AP C Review Guide CH12-13

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AP Physics C Review Guide CH12-13

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. A satellite is in a circular orbit about the Earth at an altitude at which air resistance is negligible. Which of the

following statements is true?

a

.

There is only one force acting on the satellite.

b

.

There are two forces acting on the satellite, and their resultant is zero.

c

.

There are two forces acting on the satellite, and their resultant is not zero.

d

.

There are three forces acting on the satellite.

e

.

None of the receding statements are correct.

____ !. A satellite is laced in a geosynchronous orbit. "n this e#uatorial orbit with a eriod of !$ hours, the satellite

ho%ers o%er one oint on the e#uator. Which statement is true for a satellite in such an orbit?

a

.

There is no gra%itational force on the satellite.

b

.

There is no acceleration toward the center of the Earth.

c

.

The satellite is in a state of free fall toward the Earth.

d

.

There is a tangential force that hels the satellite &ee u with the rotation of the Earth.

e. The force toward the center of the Earth is balanced by a force away from the center ofthe Earth.

____ '. Two identical lanets orbit a star in concentric circular orbits in the star(s e#uatorial lane. )f the two, the

lanet that is farther from the star must ha%e

the smaller eriod. the larger

gra%itational mass.

the greater eriod. the larger uni%ersal

gra%itational

constant.

c

.

the smaller gra%itational mass.

____ $. Which of the following #uantities is conser%ed for a lanet orbiting a star in a circular orbit? )nly the lanet

itself is to be ta&en as the system* the star is not included.

a.

+omentum and energy.

b

.

Energy and angular momentum.



c

.

+omentum and angular momentum.

d

.

+omentum, angular momentum and energy.

e.

None of the abo%e.

____ . The figure below shows a lanet tra%eling in a countercloc&wise direction on an ellitical ath around a star

located at one focus of the ellise. When the lanet is at oint A,

its seed isconstant.

its seed is ama-imum.

its seed is

increasing.

its seed is a

minimum.

c

.

its seed is decreasing.

____ . The figure below shows a lanet tra%eling in a cloc&wise direction on an ellitical ath around a star located

at one focus of the ellise. When the lanet is at oint A,

its seed isconstant.

its seed is ama-imum.

its seed is

increasing.

its seed is a

minimum.

c

.


____ /. The figure below shows a lanet tra%eling in a countercloc&wise direction on an ellitical ath around a star




its seed is

constant.

its seed is a

ma-imum.

its seed is

increasing.

its seed is a

minimum.

c

.


____ 0. The figure below shows a lanet tra%eling in a countercloc&wise direction on an ellitical ath around a star


its seed is

constant.

its seed is a

ma-imum.

its seed is

increasing.

its seed is a

minimum.

c. its seed is decreasing.

____ . The figure below shows a lanet tra%eling in a cloc&wise direction on an ellitical ath around a star located

at one focus of the ellise. When the lanet is at oint A,

its seed is

constant.

its seed is a

ma-imum.

its seed is

increasing.

its seed is a

minimum.

c

.




____ 12. The figure below shows a lanet tra%eling in a countercloc&wise direction on an ellitical ath around a star


its seed isdecreasing.

all of the abo%e arecorrect.

its angular

momentum is

increasing.

none of the abo%e

is correct.

c

.

the gra%itational force does no wor& on

the lanet.

____ 11. When two solid sheres of the same material and same radius r are in contact, the magnitude of the

gra%itational force each e-erts on the other is directly roortional to

a

.

r . b

.

r !. c

.

r '. d

.

r $. e

.

r .

____ 1!. 3uyghens claimed that near the surface of the Earth the %elocity downwards of an ob4ect released from rest,

v y, was directly roortional to the s#uare root of the distance it had fallen, . This is true if c ise#ual toa

..

b

..

c

.

g . d

. .e

.

$ g .

____ 1'. "n an isolated system of two bodies that e-ert gra%itational forces on one another, the #uantity 5#uantities6 that

remain5s6 constant is5are6

a

.

the total energy of the system.

b

.

the total angular momentum of the system.

c

.

the angular ositions of the two bodies.

d

.

all of the abo%e.

e

.

only 5a6 and 5b6 abo%e.



____ 1$. 7arla and 8enny are arguing about whether or not it is ossible to escae the gra%itational field of the Earth.

7arla shows 8enny a system where mass m is r E 5not the Earth(s radius6 distant from Earth and r P 5not lanet

9(s radius6 distant from lanet 9, the mass being on the line connecting the Earth and lanet 9. 7arla states that

the mass m has escaed if F 9 on m : − F E on m. 8enny disagrees. Which one, if either, is correct, and why?

a

.

