Download AP HW 7

AP Homework 7.1
Name: _________________________________________
Centripetal Force
Date: ___________________ Class Period: _________
(1) In each of the pairs of diagrams below, a sphere attached to a string is swung in a flat
horizontal circle. Assume that the tangential velocity remains constant.
(B)
(A)
2m
m
r
r
T=1s
T=1s
Write a sentence or two stating how centripetal acceleration and force will be affected:
(B)
(A)
m
m
r
2r
T=1s
T=1s
Write a sentence or two stating how centripetal acceleration and force will be affected:
(B)
(A)
m
m
r
T=0.7s
r
T=1s
Write a sentence or two stating how centripetal acceleration and force will be affected:
(2) Give an example of a situation in which an automobile driver turning in a circle can have a centripetal
acceleration but no tangential acceleration. Can the opposite be true? Why or why not?
(3) The emerald suite, a revolving restaurant at the top of the Space Needle in Seattle, makes a complete turn
once an hour. What is the centripetal force on an 80.0 kg customer sitting 12.5 m
center? (0.0028 N)
(4) An airplane is flying in a horizontal circle at a speed of 105 m/s. The 80.0 kg pilot does not want his
centripetal acceleration to exceed 7.00 times free-fall acceleration. (a) What is the minimum radius of the
circular path? (b) At this radius, what is the centripetal force the pilot experiences? (161 m, 5490 N)
(5) A sled with a mass of 25.0 kg rests on a horizontal sheet of frictionless ice. It is attached by a 5.0 meter
rope to a post set in the ice. Once given a push, the sled revolves uniformly in a circle around the post. If the
sled makes five complete turns every minute, find the force (F) exerted on it by the cord. (34 N)
(6) A 13,500N car traveling at 50.0 km/hr rounds a curve of radius 2.00x102 meters. Find the centripetal force
needed to maintain the turn without skidding. (1330 N)
(7) In a test of a of rotation at which the centripetal acceleration is 3g? 10g?
AP Homework 7.2
Centripetal Force
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) A small car with mass 0.800 kg travels at constant speed on the inside of a track
that is a vertical circle with radius 5.00 m. If the normal force exerted by the track
on the car when it is at the top of the track (point B) is 6.00 N, what is the normal
force on the car when it is at the bottom of the track (point A)? (21.7 N)
(2) A flat (unbanked) curve on a highway has a radius of 220.0 m. A car rounds the curve at a speed of 25.0
m/s. (a) What is the minimum coefficient of friction that will prevent sliding? (b) Suppose the highway is icy
and the coefficient of friction between the tires and pavement is only one-third what you found in part a.
What should be the maximum speed of the car so it can round the curve safely? (0.290, 14.4 m/s)
(3) A 1125 kg car and a 2250 kg pickup truck approach a curve on the expressway that has a radius of 225 m.
(a) At what angle should the highway engineer bank this curve so that vehicles traveling at 65.0 mi/h can
safely round it regardless of the condition of their tires? Should the heavy truck go slower than the lighter car?
(b) As the car and truck round the curve at 65.0 mi/h find the normal force on each one due to the highway
surface. (210, 1.18x104 N and 2.36x104 N)
county fair consists of a vertical central shaft
with a number of horizontal arms attached at its upper end. Each arm
supports a seat suspended from a cable 5.00 m long, the upper end of
the cable being fastened to the arm at a point 3.00 m from the central
shaft. (a) Find the time of one revolution of the swing if the cable
supporting a seat makes an angle of 30.0° with the vertical. (b) Does the
angle depend on the weight of the passenger for a given rate of
revolution? (6.2 s)
(5) A small button placed on a horizontal rotating platform with diameter 0.320 m will revolve with the
platform when it is brought up to a speed of 40.0 rev/min, provided the button is no more than 0.150 m from
the axis. (a) What is the coefficient of static friction between the button and the platform? (b) How far from
the axis can the button be placed, without slipping, if the platform rotates at 60.0 rev/min? (0.269, 6.67 cm)
(6) One problem for humans living in outer space is that they are apparently weightless. One way around this
ial
. (a) If the diameter of the space station is 800 m, how many revolutions per minute
2
are needed for
? (b) If the space station is a waiting area for
travelers going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian
surface (3.70 m/s2). How many revolutions per minute are needed in this case? (1.49 rev/min, 0.918 rev/min)
toward the center of the loop. The speed of the airplane is not constant; the airplane goes slowest at the top
of the loop and fastest at the bottom. (a) At the top of the loop, the pilot feels weightless. What is the speed
of the airplane at this point? (b) At the bottom of the loop, the speed of the airplane is 280 km/h. What is the
apparent weight of the pilot at this point? His true weight is 700 N. (138 km/h, 3580 N)
(8) A 50.0 kg stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her
course to a circle in a vertical
what is the minimum radius of the circle for the acceleration at this point not to exceed 4.00g? (b) What is
the apparent weight of the pilot at the lowest point of the pullout?
