Download PHY1 Review for Exam 5 Topics 1. Uniform circular Motion a

PHY1
Review for Exam 5
Topics
1. Uniform circular Motion
a. Centripetal acceleration
b. Centripetal force
c. Horizontal motion
d. Vertical motion
e. Circular motion with an angle
2. Universal gravitation
a. Gravitational force
b. Kepler’s law
Earth-sun distance = 1.49 x 108 km
Earth moon distance = 3.84 x 105 km
Equations
V = 2πr / T
F = ma
(T1/T2)2 = (r1/r2)3
ac = V2/r
F = Gm1m2/r2
FF = µFN
Constants
G = 6.67 x 10-11 N m2/kg2
Earth: Mass = 5.97 x 1024 kg
Radius = 6.38 x 103 km
Moon Mass = 7.35 x 1022 kg
Radius = 1.74 x 103 km
Sun
Mass = 1.99 x 1030 kg
Radius = 6.96 x 105 km
Multiple Choice Questions
1. A ball attached to a string is moved
at constant speed in a horizontal
circular path. A target is located
near the path of the ball as shown in
the diagram
3. The diagram below represents two
satellites of equal mass, A and B, in
circular orbits around a planet.
At which point along the ball’s path
should the string be released, if the
ball is to hit the target?
(1) A
(2) B
(3) C
(4) D
2. As an astronaut travels from the
surface of the earth to a position that
is four times as far away from the
center of the earth, the astronaut’s
(1) mass decreases.
(2) mass remains the same.
(3) weight increases
(4) weight remains the same.
Compared to the magnitude of the
gravitational force of attraction
between satellite A and the planet,
the magnitude of the gravitational
force of attraction between satellite
B and the planet is
(1)
(2)
(3)
(4)
half as great.
twice as great.
one-fourth as great.
four times as great.
PHY1
Review for Exam 5
4. The diagram below shows a 5.0
kilogram bucket of water being
swung in a horizontal circle of 0.70
meter radius at a constant speed of
2.0 meters per second.
6. In the diagram below, S is a point on
a car tire rotating at a constant rate.
Which of the following graphs best
represent the magnitude of the
centripetal acceleration of point S as
a function of time during one
complete revolution of the tire?
The magnitude of the centripetal force
on the bucket of water is approximately
(1) 5.7 N
(2) 14 N
(3) 29 N
(4) 200 N
5. In the diagram below, a cart travels
clockwise at constant speed in a
horizontal circle.
Base your answers to questions 7 thru 9
on the information and diagram below.
At the position shown in the
diagram, which arrow indicates the
direction of the centripetal
acceleration of the cart?
(1) A
(2) B
(3) C
(4) D
The diagram shows the top view of a
65 kilogram student at point A on an
amusement park ride. The ride spins
the student in a horizontal circle with
a radius of 2.5 meters, at a constant
speed of 8.6 meters per second. The
floor is lowered and the student
remains against the wall without
falling to the floor.
PHY1
Review for Exam 5
9. The magnitude of the coefficient of
friction between the students back
and the surface of the ride can not be
less than
(1) 0.33
(2) 30
7. Which vector best represents the
centripetal acceleration of the student
at point A?
(3) 9.8
(4) 0.10
10. A ball of mass M at the end of a
string is swung in a vertical circular
path with constant speed (V), as
shown in the diagram below. At
what point is the string most likely to
break because it has the greatest
tension?
V
A
B
8. The magnitude of the centripetal
force acting on the student at point A
is approximately
(1) 1.2 x 104 N
(2) 1.9 x 103 N
(3) 2.2 x 102 N
(4) 3.0 x 101 N
V
V
D
C
V
(1) A
(2) B
(3) C
(4) D
11. A 1.0 x 103 kilogram car travels at a constant speed of 20 meters per second around a
horizontal circular track. Which diagram correctly represents the direction of the
car’s velocity (v) and the direction of the centripetal force (Fc) acting on the car at one
particular moment?
PHY1
Review for Exam 5
Short Answer Questions (Show all work)
12. A child on a merry-go-round is moving with a speed of 1.35 m/s when 1.20 m from
the center of the merry-go-round. Calculate (a) the centripetal acceleration of the
child, and (b) the net horizontal force exerted on the child whose mass is 25.0 kg. (c)
What happens to the speed when the child moves towards the center of the merry-go
round assuming that the period of revolution remains the same?
13. A 0.40 kg ball attached to the end of a horizontal cord, is rotated in a circle of radius
1.3 m on a frictionless horizontal surface. If the cord will break when the tension
exceeds 60 N, what is the maximum speed the ball can have?
14. At what speed must a roller coaster be traveling when upside down at the top of a
circle if the passengers who are not wearing their seat belts don’t fall out. Assume a
radius of curvature of 8.6 m.
PHY1
Review for Exam 5
15. Using Newton’s law of universal gravitation determine the force of gravity between
the earth and the moon.
16. By combining Newton’s universal law of gravitation and F = mV2/r, calculate the
velocity of a satellite moving in a stable orbit about the earth at a height of 3600 km.
17. Qualitatively describe the orbit of Halley’s comet around the sun based on your
understanding of the elliptical orbit and the corresponding force and velocity vectors
at various positions in the orbit. Draw a picture of the orbit with vectors to support
your discussion.
PHY1
Review for Exam 5
Answers
1. 2
2. 2
3. 3
4. 3
5. 1
6. 2
7. 1
8. 2
9. 1
10. 3
11. 1
12. (a) 1.52 m/s2; (b) 38.0 N; (c) Since the radius decrease the speed also decreases,
assuming that the period of revolution remains the same.
13. 14 m/s
14. 9.2 m/s
15. 1.90 x 1020 N
16. 1.05 x 104 m/s, m1 cancels and be sure to use the mass of the earth as m2.
17. The force of gravity is greatest when the comet is closest to th sun and the
velocity is also the greatest. The velocity vector is perpendicular to the force
vector which is pointed at the sun. The velocity and force vectors are also
perpendicular at the furtherest point from the sun, where they are the smallest. At
position where the comet is moving away from the sun the angle between the
velocity and force vectors is gretaer than 90°. The force vector is always pointed
at the sun and the velocity vector is tangential to the orbit. When the comet is
moving towards the sun the angle between the force and velocity vectors is less
than 90°.