Download tll` =6ffi= 4(6ff)= 4 Fo.u

Name
Period
Date
11-1
Chapter 11: Gravitational Interactions
The equation for the law of universal gravitation is
tll'
F = G,
=d.
F it tn" force of attraction between masses rr, and m1 separated by distance
d , and, G is the universal gravitational constant (and relates to the masses and
u-here
diqbnss just as the constant rc relates the circumference of a circle to its diameter). By
substifuting changes in any of the variables into this equation, we can predict how the others
change. For example, we can see how the force changes if we know how either or both of the
masses change, or how the distance between their centers changes.
Suppose, for example, that one of the masses somehow is doubled. Then substituting
Zh, for wl in the equation gives
FN€w= ('*lf'
"-d.
So we see the force doubles also.
Then substituting
2d for d
2(6
rl'Yfrz\ -' tr
-- arouD
d. l
Or suppose, instead, that the distance of separation is doubled.
in the equation gives
[l, mr
@'=
Fn,., =
=
,.
<'
And we see the force is ortlv 1/4 as much.
Use this method to solvi: the following problems. Write the equation and make the
appropriate subs titutions.
1. If both masses are doubled, what happens to the force?
Fnu*= G
2m1?'ng
r'l
d*
rb",,
da
? FoLF}
If the
masses are not changed, but the distance of separation is reduced to "I/2 the original
distance, what happens to the force?
;l&a+i$
=6ffi= 4(6ff)= 4 Fo.u
Conceptual Physics: Concept-Development Exercises
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Exercise
11-1
29
3. If the masses are not changed, but the distance of separation is reduc ed to 1 / 4 the original
distance, what happens to the force?
t-=
I NEW
If both masses are doubled, and the distance of
separation is doubled" show what happens to the force.
r -rl^rhns - 4r hrt
F".*=Cffi
a\raF= Fo,oi No
cHANGE
If one of the masses is doubled, the other remains unchanged, and the distance of separation
is tripled, show what happens to the force.
,n 2m1m7
-FnE*,= u
=
TE;F
-,n1\ = Z C
/r
(G
T ) =" aoro
O
L^
Consider a pair of binary stars that pull on each other with a certain force. Would the force be
larger or smaller if the mass of each-star were three times ad great and if their distance apart
were three times as far? Show what the new force will be compared to the first one.
3-t3t. 9 la^r^"\-tr
tr
(] (3dr = ((]-if-)= %,o; No CHANGE!
F,,ew=e
.
6
30
Exetcise 11-1
@
Conceptual Physics: Concept-Development Exercises
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Date
Period
\::-',e
Cl"apter
1"1:
LL-2
Gr-aritational Force and Weight
has a mass of 0.1 kg has the same mass wherever
--:.:::,e{es up the apple
-r-:.
a::-e :lut
it is' The amount
of
matter
i-5:*@-@@+*€$q-
:epends
-:e
on) . (does
._..;adon of the appte.
;;tli-*r-h€f€
not dePend on) I
tt has the same resistance to acceleration wherever it is-its inertia
15
(the same) ..'i (different).
may weigl exactly 1 N in San Francisco and 9lg-\tty
-*:e rr-eiqht of the apple is a different story. It
weigh 0'17 N,
o;ifr. surfa'ce or itre mo-on the apple would does
i==
not change
that
qriantity
The
all.
at
a:,J far out in orrt.. ipu.e ir *uy nuue ai*oit no weight
rrith location is
;';[ii;;1;i"D5ff;;i"T;'^"d'
,
gt*..:i
(weight),
and the quantity that may change with location is its
;:rr:{ff:ryitrt\
(mass) (weight).;
. **:-*.,"
That's because
(mass)
il.yi,q_T],3
distance. So we see that
is a measure of gravitational force on a body, and this force varies with
in contact with the
object
small
some
weight is the force of gravity U.t*...t t*o 6odies, usually
eartl. When we refer to the
(mass)Ljy=:g_tpj
it to the earth'
of an object, we are usually speaking of the gravitational force that attracts
FilI in the blanks:
find that we are pulled toward the earth with a force of
: 1"" N. Strictly speaking, we weigh '^:, N relative to the
500 N, then we say we weigh
-- and repeat the weighing
earth. How much aoes tt,""eurtr, weigh? tf *. iipit"r. scie upside-dowo
.
force of i' I N, and
process, we can say that the earth is being attracted to us with a
If we stand on a weighing
scale and
earth
therefore, rerative to us, the whore 6 000 000 000 000 000 000 000 000-kg
Weight, unlike mass, is a relative quantity'
weigllt ::'ilir 5t
DO YOU SEE WHY IT MAKES
SENSE TO DISCUSS THE EARTH'S
A^ASS, BUT NOT ITS WEI6HT?
