Download AP Physics C IC

AP Physics C I.C
Work, Energy and Power
Amazingly, energy was not
incorporated into physics until more
than 100 years after Newton.
Still a good definition for
energy – “ Energy is the
capacity to do work”
And if the force is constant, we
have our old friend . . .
W = Fd cos θ
A note on the sign of work
• When 0º ≤ θ < 90º work is positive
• When θ = 90º work is zero
• When 90º < θ ≤ 180º work is negative
Ex. A book with a mass of 2.0 kg is lifted at a constant
velocity to a height of 3.0 m. How much work is done on
the book?
Ex. A 15 kg crate is moved along a horizontal surface by
a warehouse worker who is pulling on it with a rope that
makes an angle of 30.0° with the horizontal. The tension
in the rope is 100.0 N and the crate slides a distance of
10.0 m. a) How much work is done on the crate by the
rope? b) How much work is done on the crate by the
normal force? c) How much work is done on the crate by
the frictional force if the coefficient of kinetic friction is
0.40?
Ex. A box slides down an inclined plane that makes an
angle of 37° with the horizontal. The mass of the block
is 35 kg, the coefficient of friction between the box and
ramp is 0.30 and the length of the ramp is 8.0 m. How
much work is done by a) gravity? b) the normal force?
c) friction? d) What is the total work done?
Graphing work vs. displacement
A quick review of Hooke’s Law
Ex. What is the work done on a spring that is
stretched from equilibrium (x = 0) to final
displacement x?
Note: the previous example used
the calculus form for work since
the force was not constant (it
was a function of displacement)
The (net) Work (kinetic) Energy
Theorem
ΣW = ΔK
Ex. Use the work-kinetic energy theorem to find the
height a tennis ball with mass (0.06 kg) would reach if it
is hit upward with an initial speed of 50.0 m/s. Air
resistance is negligible.
Ex. From the box in the previous example (ΣW =
1020 J), if the box starts from rest at the top of the
ramp, with what speed does it reach the bottom?
Ex. A pool cue striking a stationary billiard ball (mass
of 0.25 kg) gives the ball a speed of 2.0 m/s? If the
average force on the cue on the ball was 200 N, over
what distance did this force act?
Potential Energy – energy an
object has because of its
configuration within a system. If
the configuration changes, the
potential energy changes.
Relationship between change in
potential energy and work
(important: if the field does work,
the potential energy of the object
decreases. That energy has been
converted to kinetic energy.)
Gravitational Potential Energy
Ug = mgh
Conservation of Mechanical
Energy (makes lots of problems
simple that might otherwise be
horrendous)
Ex. A child of mass m starts from rest at the top of a
water slide 8.5 m above the bottom of the slide.
Assuming the slide is frictionless, what is the child’s
speed at the bottom of the slide?
Note: if no non-conservative forces
(friction, tension, air resistance) are
present, the change in energy is
independent of the path taken.
Gravity is a conservative force.
Ex. A box, with an initial speed of 3.0 m/s, slides up a
frictionless ramp that makes an angle of 37° with the
horizontal. How high up the ramp will the box slide?
What distance along the ramp will it slide?
Ex. A skydiver jumps fro a hovering helicopter that is
3000 m above the ground. If air resistance is
negligible, how fast will the skydiver be falling when
his altitude is 2000 m?
Modifying conservation of
energy to include nonconservative forces
Ex. Wile E. Coyote (mass = 40 kg) falls off a 50 m high
cliff. On the way down, the average force of air
resistance is 100 N. Find the speed with which he
crashes into the ground.
Ex. A skier starts from rest at the top of a 20.0° incline
and skis in a straight line to the bottom of the slope a
distance d (measured along the slope) of 400 m. If the
coefficient of kinetic friction between the skis and the
snow is 0.20, calculate the skier’s speed at the
bottom of the run.
Potential Energy Curve
Key aspects of a potential
energy curve
•
•
•
•
The object moves in a linear path along + x and –x-axis
The force is the negative slope of the curve
Emec = U(x) + K(x)
Turning points: locations where the object is at rest; i.e.
K(x) = 0 and Emec = U(x)
• Object is in equilibrium (neutral, unstable, stable) when
slope = 0 (F(x) = 0)
• Object cannot reach locations where K is negative
• To graph: graph zeros (F(x) = 0), regions of constant
force and connect.