Download South Pasadena • A.P. Physics Name 5 · Circular Motion/Law of

South Pasadena • A.P. Physics
Name
5 · Circular Motion/Law of Gravitation
Period
Date
PRACTICE TEST
DIRECTIONS
 Assume that “up” or “right” is the positive direction, and “down” or “left” is the negative direction. Assume that air
resistance is negligible, unless otherwise specified. Use g = 9.8 m/s2, unless otherwise specified.
FORMULAS
rev
freq = t
G mM
FG = r2
v = 2 π r (freq)
2

 (T1 )

 (T 2 2 )


(r1 3 ) 

(r 2 3 ) 
v2
aC = r
mv2
FC = r
Earth-sun distance =
1.50 x 1011 m
T = 1/f
G = 6.67 × 10–11
N·m2/kg2
g = Gm
r2
SECTION 1: MULTIPLE CHOICE
1. An empty water bottle is placed on the edge of a
moving merry-go-round. However, it is unable to
stay upright. Instead, we expect it to:
a) Fall on its side, but will remain on the merry
go-round because of inertia.
b) Fly straight outward away from the merry-goround because of centrifugal force.
c) Go off in a direction tangent to the merry-go
round, because of its velocity.
d) Move toward the center of the merry-go-round
because of centripetal force.
e) Push backward in the direction opposite from
the direction of the merry-go-round, because of
gravity.
2. When an object is moving in a circle, how do the
acceleration and force vectors compare?
a) The acceleration and force vectors both point in
the direction tangent to the object’s circular
path.
b) The acceleration and force vectors both point
outward.
c) The acceleration and force vectors both poin
toward the center of the circular path.
d) The acceleration vector point toward the
circular path, and the force vector points
outward.
e) The acceleration vector points in the direction
tangent to object’s circular path, and the force
points toward the center of the circular path.
3.
If an object moves with a frequency of 12
revolutions per minute, how many seconds does it
take to make three revolutions?
a) 9
b) 12
c) 15
d) 24
e) 36
4. A ball is connected to a string and makes a circular
path. The tension on the string (which is the
centripetal force) is 6.0 N. If the radius remains
constant and the velocity doubles, what will be the
new tension on the string?
a) 1.5 N
d) 12 N
b) 3.0 N
e) 24 N
c) 6.0 N
5. A 0.020 kg stopper is connected to a string and
spun around, making ten revolutions every 4
seconds. If the radius of the circular path is 0.50 m,
what is the centripetal acceleration acting on the
stopper?
a) 0.16 m/s2
d) 12.5 m/s2
2
b) 2.5 m/s
e) 123 m/s2
c) 5.0 m/s2
6. If the radius of the earth is r meters, how much
does a 10-kg object weigh 2r meters away from the
center of the earth?
a) 24.5 N
d) 196 N
b) 49 N
e) 392 N
c) 98 N
7. A 500-kg and a 200-kg object are 200 m away from 10. The strength of the gravitational force between two
objects depends on which of the following?
each other. How would the gravitational force
I. The distance between the objects.
between the objects change if they are 400 m
II. The mass of the objects.
away?
III. The speed at which the objects are moving.
a) It would increase four-fold.
b) It would double.
a) I only.
c) It would be the same.
b) II only.
d) It would be halved.
c) I and II only.
e) It would be one-fourth of the original force.
d) II and III only.
e) I, II, and III.
8. How does the gravitational force between two
objects with masses 2.0 kg and 5.0 kg compare
with that between two objects with masses 1.0 kg
and 10.0 kg? Both sets of objects are 1.5 m away
from each other.
a) FG of the first set is four times as strong as FG
of the second set.
b) FG of the first set is twice as strong as FG of the
second set.
c) FG of the first set is the same as FG of the
second set.
d) FG of the first set is half as strong as FG of the
second set.
e) FG of the first set is one-fourth as strong as FG
of the second set.
9. Newton observed that an apple fell toward the
ground, while the moon did not. Why is this so?
a) The apple is much smaller than the moon, and
