Transcript Work and Energy

Work and Energy
 Remember that a force is a push or a pull. When
we push or pull an object through a distance, we do
work.
 Work is a form of energy. All energy is measured
in Joules (J). 1 J = 1 Nm = 1 kg m2/s2.
 But what is energy?
 Energy: The ability to do work.
Work equation
W = F d
 Where W = the work done (in J)
 F is the force (in N)
 d is the distance through which the force is exerted
(in m)
 For this equation, the force and the distance moved
must lie along the same line.
 Tug of war example
Work equation
 Often, the work done is lifting an object against the
force of gravity. In that case, the force is equal to the
weight of the object.
 If a force is exerted but there is no movement, then
there is no work!
Work example
 Sally Student lifts a 2.0 kg book 1.0 meter from the floor.
What is the work that Sally has exerted on the book?
 W = Fd in this case the force is due to the weight of the
book (F = mg)
 W = (2.0 kg) (9.8 m/s2) (1.0 m)
 W = 20 J
 Now Sally holds the book over her head. What is the
work she is now exerting on the book?
 W = 0 J (no movement = no work)
Work at an angle
 What if the work and the distance don’t lie along the
same line?
 In this case, we need to use the component of the force
that is in the same direction as the distance.
 W = Fd cos 
 Where  is the angle between the direction of the force
and the direction of the motion.
 Note if the force and the distance are perpendicular to
each other, W = o J because cos 90º = 0
Work at an angle - example
Sid Scorpion pushes a lawn mower with a force of 125N
directed at 25.0 º below the horizontal. He pushes the
lawn mower 2.00 meters horizontally. How much work
has he done?
 W=Fd cos
 W = (125 N)(2.00m) cos 25.0 º
 W = 227 J
Power
 Power is the rate at which work is done.
 P=W/t
 Where Wis work (in J)
 t is time (in s)
 P is power. Power is measured in Watts (W) – like a
light bulb.
 1 W = 1 J/s = 1 Nm/s = 1 kg m2/s3
Potential Energy
 Potential energy is stored energy.
 It has the same meaning as when your teacher looks
at you sadly and says with a sigh, “You have such
potential.”
 She means you could do the work.
 Just like you, potential energy could do the work
under certain circumstances.
Potential Energy – derive the equation
 Demonstration to derive the equation
 PE = mgh
 PE is Potential Energy (in Joules)
 m is mass (in kg)
 g is 9.8 m/s2
 h is height (in m)
Potential Energy – example
 What is the potential energy of a 7.5
kg brick resting on a windowsill 25
meters above the sidewalk?
 PE = mgh
 PE = (7.5 kg)(9.8 m/s2)(25 m)
 PE = 1800 J
Kinetic Energy – derive the equation
 Kinetic energy is the energy of
motion.
 Demonstration to derive the equation
 KE = ½ mv2 where
 KE = kinetic energy ( in Joules)
 m = mass (in kg)
 v = velocity (in m/s)
Kinetic Energy – example
 What is the kinetic energy of a 5.0 kg
bowling ball moving at 12 m/s?
 KE = ½ mv2
 KE = ½ (5.0 kg) (12 m/s)2
 KE = 360 J
Kinetic Energy – example
 What is the velocity of the same
bowling ball that has a kinetic energy
of 450 J?
 KE = ½ mv2
 450 J = ½ (5.0 kg) v2
 v = 13 m/s
Work - Kinetic Energy Theorem
 The Work - Kinetic Energy Theorem says
that the work that goes into a system
becomes the kinetic energy of that system.
 For example, if I do 150 J of work lifting a
bowling ball to the top of a hill, and then
released it from rest to roll down the hill,
the kinetic energy of the bowling ball
would be 150 J at the bottom of the hill.
Law of Conservation of Energy
 Energy can not be created or destroyed.
In a closed, isolated system, the total
amount of energy must remain the same.
 However, the energy can change forms.
For example, from work to potential
energy, to kinetic energy to other forms of
energy (sound, heat, light, etc).
Law of Conservation of Energy example
 What is the work required to lift a
1100 kg car 35 meters up to the top
of Elitch’s Tower of Terror?
W = F d
 W = (1100 kg) (9.8 m/s2) (35 m)
 W = 380,000 J
Law of Conservation of Energy –
example (continued)
 At the top of Elitch’s Tower of Terror,
what is the potential energy of the
car?
 The work has now become the
potential energy of the system. The
law of conservation of energy says
the amount must remain the same.
 PE = 380,000 J
Law of Conservation of Energy –
example (continued)
 Once the car has been released, the total energy
becomes part KE and part PE. What is the
potential energy of the car halfway down (after
falling 17.5 m)?
 PE = mgh
 PE = (1100 kg) (9.8 m/s2) (17.5 m)
 PE = 190,000 J
 Half the height = half the potential energy.
Law of Conservation of Energy –
example (continued)
 What is the kinetic energy of the car halfway down
(after falling 17.5 m)?
 Law of conservation of energy says the total energy
must still be 380,000 J.
 KE + PE = 380,000 J
 KE + 190,000 J = 380,000 J
 KE = 190,000 J
Law of Conservation of Energy –
example (continued)
 What is the velocity of the car halfway
down (after falling 17.5 m)?
 KE = 190,000 J = ½ mv2
 190,000 J = ½ (1100 kg) v2
 v = -19 m/s
Law of Conservation of Energy –
example (continued)
 What is the velocity of the car just as
it reaches the bottom of the Tower of
Terror?
 Now the energy is all kinetic (because
h=0).
 KE = 380,000 J = ½ mv2
 380,000 J = ½ (1100 kg) v2
 v = -26 m/s
Law of Conservation of Energy –
example (continued)
 What is the height of the car when the velocity is -
7.5 m/s?
 KE + PE= 380,000 J
 ½ mv2 + mgh = 380,000 J
 ½ (1100 kg) (7.5 m/s)2 + (1100 kg) (9.8 m/s2) h =
380,000 J
 h = 32 m
Law of Conservation of Energy
 The trick is to remember that the total
amount of energy stays the same
throughout the “closed, isolated
system” (in this case: the Tower of
Terror).
 Calculate the total energy at the most
convenient spot (usually the top since
it will all be PE).
Law of Conservation of Energy
 Remember: If a mass has height it
has potential energy.
 If a mass has velocity it has kinetic
energy.
 If a mass starts from rest at the top
of a hill, it can never go higher
without adding energy.
 Pendulum examples