-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) An old oaken bucket of mass 6.75 kg hangs in a well at the
end of a rope. The rope passes over a frictionless pulley at the
top of the well, and you pull horizontally on the end of the rope
to raise the bucket slowly a distance of 4.00 m. (a) How much work
do you do on the bucket in pulling it up. (b) How much work does
gravity do on the bucket? (c) What is the total work done on the
bucket? (3.60 J, -0.900 J, 2.70 J) (2) A factory worker pushes a
30.0 kg crate a distance of 4.5 m along a level floor at constant
velocity by pushing horizontally on it. The coefficient of kinetic
friction between the crate and the floor is 0.25. (a) What
magnitude of force must the worker apply? (b) How much work is done
on the crate by this force? (c) How much work is done on the crate
by friction? (d) How much work is done on the crate by the normal
force? By gravity? (e) What is the total work done on the crate?
(74 N, 330 J) (3) A 75.0 kg painter climbs a ladder that is 2.75 m
long leaning against a vertical wall. The ladder makes a 30.0°
angle with the wall. (a) How much work does gravity do on the
painter? (b) Does the answer to part a depend on whether the
painter climbs at constant speed or accelerates up the ladder?
(-1750 J) (4) Two blocks are connected by a very light string
passing over a massless and frictionless pulley. Traveling at
constant speed, the 20.0 N block moves 75.0 cm to the right and the
12.0 N block moves 75.0 cm downward. During this process, how much
work is done (a) on the 12.0 N block by (i) gravity and (ii) the
tension in the string? (b) On the 20.0 N block by (i) gravity, (ii)
the tension, (iii) friction, and (iv) the normal force? (c) Find
the total work done on each block. (9.00 J)
AP Homework 5.1 Work
-
(5) An 8.00 kg package in a mail-sorting room slides 2.00 m down
a chute that is inclined at 53.0° below the Calculate
the work done on the package by (a) friction, (b) gravity, and
(c) the normal force. (d) What is the net work done on the package?
(-38 J, 125 J, 0, 87 J) (6) A child applies a force F parallel to
the x-axis to a 10.0 kg sled moving on the frozen surface of a
pond. As the child controls the speed of the sled, the x-component
of the force she applies varies with the sled as shown. Calculate
the work done by the force F when the sled moves (a) from x = 0 to
x = 8.0 m; (b) from x = 8.0 m to x = 12.0 m; (c) from x = 0 to 12.0
m. (40.0 J, 20.0 J, 60.0 J) (7) A force F is applied to a 2.0 kg
radio-controlled model car parallel to the x-axis as it moves along
a straight track. The x-component of the force varies with the
x-coordinate of the car as shown. Calculate the work done by the
force F when the car moves from (a) x = 0 to x = 3.0 m; (b) x = 3.0
m to x = 4.0m; (c) x = 4.0 m to x = 7.0 m; (d) x = 0 to x = 7.0 m;
(e) x = 7.0 m to x = 2.0 m. (4.0 J, 0, -1.0 J, 3.0 J, -1.0 J) (8) A
boxed 10.0 kg computer monitor is dragged by friction 5.50 m up
along the moving surface of a
cm/s, how much work is done on the monitor by (a) friction, (b)
gravity, and (c) the normal force of the conveyor belt?
-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) Adult cheetahs, the fastest of the great cats, have a mass
of about 70 kg and have been clocked running at up to 72 mph 132
m/s2. (a) How many joules of kinetic energy does such a swift
cheetah have? (b) By what factor would its kinetic energy change if
its speed were doubled? (36,000 J) (2) About 50,000 years ago, a
meteor crashed into the earth near present-day Flagstaff, Arizona.
