Work and Energy 2
Work and Energy 2
Work and Energy 2
Work
Work is the transfer of energy through motion. In order for work to take place, a force must be exerted through a distance. The amount of work done depends on two things: the amount of force exerted and the distance over which the force is applied. There are two factors to keep in mind when deciding when work is being done: something has to move and the motion must be in the direction of the applied force. Work can be calculated by using the following formula: Work=force x distance
Work
Work is done on the books when they are being lifted, but no work is done on them when they are being held or carried horizontally.
Man does positive work lifting box Man does negative work lowering box
Gravity does positive work when box lowers Gravity does negative work when box is raised
Ekin = Wnet
y Yf = hf x
= Epot,initial Epot,final
mg
y
Yf = hf x
mg S
hf
Work done by gravity is independent of path taken between h0 and hf => The gravitational force is a conservative force.
W = S Wi = S Fs(si) s = (Fs(s1)+Fs(s2)+) s
Concept Question
Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed? 1. 2. 3. 4. Dropping Slide on ramp (no friction) Swinging down All the same correct
In all three experiments, the balls fall from the same height and therefore the same amount of their gravitational potential energy is converted to kinetic energy. If their kinetic energies are all the same, and their masses are the same, the balls must all have the same speed at the end.
Types of Energy
Kinetic Energy
Potential Energy
Forms of Energy
Radiant
Electrical
Chemical
Sound
Magnetic
Mechanical Energy
Mechanical energy is the movement of machine parts. Mechanical energy is also the total amount of kinetic and potential energy in a system. Wind-up toys, grandfather clocks, and pogo sticks are examples of mechanical energy. Wind power uses mechanical energy to help create electricity.
Mechanical Energy
Potential energy + Kinetic energy = Mechanical energy
or
Total mechanical energy of an object remains constant provided the net work done by non-conservative forces is zero: Etot = Ekin + Epot = constant
Ekin,f+Epot,f = Ekin,0+Epot,0
Otherwise, in the presence of net work done by non-conservative forces (e.g. friction):
Example Problem
Suppose the initial kinetic and potential energies of a system are 75J and 250J respectively, and that the final kinetic and potential energies of the same system are 300J and -25J respectively. How much work was done on the system by non-conservative forces? 1. 0J 2. 50J correct 3. -50J 4. 225J 5. -225J
Work done by non-conservative forces equals the difference between final and initial kinetic energies plus the difference between the final and initial gravitational potential energies. W = (300-75) + ((-25) - 250) = 225 - 275 = -50J.
Samar Hathout
Kinetic Energy
1 2 KE = mv 2
Same units as work
v2 f
Multiply both sides by m,
vi2 = ax 2 2
Example
Samar Hathout
Potential Energy
Potential energy exists whenever an object which has mass has a position within a force field (gravitational, magnetic, electrical). We will focus primarily on gravitational potential energy (energy an object has because of its height above the Earth)
Potential Energy
If force depends on distance,
PE = Fx
For gravity (near Earths surface)
PE = mgh
Samar Hathout
Conservation of Energy
PE f KE f = PEi KEi KE = PE
Conservative forces: Gravity, electrical, QCD Non-conservative forces: Friction, air resistance Non-conservative forces still conserve energy! Energy just transfers to thermal energy
Samar Hathout
Example
A diver of mass m drops from a board 10.0 m above the water surface, as in the Figure. Find his speed 5.00 m above the water surface. Neglect air resistance.
9.9 m/s
Example
A skier slides down the frictionless slope as shown. What is the skiers speed at the bottom?
start
H=40 m L=250 m
finish
28.0 m/s
Example
Three identical balls are thrown from the top of a building with the same initial speed. Initially, Ball 1 moves horizontally. Ball 2 moves upward. Ball 3 moves downward. Neglecting air resistance, which ball has the fastest speed when it hits the ground? A) B) C) D) Ball 1 Ball 2 Ball 3 All have the same speed.
F = kx
1 PE = (kx)x 2 1 2 PE = kx 2
PE=-Fx
F x
Example
A 0.50-kg block rests on a horizontal, frictionless surface as in the figure; it is pressed against a light spring having a spring constant of k = 800 N/m, with an initial compression of 2.0 cm.
x
b) To what height h does the block rise when moving up the incline? 3.2 cm
Power
Average power is the average rate at which a net force does work:
Pav = Wnet / t
Example
A 1967 Corvette has a weight of 3020 lbs. The 427 cu-in engine was rated at 435 hp at 5400 rpm.
a) If the engine used all 435 hp at 100% efficiency during acceleration, what speed would the car attain after 6 seconds? b) What is the average acceleration? (in gs) a) 120 mph b) 0.91g
Example
Consider the Corvette (w=3020 lbs) having constant acceleration of a=0.91g a) What is the power when v=10 mph? b) What is the power output when v=100 mph? a) 73.1 hp b) 732 hp (in real world a is larger at low v)