7arla, because the total gra%itational force on m is zero at that oint.

b.

7arla, because there is no gra%itational force from Earth on m at that oint.

c

.

7arla, because there is no gra%itational force on m from Earth when r ; r E .

d

.

8enny, because there is a gra%itational force on m from Earth no matter how great the

distance from the Earth.

e

.

8enny, because the gra%itational force from the Earth can only be bloc&ed by a body that

is larger than the Earth.

____ 1. 9airs of forces of e#ual magnitude act on identical cylinders as shown in the figures. "n which e-amle is the

cylinder in translational and rotational e#uilibrium?

a

.

b

.

c

.

d

.

e

.

____ 1. Angie says that an ob4ect is in e#uilibrium if the net tor#ues about the center of mass is zero. <obbie says that

an ob4ect is in e#uilibrium if the sum of e-ternal forces is zero. Which one, if either, is correct?

a

.

=oth are correct> an ob4ect is in e#uilibrium if either condition holds.

b

.

Neither is correct> both conditions must hold simultaneously.

c.

Neither is correct> the net e-ternal force and the net e-ternal tor#ue about any a-is must be zero.

d

.

Neither is correct> an ob4ect is in e#uilibrium only if its %elocity is zero in all coordinate

systems.e

.

=oth are correct> if the sum of the e-ternal forces is zero, the net tor#ue about any a-is is

automatically zero, and %ice %ersa.

____ 1/. ebastian has drawn a free@body diagram for a ladder of mass m leaning against a frictionless wall. 3is

diagram is shown below. What is his error?



a

. is in the wrong direction.

b

. should be directed uwards, not down.

c

. should be erendicular to the wall, not arallel to it.d

. should be down into the floor for to ha%e the gi%en direction.

e

. is correct, but there should also be a force erendicular to the wall.

____ 10. 8ohn is carrying a sho%elful of snow. The center of mass of the '.22 &g of snow he is holding is 1.2 cm from

the end of the sho%el. 3e is ushing down on the oosite end of the sho%el with one hand and holding it u

'2.2 cm from that end with his other hand. "gnore the mass of the sho%el. arah says that his hand ushing

down on the sho%el must be e-erting a greater force than the hand ushing u. 8ames says it is 4ust the

re%erse. Which one, if either, is correct?

a

.

arah, because the hand ushing down must e-ert a greater force to match the tor#ue

e-erted by the snow.

b

.

8ames, because, deending on the location of the a-is of rotation, the hand ushing down

can counteract the tor#ue e-erted by the snow.

c

.

8ames, because the hand ushing u must e-ert a force that e#uals the sum of the force of

the hand ushing down and the weight of the snow.

d

.

8ames, because both 5b6 and 5c6 abo%e are correct.

e

.

Neither, because the hands e-ert forces of e#ual magnitudes.

____ 1. The free body diagram below reresents a 1 22 &g car sitting on a ' 222 &g bridge suorted at its far ends.

The car(s osition is three #uarters of the length L from the left end of the bridge. "dentify the one error in the

tor#ue e#uation below>

a

. ne%er roduces a tor#ue on the bridge no matter where the a-is of rotation is laced.

b

. ne%er roduces a tor#ue on the bridge no matter where the a-is of rotation is laced.



c

. cannot roduce a tor#ue on the bridge no matter where the a-is of rotation is

ta&en since it is at the center of the bridge.

d

.=ecause the erendicular distance to from the left end of the bridge is 2, F 1 L should

be 2.e

. =ecause the erendicular distance to from the right end of the bridge is 2, F 2 L should be 2.

Short Answer

!2. A uniform ladder 1 ft long is leaning against a frictionless wall at an angle of '° abo%e the horizontal. The

weight of the ladder is '2 ounds. A /@lb boy climbs .2@ft u the ladder. What is the magnitude of the

friction force e-erted on the ladder by the floor?

!1. A horizontal uniform meter stic& suorted at the 2@cm mar& has a mass of 2.2 &g hanging from it at the

!2@cm mar& and a 2.'2 &g mass hanging from it at the 2@cm mar&. etermine the osition on the meter stic&

at which one would hang a third mass of 2.2 &g to &ee the meter stic& balanced.

!!. The figure shows a uniform, horizontal beam 5length : 12 m, mass : ! &g6 that is i%oted at the wall, with

its far end suorted by a cable that ma&es an angle of 1° with the horizontal. "f a erson 5mass : 2 &g6

stands '.2 m from the i%ot, what is the tension in the cable?