is more attracted to the earth than the moon is.
b) The moon actually is falling toward the earth,
in order to maintain its circular orbit.
c) The moon is much further away from the earth
than the apple, so it does not experience earth’s
gravity.
d) The moon’s inertia keeps it in orbit and from
falling to the earth.
e) None of the statements above are correct.
The Next Five Questions are Related To Each Other
11. If two masses are separated by a certain distance,
producing a certain gravitational force of F, how
would the force change if both masses are doubled?
a) It would increase four-fold.
b) It would double.
c) It would be the same.
d) It would be halved.
e) It would be one-fourth of the original force.
12. If the two masses in the previous question were not
changed, but the distance of separation was reduced
to ½ of the original distance, what happens to the
force?
a)
b)
c)
d)
e)
It would increase four-fold.
It would double.
It would be the same.
It would be halved.
It would be one-fourth of the original force.
13. What would happen to the force in the previous
question if the masses are still not changed, but the
distance of separation is reduced to ¼ the original
distance?
a) It would double.
b) It would increase four-fold.
c) It would increase eight-fold.
d) It would increase sixteen-fold.
e) It would be one-fourth of the original force.
14. If the two masses were both doubled, and the
distance of separation is doubled, what would
happen to the force?
a) It would increase four-fold.
b) It would double.
c) It would remain the same.
d) It would be halved.
e) It would be one-fourth of the original force.
15. If one of the masses is doubled, and the other mass
remains unchanged, and the distance of separation
is tripled, what would happen to the gravitational
force?
a)
b)
c)
d)
e)
16. Consider a pair of binary stars that pull on each
other with a certain force. Would the force become
larger or smaller if the mass of each star were three
times as great and their distance of separation
became three times greater?
It would become 3 times bigger.
It would become 2 times bigger
It would become 2/3 as big.
It would become 2/9 as big.
It would become 1/9 as big.
a) It would become larger.
b) It would become smaller.
c) It would remain the same.
SECTION 2: FREE RESPONSE
17. A 0.050 kg weight attached to a string is spinning clockwise (to the right) in a circle with a radius of 0.80 m.
It makes ten revolutions every 4.6 seconds.
(a) Draw the vectors indicating the acceleration, force, and velocity experienced by the weight.
(b) Calculate the frequency at which the weight is spinning (in rev/s).
(c) Calculate the velocity of the weight.
(d) Calculate the acceleration experienced by the weight.
(e) Calculate the force experienced on the weight.
18. The planet Mars has a mass of 6.42 × 1023 kg. Phobos, one of the moons of Mars, makes a circular orbit with
a radius of 9400 km around Mars. If the mass of Phobos is 1.08 ×1016 kg, what is the gravitational force
between Phobos and Mars?
19.
The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the other planets. Its
period (T) is about 410 d. What is its mean distance from the Sun?
A.P. Physics Chapter 5 Practice Test ANSWERS:
1.
2.
3.
4.
C
C
C
E
5.
6.
7.
8.
17. (a)
E
A
E
C
9.
10.
11.
12.
B
C
A
A
13.
14.
15.
16.
D
C
D
C
v
ac
Fc
17. (b)
n = 10 rev
f=
n 10 rev
=
= 2.2 s–1
t
4.6 s
t = 4.6 s
17. (c)
r = 0.80 m
f = 2.2 s–1
v = 2 π r f = (2)(3.1416)(0.80 m)(2.2 s–1) = 11 m/s
17. (d)
v = 11 m/s
a=
v2 (11 m/s)2
=
= 150 m/s2
r (0.80 m)
r = 0.80 m
17. (e)
m = 0.050 kg
a = 150 m/s2
F = ma = (0.050 kg)(150 m/s2) = 7.5 N
18.
m = 1.08 × 1016 kg
M = 6.42 × 1023 kg
FG =
GmM (6.67 × 10–11 N-m2/kg2)(1.08 × 1016 kg)(6.42 × 1023 kg)
=
= 5.2 × 1015 N
d2
(9400000 m)2
d = 9,400,000 m
19.
2

 (T1 )

 (T 2 2 )


(r1 3 ) 

(r 2 3 ) 
Mean Distance of asteroid Icarus from Sun
r = { [(1.5 x 1011 m)3 x (410 d)2] / (365 d)2}1/3 = 1.62 x 1011 meters