AP Homework 7.3
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) What is the ratio of the gravitational pull of the sun on the moon to that of the earth on the moon?
(Assume the distance of the moon from the sun can be approximated by the distance of the earth from the
sun.) Is it more accurate to say that the moon orbits the earth, or that the moon orbits the sun? (2.18)
(2) An interplanetary spaceship passes through the point in space where the gravitational forces from the sun
and the earth on the ship exactly cancel. (a) How far from the center of the earth is it? (b) Once it reached
this point, could the spaceship turn off its engines and just hover there indefinitely? Explain. (2.59x108 m)
(3) A couple of astronauts agree to rendezvous in space after hours. Their plan is to let gravity bring them
together. One of them has a mass of 65 kg and the other a mass of 72 kg, and they start from rest 20.0 m
apart. (a) Make a free-body diagram of each astronaut, and use it to find his or her initial acceleration. (b) If
other? (Careful! They both have acceleration toward each other.) (c) Would their acceleration, in fact, remain
constant? If not, would it increase or decrease? Why? (1.2x10-11 m/s2, 15 days)
(4) A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human
when it is directly overhead with its center 378,000 km away? (b) Compare this force with the force exerted
on the human by the earth. (2.4x10-3 N)
(5) Find the magnitude and direction of the net gravitational
force on mass A due to masses B and C for both situations
shown. Each mass is 2.00 kg. (1.11x10-7 N, 1.00x10-7 N)
(6) A particle of mass 3m is located 1.00 m from a particle of mass m. (a) Where should you put a third mass M
so that the net gravitational force on M due to the two masses is exactly zero? (b) Is the equilibrium of M at
this point stable or unstable (i) for points along the line connecting m and 3m, and (ii) for points along the line
passing through M and perpendicular to the line connecting m and 3m? (0.366 m from mass m)
(7) Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B.
Find the magnitude and direction of the initial acceleration of a uniform
sphere with mass 0.010 kg if released from rest at point P and acted on only
by forces of gravitational attraction of the spheres at A and B.
AP Homework 7.4
Weight & GPE
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) Use the mass and radius of the dwarf planet Pluto to calculate the acceleration due to gravity at the
surface of Pluto. (0.757 m/s2)
2
2
if the
7
acceleration due to gravity at the surface has magnitude 9.80 m/s ? (1.38x10 m)
(3) The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. (a) Compute the
acceleration due to gravity on the surface of Venus from these data. (b) If a rock weighs 75.0 N on earth, what
would it weigh at the surface of Venus? (0.905g, 67.9 N)
-kg astronaut who is repairing the
why we say astronauts are weightless when they orbit the earth in a satellite
such as a space shuttle. Is it because the gravitational pull of the earth is
negligibly small? (610 N, 83% of surface weight)
(5) An experiment using the Cavendish balance to measure the gravitational constant G found that a uniform
0.400 kg sphere attracts another uniform 0.00300 kg sphere with a force of 8.00x10 -10 N, when the distance
surface is 9.80
m/s2, and the radius of the earth is 6380 km. Compute the mass of the earth from these data. (5.98x1024 kg)
(6) Calculate the escape speed for a spacecraft (a) from the surface of Mars and (b) from the surface of Jupiter.