!'. A uniform 122@lb beam is held in a %ertical osition by a in at its lower end and a cable at its uer end. A

horizontal force 5magnitude P 6 acts as shown in the figure. "f P : / lb, what is the tension in the cable?

!$. A !@ft long crane suorted at its lower end by a in is ele%ated by a horizontal cable as shown in the figure.A !2@lb load is susended from the outer end of the crane. The center of gra%ity of the crane is 12 ft from the

in, and the crane weighs !22 lb. What is the tension in the horizontal cable?



!. A uniform beam ha%ing a mass of 2 &g and a length of !.0 m is held in lace at its lower end by a in. "ts

uer end leans against a %ertical frictionless wall as shown in the figure. What is the magnitude of the force

the in e-erts on the beam?

!. A uniform 1!2@lb beam is suorted in a horizontal osition by a in and cable as shown in the figure. What

is the magnitude of the force by the in on the beam?

!/. The diagrams below show forces alied to a wheel that weighs !2 N. The symbol stands for the weight. "n

which diagram5s6 is5are6 the wheel in e#uilibrium?

!0. The diagrams below show forces of magnitude B alied to an e#uilateral triangular bloc& of uniform

thic&ness. "n which diagram5s6 is5are6 the bloc& in e#uilibrium?



!. An ob4ect of mass m is susended by two colanar wires, as shown below. The tension in each wire has a

magnitude gi%en by

'2. The 1 2 &g solid steel door to a ban& %ault is !.22 m high, 1.22 m wide and 12 cm thic&. )ne hinge is 2.2

cm down from the to on the left hand side of the door. The other hinge is '2.2 cm u from the bottom. What

horizontal force, in what direction, does the door e-ert on the uer hinge?

'1. The 1 2 &g solid steel door to a ban& %ault is !.22 m high, 1.22 m wide and 12 cm thic&. )ne hinge is 2.2

cm down from the to on the left hand side of the door. The other hinge is '2.2 cm u from the bottom. What

horizontal force, in what direction, does the door e-ert on the lower hinge?

'!. A horizontal uniform 1.!2@N meter stic& is held u by two %ertical strings, one at the !2@cm mar& and the

other at the 2@cm mar&. What is the tension in the string at the 2@cm mar&?

''. A satellite circles lanet <oton e%ery !.0 h in an orbit ha%ing a radius of 1.! × 12/ m. "f the radius of <oton is

.2 × 12 m, what is the magnitude of the free@fall acceleration on the surface of <oton?

'$. The eriod of a satellite circling lanet Nutron is obser%ed to be 0$ s when it is in a circular orbit with a

radius of 0.2 × 12 m. What is the mass of lanet Nutron?

'. A 2@&g satellite circles lanet 7ruton e%ery . h in an orbit with a radius of 1! × 12 m. What is the

magnitude of the gra%itational force on the satellite by lanet 7ruton?

'. Two stars of masses ! and ! are searated by a distance ". etermine the distance 5measured from ! 6 to a

oint at which the net gra%itational force on a third mass would be zero.

'/. What is the magnitude of the free@fall acceleration at a oint that is a distance ! # abo%e the surface of the

Earth, where # is the radius of the Earth?

Exhiit 13-1

Three .2@&g masses are located at oints in the $y lane as shown in the figure.



Cse this e-hibit to answer the following #uestion5s6.

'0. <efer to E-hibit 1'@1. What is the magnitude of the resultant force 5caused by the other two masses6 on the

mass at the origin?

'. <efer to E-hibit 1'@1. What is the magnitude of the resultant force 5caused by the other two masses6 on the

mass at $ : 2.$2 m, y : 2?

$2. Three .2@&g masses are located at oints in the $y lane, as shown. What is the magnitude of the resultant

force 5caused by the other two masses6 on the mass at $ : 2, y : 2.'2 m?

$1. What is the gra%itational force on a !2@&g satellite circling the Earth 5radius : .$ × 12 m, mass : .2 × 12!$

&g6 with a eriod of .2 h?

$!. A saceshi of mass m circles a lanet 5mass : ! 6 in an orbit of radius #. 3ow much energy is re#uired to

transfer the saceshi to a circular orbit of radius ' #?

$'. A sacecraft 5mass : m6 orbits a lanet 5mass : ! 6 in a circular orbit 5radius : #6. What is the minimum

energy re#uired to send this sacecraft to a distant oint in sace where the gra%itational force on the

sacecraft by the lanet is negligible?

$$. A ro4ectile is launched from the surface of a lanet 5mass : ! , radius : #6. What minimum launch seed is

re#uired if the ro4ectile is to rise to a height of ! # abo%e the surface of the lanet? isregard any dissiati%eeffects of the atmoshere.