Measurements from 2005 estimate that this meteor had a mass of
about 1.4x108 kg (around 150,000 tons) and hit the ground at a
speed of 12 km/s. (a) How much kinetic energy did this meteor
deliver to the ground? (b) How does this energy compare to the
energy released by a 1.0 megaton nuclear bomb? (A megaton bomb
releases the same amount of energy as a million tons of TNT, and
1.0 ton of TNT releases 4.184x109 J of energy.) ( 1.0x1016 J) (3)
The mass of a proton is 1836 times the mass of an electron. (a) A
proton is traveling at speed V. At what speed (in terms of V) would
an electron have the same kinetic energy as the proton? (b) An
electron has kinetic energy K. If a proton has the same speed as
the electron, what is its kinetic energy (in terms of K)? (42.85V,
1836K) (4) A 4.80 kg watermelon is dropped from rest from the roof
of a 25.0 m-tall building and feels no air resistance. (a)
Calculate the work done by gravity on the watermelon during its
displacement from the roof to
(c) Which of the answers in parts a and b would be different if
there were air resistance? (1180 J, 22.1 m/s)
AP Homework 5.2 Work-Kinetic Energy Theorem
-
(5) A sled with mass 8.00 kg moves in a straight line on a
frictionless horizontal surface. At one point in its path, its
speed is 4.00 m/s; after it has traveled 2.50 m beyond this point,
its speed is 6.00 m/s. Use the workenergy theorem to find the force
acting on the sled, assuming that this force is constant and that
it acts in the
(32.0 N) (6) A 12-pack of Omni-Cola (mass 4.30 kg) is initially
at rest on a horizontal floor. It is then pushed in a straight line
for 1.20 m by a trained dog that exerts a horizontal force with
magnitude 36.0 N. Use the work energy theorem to find the final
speed of the 12-pack if (a) there is no friction between the
12-pack and the floor, and (b) the coefficient of kinetic friction
between the 12-pack and the floor is 0.30. (4.48 m/s, 3.61 m/s) (7)
A block of ice with mass 2.00 kg slides 0.750 m down a frictionless
inclined plane that slopes downward at an angle of 36.90 below the
horizontal. If the block of ice starts from rest, what is its final
speed? (2.84 m/s) (8) A 30.0 kg crate is initially moving with a
velocity that has magnitude 3.90 m/s in a direction 37.00 west of
north. How much work must be done on the crate to change its
velocity to 5.62 m/s in a direction 63.00 south of east?
-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) How many joules of energy does a 100-watt light bulb use per
hour? How fast would a 70 kg person have to run to have that amount
of kinetic energy? (3.6x105 J, 100 m/s) (2) On December 27, 2004,
astronomers observed the greatest flash of light ever recorded from
outside the solar system. It came from the highly magnetic neutron
star SGR 1806-20 (a magnetar). During 0.20 s, this star released as
much energy as our sun does in 250,000 years. If P is the average
power output of our sun, what was the average power output (in
terms of P) of this magnetar? (4.0x1013P) (3) A tandem (two-person)
bicycle team must overcome a force of 165 N to maintain a speed of
9.00 m/s. Find the power required per rider, assuming that each
contributes equally. Express your answer in watts and in
horsepower. (743 W, 0.995 hp)
AP Homework 5.3 Power
-
(4) Your job is to lift 30 kg crates a vertical distance of 0.90
m from the ground onto the bed of a truck. (a) How many crates
would you have to load onto the truck in 1 minute for the average
power output you use to lift the crates to equal 0.50 hp? (b) How
many crates for an average power output of 100 W? (1.4, 0.38) (5) A
ski tow operates on a 15.00 slope of length 300 m. The rope moves
at 12.0 km/h and provides power for 50 riders at one time, with an
average mass per rider of 70.0 kg. Estimate the power required to
operate the tow. (2.96x104 W) (6) It is not unusual for a 1000 kg
car to get 30 mi/gal when traveling at 60 mi/h. IF this car makes a
200 km trip, (a) how many joules of energy does it consume, and (b)
what is the average rate of energy consumption during the trip?
Note that 1.0 gal of gasoline yields 1.3x109 J (Consult Appendix
E). (5.4x109 J, 0.72 MW) (7) It is 5.0 km from your home to the
physics lab. As part of your physical fitness program, you could
run that distance at 10 km/h (which uses up energy at the rate of
700 W), or you could walk it leisurely at 3.0 km/h (which uses
energy at 290 W). Which choice would burn up more energy, and how
much energy (in joules) would it burn? Why is it that the more
intense exercise actually burns up less energy than the less
intense exercise?
-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) In one day, a 75 kg mountain climber ascends from the 1500 m
level on a vertical cliff to the top at 2400 m. The next day, she
descends from the top to the base of the cliff, which is at an
elevation of 1350 m. What is her change in gravitational potential
energy (a) on the first day and (b) on the second day? (6.6x105 J,
-7.7x105 J) (2) The maximum height a typical human can jump from a
crouched start is about 60.0 cm. By how much does the gravitational
potential energy increase for a 72.0 kg person in such a jump?