44:
i', e are pulled to the earth with a
iote of 60Q N, so we weigh 500 N.
The earth is pulled toward us with
force of 500 N, so it weighs 500 N.
a
tfr
Conceptual Phvsics: Concept-DeveloPmcnt Exercises
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Exercise 11-2
31
\:::e
Date
Period
12-1
C:ep:er l-:: Satetrlite \{otion
::;*-- -i is r-rf ,,Newton's
Mountain," high enough so_ its top is.above the drag
::---:: a:r.L1sphere. The cannonball is fired and hits the ground aS shown' . *,
the path the cannonball might take if it were fired a
':-ie -it faster.
: ]a.-r
t
:
?
t
5 i<m/s.
c
d
t
3
t
Then draw the orbital path of the cannonball if its speed
rvere 8
E
t
Repeat for a speed that is greater still, but still less than
s.
km/s.
lVhat is the shape of the curve for a speed of 8 km/s?
*
:,-'lr=
Tfgure a
What would be the shape of the orbital path if the
cannonball were fired at a speed of about 9 km/s?
e
llrose
Figure B shows a satellite in circular orbit'
,or
a. At each of the four positions draw a vector that represents
the gravitational foice exerted on the satellite'
F
,*
b. Label the force vectors F.
c. Then draw at each position a vector to represent the uelocity
of the satellite at thit position, and lable itV'
d. Are all four F vectors the same length? Why or why not?
Yes, n*ear.rs* the foree i3
l,:-:e
san-ir: girengih at equa! distane e*
Figure
B
12-1
33
ir*nr the earlh'
3: i\
vu :-!, rlan
r,vYr re,a
What is the angle between Your F and V vectors?
f.lo, Fand Vare
f. Is there any comPonent of F along V ?
e.
o
6'
PerPendiei":lar.
satellite?
What does this tell you about the work the force of gravity does on the
i-ile foree cf gravity dees no 1r,'ork on ihe sateiiite
h. Are all four V vectors the same length? Why or why not?
: :':;,..ijS* thgre is no er:-;ii];eratloi'i alonq thr': :'ateiiite's path"
Conceptual Phvsics: Concept-DcveloPment Exerciscs.
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O
Exercise
1.
Does the KE of the satellite in Figure B remain constant, or does
li remains constant.
it vary?
k. Does the PE of the satellite remain constant, or does it vary?
it rernain* c0flslanr"
Figure C shows a satellite in elliptical orbit.
3.
a. Repeat the procedure you used for the circular orbit, drawing vectors F and V for each
position, including proper labeling. Show equal magnitudes with equal lengths, and
greater magnitudes with greater lengths, but don't bother making the scale accurate.
b. Are your F vectors all the same length? Why or why not?
Na, the fo;'ee decreases wh*r'lthe elistance fro!'n the earth
increases
c. Is the angle between your F and V vectors the same
everywhere, or does it vary?
l+
{,^,,.it !{;llrijiJ-
d. Are there places where there is a component
Yss, q;veri,ivhere excspt
of F along
V?
:t th9 apE.qee ind the nerigee"
e. Is work done on the satellite when there is a component of
F along and in the same direction asVT If so, does this
increase or decrease the KE of the satellite?
\r'e*. This inr:;'-;a:e
I ihe {[ {f
the satellite"
f. When there is a component of F along and opposite to the
direction of V, does this increase or deirease th-e KE of the
satellite?
This cieer*ases ii-,s KF of the satellit*.
g. Are your V vectors all the same length? Why or why not?
f.ia. When ihe KH ,isgsr,;;5gs ias the saieilite moves farther f:.om
ti:e earthl, th*
speeeJ qjprr*ases. \lJhen
sa:eliite nrrves iorryai'd
Figure
C
the KE increases {as the
ii:* elrth], the speed
increases.
h. What can you say about the sum KE + PE along the orbit?
ll ir,' g9ns1s6t {in accord wilh eonservatlon r:f energy].
34
Exercise 12-1
Conceptual Physics: Concept-Development Exercises
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