$. An ob4ect is released from rest at a distance h abo%e the surface of a lanet 5mass : ! , radius : # D h6. With

what seed will the ob4ect stri&e the surface of the lanet? isregard any dissiati%e effects of the atmoshere

of the lanet.



$. What is the &inetic energy of a !22@&g satellite as it follows a circular orbit of radius 0.2 × 12 m around the

Earth? 5+ass of Earth : .2 × 12!$ &g.6

$/. An ob4ect is released from rest when it is a height h abo%e the surface of a lanet of mass ! and radius #.

What is the seed of the ob4ect 4ust before stri&ing the surface of the lanet? Neglect any air resistance. et h

: $.2×

12

m, # : .2×

12

m, and ! : $.2×

12

!$

&g.

$0. A 2@&g satellite circles the Earth in an orbit with a eriod of 1!2 min. What minimum energy is re#uired to

change the orbit to another circular orbit with a eriod of 102 min? 5Earth> radius : .$ × 12 m, mass : .2 ×

12!$ &g6

$. 9lanet <oton has a mass of $.2 × 12!' &g and a radius of !.2 × 12 m. With what seed should a sace robe

be launched from the surface of <oton so as to achie%e a ma-imum distance of '.2 × 12 m from the center of

<oton?

2. 9lanet Fero has a mass of .2 × 12!' &g and a radius of !.2 × 12 m. A sace robe is launched %ertically from

the surface of Fero with an initial seed of $.2 &mGs. What is the seed of the robe when it is '.2 × 12 m

from Fero(s center?

1. What is the escae seed from a lanet of mass ! and radius # if ! : '.! × 12!' &g and # : !.$ × 12 m?

!. A satellite of mass m circles a lanet of mass ! and radius # in an orbit at a height ! # abo%e the surface of

the lanet. What minimum energy is re#uired to change the orbit to one for which the height of the satellite is

' # abo%e the surface of the lanet?

'. 9lanet Fero has a mass of $.2 × 12!' &g and a radius of !.2 × 12 m. A 12@&g sace robe is launched %ertically

from the surface of Fero with an initial &inetic energy of 0.2 × 12/ 8. What ma-imum distance from the center

of Fero is achie%ed by the robe?

$. Two satellites are laced in geosynchronous orbits, orbits with a eriod of !$ hours, where each satellite

ho%ers o%er a sot on the Earth(s e#uator. atellite = has three times the mass of satellite A. What is the

relationshi between the magnitudes of the gra%itational forces of the Earth on the two satellites?

. The eriod of oscillation of a near@Earth satellite 5neglecting atmosheric effects6 is 0$.' min. What is the

eriod of a near@+oon satellite? 5 # E : .'/ × 12 m* # ! : 1./$ × 12 m* ! E : .0 × 12!$ &g* ! ! : /.' × 12!!

&g.6

. Three gala-ies, each of mass ! : $.2 × 12$1 &g, lie in a lane at the corners of an e#uilateral triangle with

sides of .2 × 12!! m length. The magnitude of the force the other two gala-ies e-ert on each gala-y is

/. Hnowing that at sea le%el and that # E : .'/ × 12 m, we find that the %alue of g in at a

distance # E from the surface of the Earth is



0. uose the gra%itational force of the Earth on a body was . What escae %elocity ve would a

body need to escae the gra%itational field of the Earth?

. An asteroid re%ol%es around the un with a erihelion 2. AC and an ahelion of /. AC. What is its eriod

of re%olution?



2. A satellite re%ol%es around the Earth in a circular orbit with a mechanical energy of 8.

What is its &inetic energy?

AP Physics C Review Guide CH12-13

Answer Section

M!"#$P"E CH%$CE

1. A

!. 7

'. =

$. =

. =

. 7

/. E

0. 7

. =

12. E

11. =

1!.

1'. E

1$.

1. =

1. 7

1/. 7

10. 7

1.

SH%R# A&S'ER

!2. '$ lb



!1. /2 cm

!!. 2.'0 &N

!'. $ lb

!$. /2 lb

!. 2.0 &N

!. / lb

!/. 7

!0. =

!. mg .

'2. 2 N, right

'1. 2 N, left

'!. 2.2 N

''. !/ mGs!

'$. $.' × 12!0 &g

'. 0 N

'. 2.! "

'/. 1.1 mGs!

'0. !.1 × 12−0 N

'. 1. × 12−0 N

$2. !.' × 12−0 N

$1. ' N

$!. %m! G5' #6

$'. %m! G5! #6

AP C Review Guide CH12-13

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