Where does this energy come from? (423 J) (3) A baseball is thrown
from the roof of a 22.0 m tall building with an initial velocity of
magnitude 12.0 m/s and directed at an angle of 53.10 above the
horizontal. (a) What is the speed of the ball just before it
strikes the ground? Use energy methods and ignore air resistance.
(b) What is the answer for part (a) if the initial velocity is at
an angle of 53.10 below the horizontal? (c) If the effects of air
resistance are included, will part a or b give the higher speed?
(24.0 m/s) (4) For its size, the common flea is one of the most
accomplished jumpers in the animal world. A 2.0 mm-long, 0.50 mg
critter can reach a height of 20 cm in a single leap. (a)
Neglecting air drag, what is the takeoff speed of such a flea? (b)
Calculate the kinetic energy of this flea at takeoff and its
kinetic energy per kilogram of mass. (c) If a 65 kg, 2.0 m- tall
human could jump to the same height compared with his length as the
flea jumps compared with its length, how high could the human jump,
and what takeoff speed would he need? (d) In fact, most humans can
jump no more than 60 cm from a crouched start. What is the kinetic
energy per kilogram of mass at takeoff for such a 65 kg person?
(2.0 m/s, 9.8x107 J & 2.0 J/kg, 200 m & 63 m/s, 5.9
J/kg)
AP Homework 5.4 Gravitational Potential Energy
-
(5) Tarzan, in one tree, sights Jane in another tree. He grabs
the end of a vine with length 20 m that makes an angle of 450 he
arrives, his vine makes an angle of 300 with the vertical.
Determine whether he gives her a tender embrace or knocks her off
her limb by calculatresistance and the mass of the vine. (7.9 m/s)
(6) A small rock with mass 0.20 kg is released from rest at point
A, which is at the top edge of a large, hemi-spherical bowl with
radius R = 0.50 m . Assume that the size of the rock is small
compared to R, so that the rock can be treated as a particle, and
assume that the rock slides rather than rolls. The work done by
friction on the rock when it moves from point A to point B at the
bottom of the bowl has magnitude 0.22 J. (a) Between points A and
B, how much work is done on the rock by (i) the normal force and
(ii) gravity? (b) What is the speed of the rock as it reaches point
B? (c) Of the three forces acting on the rock as it slides down the
bowl, which (if any) are constant and which are not? Explain. (0.98
J, 2.8 m/s) (7) You are testing a new amusement park roller coaster
with an empty car of mass 120 kg. One part of the track is a
vertical loop with radius 12.0 m. At the bottom of the loop (point
A) the car has speed 25.0 m/s, and at the top of the loop (point B)
it has speed 8.0 m/s. As the car rolls from point A to point B, how
much work is done by friction. (-5400 J) (8) A 10.0 kg microwave
oven is pushed 8.00 m up the sloping surface of a loading ramp
inclined at an angle of 36.90 above the horizontal, by a constant
force F with a magnitude 110 N and acting parallel to the ramp. The
coefficient of kinetic friction between the oven and the ramp is
0.250. (a) What is the work done on the oven by the force F? (b)
What is the work done on the oven by the friction force? (c)
Compute the increase in potential energy for the oven. (d) Use your
answers to parts a-kinetic energy. (e) Use F = ma to calculate the
acceleration of the oven. Assuming that the oven is initially
m. From this, compute the
-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) A force of 800 N stretches a certain spring a distance of
0.200 m. (a) What is the potential energy of the spring when it is
stretched 0.200 m? (b) What is its potential energy when compressed
5.00 cm? (80.0 J, 5.00 J) (2) A slingshot will shoot a 10 gram
pebble 22.0 m straight up. (a) How much potential energy is
ststored in the rubber band, how high can the slingshot shoot a 25
gram pebble? (c) What physical effects did you ignore in solving
this problem? (2.2 J, 9.0 m) (3) A spring of negligible mass has
force constant k = 1600 N/m. (a) How far must the spring be
compressed for 3.20 J of potential energy to be stored in it? (b)
You place the spring vertically with one end on the floor. You then
drop a 1.20 kg book onto it from a height of 0.80 m above the top
of the spring. Find the maximum distance the spring will be
compressed. (6.32 cm, 12 cm)
AP Homework 5.5 Elastic Potential Energy
-
(4) A 1.20 kg piece of cheese is placed on a vertical spring of
negligible mass and force constant k = 1800 N/m that is compressed
15.0 cm. When the spring is released, how high does the cheese rise
from this initial position? (The cheese and the spring are not
attached.) (1.72 m) (5) A 2.50 kg mass is pushed against a
horizontal spring of force constant 25.0 N/cm on a frictionless air
table. The spring is attached to the tabletop, and the mass is not
attached to the spring in any way. When the spring has been
compressed enough to store 11.5 J of potential energy in it, the
mass is suddenly released from rest. (a) Find the greatest speed
the mass reaches. When does this occur? (b) What is the greatest
acceleration of the mass, and when does it occur? (3.03 m/s, 95.9
m/s2) (6) You are asked to design a spring that will give a 1160 kg
satellite a speed of 2.50 m/s relative to an orbiting space
shuttle. Your spring is to give the satellite a maximum
acceleration of 5.00grecoil energy of the shuttle, and changes in
gravitational potential energy will be negligible. (a) What must
the force constant of the spring be? (b) What distance must the
spring be compressed? (4.46x105 N/m, 0.128 m) (7) A 2.50 kg block
on a horizontal floor is attached to a horizontal spring that is
initially compressed 0.0300 m. The spring has force constant 840
N/m. The coefficient of kinetic friction between the floor and the
block
k = 0.40. The block and spring are released from rest and the
block slides along the floor. What is the speed of the block when
it has moved a distance of 0.0200 m from its initial position? (At
this point the spring is compressed 0.0100 m.)
