Energy and Work

Energy  Energy – the ability to produce a change in itself or the environment.  If an objects position is changing, that may indicate that it has energy.  Energy due to an objects motion is called Kinetic Energy

Kinetic Energy and Work  KE = ½ mv 2  Energy is a scalar number. There is no direction associated with energy.  Work is defined as a process changing the energy in a system. Work is a vector.  W = Fd  ∆KE = W  This is called the Work-Energy Theorem

Mathematical Proof  v f 2 = v i 2 + 2ad  F=ma or a = F/m substitute for a  v f 2 - v i 2 = 2Fd/m  Multiply each side by 1/2m  ½mv f 2 - ½mv i 2 = Fd  KE f – KE i = W Or ∆KE = W  Units of Energy and Work are Nm or kgm 2 /s 2 or Joules (J)

Work  An agent in the environment exerts a force that displaces an object a distance and changes the amount of energy that object has.  If work goes in to the system W is + and energy If the system does work on the environment W is – and energy of the system

Work cont’d  Work only happens when force and displacement are occurring in the same direction.  Why does a planet in a circular orbit not have any work done to it?  If the force is at an angle to the direction of displacement, you must find the component of force in the same direction as the displacement.

 Work Clip Work Clip Work Clip  Assume he lifts the weight.3m how much work did he do? (2.2lbs/kg)  How much work does this guy do?  cAKShA&feature=related cAKShA&feature=related cAKShA&feature=related

Finding Work from a Graph  Since W=Fd  Finding the area under a force vs distance graph will give the work done by that force.  This is especially helpful if the magnitude of the force is changing.

Power  Power is the rate of doing work.  Lifting an entire box of books onto a shelf may take two seconds, lifting each book up on the shelf may take 20 minutes. The same amount of work is done but the power is different.  P = W/t  Units are J/s or Watts (W)  A watt is fairly small so many things are measured in kilowatts kW (1000W)

Power Practice  An electric motor lifts an elevator 9.00m in 15.0s by exerting an upward force of 1.20x10 4 N. What power does the motor produce in watts and kilowatts?  W = Fd W = (1.20x10 4 N)(9.00m)  W=10.8x10 6 J  P = W/t P = 10.8x10 6 /15.0s  P=7.2x10 3 W or 7.2 kW