Transcript KE - baier10physics

Work-Energy Theorem
• Recall that Work equals a change in the
kinetic energy of an object ( W = ∆KE).
• Therefore, W = KEafter - KEbefore
• Also recall that W = F • d cosθ
• And that KE = ½ mv2
Throwing a Baseball
• The baseball before being thrown
has zero velocity, therefore, its
KEbefore = 0.
• You add work to the baseball to get
it moving, therefore, W > 0.
• The baseball after being thrown has
velocity and mass, therefore it has
KE > 0.
• This KE is equal to the initial W
done.
• KEbefore + W = KEafter
Catching a Baseball
• The baseball before being
caught has mass and velocity,
therefore it has KE > 0.
• The baseball after being
caught has no velocity,
therefore its KE = 0.
• Therefore a work that is less
than zero (W < 0) must have
be done.
• KEbefore + (-W) = KEafter
Practice Problem
An 875.0-kg car speeds up from 22.0 m/s to
44.0 m/s while passing another car. What are its
initial and final energies? How much work is
done on the car to increase its speed?
Answer
• KEinital = ½ (875 kg)(22 m/s)2 = 212000 J
• KEfinal = ½ (875 kg)(44 m/s)2 = 847000 J
• W = KEf - KEi = 847000 - 212000 = 635000 J
Gravitational Potential Energy
• Potential energy can be thought
of as stored energy.
• PE = mgh
• An object will have potential
energy based upon the product
of its mass, acceleration due to
gravity, and the distance from a
reference level.
• Each of these different objects
on the shelf have different PE
based upon their masses and
their distances from a reference
level.
Remember Correct Signs!
• Looking at this juggler it is important
to remember that when the ball is
going up, its displacement is upward,
but the force of gravity (Fg) on the ball
is downward. Hence, the work done by
gravity is negative Wg = -mgh.
• When the ball is going down the force
and displacement are in the same
direction. Hence the work done by
gravity is positive Wg = +mgh.
Practice Problem
A boy lifts a 2.2 kg book from his desk, which
is 0.80 m high, to a bookshelf that is 2.10 m
high. What is the potential energy of the book
relative to the desk? What is the potential
energy of the book relative to the ground?
Answer
• PE = mgh = (2.2 kg)(9.8 m/s2)(2.1 m - 0.8 m)
= 28 J
• PE = mgh = (2.2 kg)(9.8 m/s2)(2.1 m)
= 45.3 J
Law of Conservation of Energy
• In a closed system,
energy is neither
created nor
destroyed, rather it
changes from one
form of energy to
another. The total
energy of the system
remains constant.
Mechanical Energy
• The mechanical energy of a system is equal to the sum of
the kinetic and potential energies (provided no other forms
of energy are present).
• ME = KE + PE
Conservation of Mechanical Energy
• When mechanical energy is conserved, the
sum of the kinetic and potential energies in
a system before an event is equal to the sum
of the kinetic and potential energies during
and after the event.
• KEbefore + PEbefore = KEafter + PEafter
Fill in the values for this event (remember
the mechanical energy is conserved).
Answers
1.
PE = (50 kg)(10 m/s2)(4 m) = 2000 J
KE = ½ (50 kg)(0 m/s)2 = 0 J
ME = 0 J + 2000 J = 2000 J
v = 0 m/s
2.
ME = still equals 2000 J
PE = (50 kg)(10 m/s2)(3 m) = 1500 J
KE = ME - PE = 2000 J – 1500 J = 500 J
v =?
3. Continue calculating!