-
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) A 10.0 kg box is pulled by a horizontal wire in a circle on
a rough horizontal surface for which the coefficient of kinetic
friction is 0.250. Calculate the work done by friction during one
complete circular trip if the radius is (a) 2.00 m and (b) 4.00 m.
(c) On the basis of the results you just obtained, would you say
that friction is a conservative or nonconservative force? Explain.
(-308 J, -616 J) (2) A 75 kg roofer climbs a vertical 7.0 m ladder
to the flat roof of a house. He then walks 12 m on the roof, climbs
down another vertical 7.0 m ladder, and finally walks on the ground
back to his starting point. How much work is done on him by gravity
(a) as he climbs up; (b) as he climbs down; (c) as he walks on the
roof and on the ground? (d) What is the total work done on him by
gravity during this round trip? (e) On the basis of your answers,
would you say that gravity is a conservative or nonconservative
force? Explain. (5.1x102 J) (3) A 50.0 kg diver steps off a 10.0 m
high diving board and drops straight down into the water. If the
diver comes to a rest 5.0 meters below the surface, determine the
average resistance force exerted on the diver by the water. (-1470
N) (4) While a roofer is working on a roof that slants at 36° above
the horizontal, he accidentally nudges his 85.0 N toolbox, causing
it to start sliding downward, starting from rest. If it starts 4.25
m from the lower edge of the roof, how fast will the toolbox be
moving just as it reaches the edge of the roof if the kinetic
friction force on it is 22.0 N? (5.23 m/s)
AP Homework 5.6 Conservation of Energy
-
(5) In a circus performance, a monkey on a sled is given an
initial speed of 4.0 m/s up a 250 incline. The combined mass of the
monkey and the sled is 20.0 kg, and the coefficient of friction
between the sled and the incline is 0.20. (a) How far up the
incline does the sled move before coming to a stop? (b) How much
internal energy is generated in the sled? What form of
non-mechanical energy does this take? (1.25 m) (6) An 80.0 kg box
of clothes is pulled 20.0 meters up a 30.00 ramp by a force of 115
N that points along the ramp. (a) If the coefficient of kinetic
friction between the box and the ramp is 0.220, calculate the
change in
(b) How much of this lost kinetic energy became potential energy
and how much became internal energy? (8.53x103 J) (7) A skier
starts from rest at the top of a hill that is inclined at 10.50
from the horizontal. The hillside is 200.0 meters long, and the
coefficient of friction is 0.0750. At the bottom of the hill, the
snow is level and the coefficient of friction is unchanged. How far
does the skier move along the horizontal portion of the snow before
coming to rest? (289 m) (8) A 62.0 kg skier is moving at 6.50 m/s
on a frictionless, horizontal, snow-covered plateau when she
encounters a rough patch 3.50 m long. The coefficient of kinetic
friction between this patch and her skis is 0.300. After crossing
the rough patch and returning to friction-free snow, she skis down
an icy, frictionless hill 2.50 m high. (a) How fast is the skier
moving when she gets to the bottom of the hill? (b) How much
internal energy was generated in crossing the rough patch?
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Keeping Track of Success Codes
