = 746 W

and in horsepower, must the motor operate at to lift the elevator up at a constant rate of 3.00 m/s?