Chapter 6

 Energy is “conserved” meaning it can not be created nor destroyed Can change form Can be transferred  Total energy does not change with time.

 Forms  Kinetic Energy  Potential Energy  Heat  Unit: J (Joules)  1J = 1Nm = 1kg m 2 / s 2

s F W F > 0 s F W F = 0 s F W F < 0 s F W F > 0 Work means energy transfer.

angle  The angle  between the force and the displacement determines the sign of W.

θ=20º

F= 10 N  A force F = 10 N pushes a box across a frictionless floor for a distance s = 5 m. s F

30° 50 N W F = F s cos  =(50N)(5m)cos30 o = J You pull a chest (of weight 30N ) 5m across the floor at a constant speed by applying a force of 50N at an angle of 30°. How much work have you done?

You pull a 30 N chest 5m across the floor at a constant speed, by applying a force of 50 N at an angle of 30°. How much work did gravity do? How much work did normal force do? How much work did friction do? N

30° F=50 N

WFWF J WGWG 0J WNWN WfWf J W total 0J

You spent 216.5J of energy pulling. Gravity and normal force absorbed none of the energy. Friction absorbed all 216.5J of energy. Negative work doneabsorbs Negative work done means it absorbs instead of supplying energy.

W>0 gives If W>0, it means the force gives energy to the object. W<0 absorbs If W<0, it means the force absorbs energy from the object.

which force Make sure when you calculate the work done W, you know which force you are dealing with. In general, different force gives different work. Like in the previous example:

You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: 1. positive 2. negative 3. zero W W T T FNFN FNFN V V

You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: 1. positive 2. negative 3. zero W W T T FNFN FNFN V V

You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is: W W T T FNFN FNFN V V

You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: 1. positive 2. negative 3. zero W W T T FNFN FNFN V V

100J2kg If I did 100J of work to push an object of 2kg on a frictionless surface, what KE does it have in the end? Assume the object was initially at rest. What is the final velocity?

total work All this says is that the total work we do on an object goes into its KE. total work done all the forcesadd Note that this is total work done, not just the work of one of the forces. To calculate W total, you need to find the work of all the forces and add them up.

Alice and Bob are both pushing a box. Alice does 200J of work, Bob does -150J. What is the change in the KE of the box?

 You pull a 30 N chest 5 meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. What is the total work done? N

You are towing a car up a hill with constant velocity. The total work done on the car by all forces is: 1. positive 2. negative 3. zero W W T T FNFN FNFN V V

 3/6  Weighs the same as a quiz  HW + Lecture notes  Format similar to exam  More difficult questions than the quizzes

A 100W ( =100J/s ) light bulb consumes 100J of energy per second.

Engine of a jet develops a thrust of 15,000 N when plane is flying at 300 m/s. What is the power of the engine ?

 I swing a sling shot over my head. The tension in the rope keeps the shot moving in a circle. How much power must be provided by me, through the rope tension, to keep the shot in circular motion ? Rope Length = 1m Shot Mass = 1 kg Angular frequency = 2 rad/s v A) 16 J/sB) 8 J/sC) 4 J/sD) 0J/s

 Note that the string expends no power, i.e. does no work. Makes sense ?  By the work – kinetic energy theorem, work done equals change in kinetic energy.  KE = 1/2 mv 2, thus since v does not change, neither does KE.  A force perpendicular to the direction of motion does not change speed, v, and does no work.

Both measures power 1hp = 746W

Both measure energy 1kWh is the amount of energy dissipated by a 1000 Watts light bulb in one hour. Therefore: 1kWh = (1000J/s) (3600s)=3.6 × 10 6 J