Circular Motion and Gravitation
4.
Objects dropped near the surface of the moon fall with one sixth the
acceleration of objects dropped near the surface of the earth. Which
of the following is the correct value for the gravitational field strength
at the moon’s surface?
(a) 0.0027 N/kg
(b) 0.27 N/kg
(c) 1.6 N/kg
(d) 9.8 N/kg
5.
An unpowered 1600 kg object has an upward velocity of 7.0 x 10 3 m/s at
an altitude of 100 km above the earth. The object reaches a maximum
altitude of 400 km.
Release 07-08
1.
2.
A car completes a horizontal circle of radius r in time T. The same car
then completes a larger horizontal circle of radius 2r in twice the time,
2T. What is the ratio of the centripetal acceleration ac for the car in
the second circle to that in the first circle ac2/ac1?
(a) 1/4
(b) 1/2
(c) 2/1
(d) 4/1
An object is in uniform horizontal circular motion.
Which of the following shows the correct direction for the velocity,
centripetal acceleration, and centripetal force on the object at the
point shown?
What is the heat energy generated during the object’s increase in
altitude from 100 km to 400 km?
(a) 3.3 x 1010 J
(b) 3.4 x 1010 J
10
(c) 3.5 x 10 J
(d) 5.5 x 1010 J
6.
3.
A planet is in orbit of radius R around a star. The star collapses to 1/10
of its original volume while maintaining all of its mass.
A roller coaster car carrying a 75.0 kg man has a speed of 11.0 m/s at
the top of a circular loop of radius 12.0 m.
What is the normal force acting on the man at the top of the loop?
(a) 0.0 N
(b) 21 N
(c) 735 N
(d) 756 N
What happens to the centripetal acceleration, ac, of the planet due to
the collapse of the star?
(a) reduced to 1/100 original ac (b) reduced to 1/10 original ac
(c) remains unchanged
(d) increased to 10 X original ac
Release 06/07
7.
11. A meteor passes by a moon as shown below.
A 4.0 kg bucket of paint tied to a rope is being swung in a vertical circle
with a radius of 2.0 m. The speed of the bucket at the top of its swing is
5.0 m/s.
Which EK versus time graph shows how the kinetic energy of the meteor
changes from position a to position b?
What is the tension in the rope at this point?
(a) 11 N
(b) 39 N
(c) 50 N
(d) 89 N
8.
9.
Two objects of unequal mass are dropped from the same height near the
surface of the earth. Which of the following is the same for both
objects just before they hit the surface? (Ignore friction).
(a) velocity
(b) net force
(c) momentum
(d) kinetic energy
Release 05/06
12. An object moves in uniform circular motion in a vertical plane. Which is
the direction of the acceleration at P?
What is the gravitational field strength on the surface of a moon with a
mass of 3.7 x 1021 kg and a radius of 8.4 x 105 m?
(a) 0.35 N/kg
(b) 9.8 N/kg
(c) 540 N/kg
(d) 2.9 x 105 N/kg
10. What is the speed required to maintain a stable orbit around a planet of
mass 2.5 x 1027 kg at a radius (from the centre of the planet) of
8.5 x 107 m?
(a) 23 m/s
(b) 3.3 x 104 m/s
(c) 4.4 x 104 m/s
(d) 9.8 x 108 m/s
(a) W
(c) Y
(b) X
(d) Z
13. A 1600 kg car moves at a constant speed of 28 m/s around a level 100 m
radius circular track. What is the minimum coefficient of friction
between the tires and the road surface?
(a) 0.18
(b) 0.57
(c) 0.80
(d) 1.25
14. In an amusement park ride, riders are inside an 18 m diameter rotating
cylinder.
If the cylinder rotates once every 5.4 s, what force does the wall exert
on a 58 kg rider at the top and bottom of the ride?
15. Matter is orbiting around a collapsed star of mass 3.6 x 1030 kg at an
orbital radius of 8.5 x 104 m. What is the orbital period of this matter?
(a) 1.2 x 10-7 s
(b) 1.0 x 10-4 s
-2
(c) 1.0 x 10 s
(d) 1.0 x 101 s
16. A 4.5 x 104 kg vehicle is orbiting the earth with an orbital radius of
9.38 x 106 m and a speed of 6.52 x 103 m/s. What minimum energy is
needed for this vehicle to reach a position infinitely far away from the
earth?
(a) 9.6 x 1011 J
(b) 1.9 x 1012 J
12
(c) 2.9 x 10 J
(d) 4.1 x 1012 J
17. Which of the following graphs shows how the gravitational potential
energy of an object varies with its distance from the earth?
Release 04/05
18. A small spider is accidentally taking a ride on a CD rotating with a period
T. Its centripetal acceleration is 10 m/s2. The CD player is turned off
and the disc slows down. What is the spider’s centripetal acceleration
when the disc has slowed so the period is 2T?
(a) 2.5 m/s2
(b) 5.0 m/s2
(c) 20 m/s2
(d) 40 m/s2
19. The 2.5 kg lead mass shown below is moving in a horizontal circle. The
tension in the line is 30 N.
What is the centripetal force on the lead mass?
(a) 17 N
(b) 25 N
(c) 30 N
(d) 55 N
20. A car is going around a curve at constant speed on a level road as shown
in the diagram below.
Which of the following free body diagrams shows the forces acting on
the car?
21. A satellite is in a circular orbit around a planet. Which of the following
describes the magnitude of the force due to gravity on the satellite as
it moves around the planet?
(a) constant
(b) increasing
(c) decreasing
(d) increasing then decreasing
25. A mass is launched from the surface of a large moon at high speed.
Which of the following graphs shows the potential and kinetic energies
of the mass as it moves away from the moon?
22. A planet has a larger gravitational field strength on its surface than
does the earth. