Transcript Chapter 5

Chapter 5
Work and Energy
Question
• A crate of mass 10 kg is on a ramp that is
inclined at an angle of 30⁰ from the horizontal.
A force with a magnitude of 135 N directed
parallel to the ramp is used to pull the crate
with a constant speed up the ramp a distance
of 6 m. What is the work done on the crate by
the frictional force?
Answer
• W = -516 J
– It is negative because friction acts in the exact
opposite direction as the displacement
– Figure out the parallel component of the weight
– Use the net force (set equal to zero) in the parallel
direction to find the frictional force
– Use W=Fd where F is the frictional force to find
out the work done by friction
Question
• An empty coffee mug with a mass of 0.40 kg
gets knocked off a tabletop 0.75 m above the
floor onto the seat of a chair 0.45 m above the
floor. Assume that the gravitational potential
energy is measured using the floor as the zero
reference level. What is the change in
gravitational potential energy for the mug?
Answer
• ∆GPE = -1.1772 J
– Answer is negative because final gravitational
potential energy is less than initial
Question
• A pendulum swings back and forth. If you take
its lowest point as your zero reference level,
where would its kinetic energy be greatest?
Where would its GPE be greatest?
Answer
• KE is greatest at lowest point of swing (zero
reference level)
• GPE is greatest a highest points of swing
Greatest GPE
Greatest GPE
Greatest KE
Question
• A satellite is in a circular orbit above Earth’s
surface. There is no work done on the satellite
because the force of gravity is always
perpendicular to the satellite’s motion. Based
on this, what does the work-kinetic energy
theorem predict about it’s speed?
Answer
• The speed is constant
Question
• Advertisements for a toy ball once stated that
it would rebound to a height greater than the
height from which it was dropped. Is this
possible?
Answer
• No, because energy would not be conserved
Question
• A student walks up a staircase on their way to
class and then runs down it on their way to
lunch. In which situation do they exert more
power?
Answer
• Running down it
– The same amount of work is done going up and
down the staircase; however, running decreases
the amount of time it takes to do that work
therefore increasing the power exerted
Question
• If the speed of a car is doubled and the mass
is tripled, by what factor does the kinetic
energy of the car increase?
Answer
• 12
– KE = 1/2mv2 changes to KE = ½(3m)(2v)2 =
½(3m)(4v2) and 4x3 = 12
Question
• A 70 kg base runner moving at a speed of 4.0
m/s begins to slide into second base. The
coefficient of friction between his clothes and
Earth is 0.70. His slide lowers his speed to zero
just as he reaches the base. How far does the
runner slide?
Answer
• 1.2 m
– Use the work kinetic energy theorem; the force
doing the work is friction
Question
• A spring scale has a spring with a force
constant of 250 N/m and a weighing pan with
a mass of 0.075 kg. During one weighing, the
spring is stretched a distance of 12 cm from
equilibrium. During a second weighing, the
spring is stretched a distance of 18 cm. How
much greater is the elastic potential energy of
the stretched spring during the second
weighing than during the first weighing?
Answer
• 2.25 times greater
– Don’t forget to convert cm to m
– Remember “x” is the difference between the
relaxed length and the stretched length
Question
• A student with a mass of 66 kg climbs a
staircase in 44 s. If the distance between the
base and the top of the staircase is 14.0 m,
how much power will the student deliver by
climbing the stairs?
Answer
• 206 W
– The force that the student exerts in climbing the
stairs that does work is exactly equal and opposite
to the student’s weight
Question
• A 75 kg man drops from a window that is 1 m
high. Calculate the man’s speed when he
strikes the ground.
Answer
• 4.4 m/s
– Use conservation of energy equation to solve
Question
• A sled is pulled along a flat surface with a
force of 17 N directed at an angle of 25⁰ above
the horizontal. If the sled is pulled a distance
of 3 m, how much work is being done?
Answer
• 46.2 J
Question
• There are 2 situations that others, not as
enlightened as you, may be inclined to say
that “work is being done”. Name them.
Answer
• When a force is applied but there is not
resulting displacement (ex: you push on a car
but it doesn’t move)
• When the force is applied perpendicular to
the displacement (ex: a waitress carrying a
tray)
Question
• If I am looking to find the net work done on an
object (as required when using the workkinetic energy theorem), what force must be
used in the equation W = Fd?
Answer
• The net force
Question
• An object slides down an incline and it is
stated that mechanical energy is conserved in
this situation. What is being ignored in that
statement?
Answer
• Friction
– When friction is present, mechanical energy is
NOT conserved
Question
• What form of the conservation of energy
equation would you use to solve a problem
involving a roller coaster climbing a hill?
Answer
• KEi = GPEf
Question
• Are work and energy scalar or vector
quantities?
Answer
• Both are scalar
Question
• For conservation of energy, what type of
energy is ALWAYS conserved?
Answer
• Total
– The answer is NOT mechanical because in the
presence of friction, mechanical energy is NOT
conserved
Question
• How is an object’s kinetic energy affected by
friction?
Answer
• Decreased
– Friction slows things down; KE is based upon
speed
Question
• There are 2 springs. A 1 kg mass is hung from
each spring. As a result, spring 1 stretches 7
cm and spring 2 stretches 2 cm. Which spring
has a greater spring constant, k?
Answer
• Spring 2
– Stiffer springs have larger k and therefore will
stretch/compress less when subjected to a force
Question
• Bud, a very large man of mass 130 kg, stands
on a pogo stick. How much work is done as
Bud compresses the spring of the pogo stick
0.50 m?
Answer
• 637.65 J
Question
• Frank, a San Francisco hot dog vendor, has
fallen asleep on the job. When an earthquake
strikes, his 300 kg hot dog cart rolls down Nob
Hill and reaches point A at a speed of 8 m/s.
How fast is the hot dog cart going at point B
when Frank finally wakes up and starts to run
A
after it?
B
30.0 m
50.0 m
Answer
• 21.4 m/s
Question
• On a ski weekend in Colorado, Bob, whose
mass is 75.0 kg, skis down a hill that is inclined
at an angle of 15.0° to the horizontal and has a
vertical rise of 25.0 m. How much work is
done by gravity on Bob as he goes down the
hill?
Answer
• 18,391.2 J
Question
• At an amusement park, a ride called “Cyclone”
is a giant roller coaster that ascends a 34.1 m
hill and then drops 21.9 m before ascending
the next hill. The train of cars has a mass of
4727 kg. What power must be generated to
bring the train to the top of the first hill in
30.0 s?
Answer
• 52,709.4 W