(c)
(5.02x103 m/s, 6.06x104 m/s)
(7) Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft (mass
629 kg) was 2.87x106 km from the earth and traveling at 1.20x104 km/h relative to the earth. At this time,
spacecraft system? (3.49x109 J, -8.73x107 J)
(8) On July 4, 2005, the NASA spacecraft Deep Impact fired a projectile onto the surface of Comet Tempel
1. This comet is about 9.0 km across. Observations of surface debris released by the impact showed that
dust with a speed as low as 1.0 m/s was able to escape the comet. (a) Assuming a spherical shape, what is
the mass of the comet? (b) How far from the comet's center will this debris be when it has lost (i) 90% of its
initial energy at the surface; and (ii) all of its kinetic energy at the surface?
AP Homework 7.5
Name: _________________________________________
Date: ___________________ Class Period: _________
(1) For a satellite to be in a circular orbit 780 km above the surface of the earth, (a) what orbital speed must it
be given, and (b) what is the period of the orbit (in hours)? (7.46x103 m/s, 1.68 h)
(2) Two satellites are in circular orbits around a planet that has radius 9.00x10 6 m. One satellite has mass 68.0
kg, orbital radius 5.00x107 m, and orbital speed 4800 m/s. The second satellite has mass 84.0 kg and orbital
radius 3.00x107 m. What is the orbital speed of this second satellite? (6200 m/s)
(3) The International Space Station makes 15.65 revolutions per day in
its orbit around the earth. Assuming a circular orbit, how high is this
satellite above the surface of the earth? (370 km)
(4) Deimos, a moon of Mars, is about 12 km in diameter with mass 2.0x 1015 kg. Suppose you are stranded
alone on Deimos and want to play a one-person game of baseball. You would be the pitcher, and you would
be the batter! (a) With what speed would you have to throw a baseball so that it would go into a circular orbit
just above the surface and return to you so you could hit it? Do you think you could actually throw it at this
speed? (b) How long (in hours) after throwing the ball should you be ready to hit it? (4.7 m/s, 2.2 h)
(5) The star Rho Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has
been detected in a circular orbit around Rho Cancri with an orbital radius equal to 0.11 times the radius of the
Cancri? (8.3x104 m/s, 1.3x106 s)
(6) The Helios B spacecraft had a speed of 71 km/s when it was 4.3x107 km from the sun. (a) Prove that is was
not in a circular orbit around the sun.
(7) In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star
it takes the planet only 3.09 days to make one orbit (assumed to be circular). (a) What is the mass of the
st
planet moving?
Keeping Track of Success Codes
Minds On Physics Internet Modules
N ame:
CG8
CG7
CG6
CG5
CG4
CG3
CG2
CG1
Assignment
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
g ____ ____ - ____ ____ - ____ ____ ____
Gold Medal Success Code*
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
s ____ ____ - ____ ____ - ____ ____ ____
Silver Medal Success Code*
ID #:
D ate
D ue:
Up on com p letion of an assignm ent, the Mind s On Physics p rogram creates an encryp ted set of characters know n as a Su ccess Cod e . The cod e is
generated u sing you r teacher cod e, you r stu d ent ID nu m ber, and a few other invisible p aram eters. The cod e can be u sed to verify that a stu d ent has
su ccessfu lly com p leted the assignm ent. Becau se the cod e is based u p on a teacher cod e and a stu d ent ID, it is im p ortant that su ch inform ation is accu rate.
Su ccess cod es have to be w ritten d ow n by the stu d ent in ord er to receive cred it; there is no d atabase to keep track of them . Th e form below can be u sed to
assist in record ing Su ccess Cod es as you p rogress throu gh you r set of assignm ents. Record all cod es ac cu rately. Tu rn the cod es in by the d u e d ate (to be
annou nced by teacher).
Teacher Code:
CG9
g ____ ____ - ____ ____ - ____ ____ ____
Circular Motion and Gravitation Module
CG10
* Alw ays Go for the Gold ! It's w orth m ore cred it. The Silver Med al earns a stu d ent p artial cred it for near com p letion of an ass ignm ent on several
occasions. The cred it valu e of a Silver Med al su ccess cod e is less than that of a Gold Med al su ccess cod e.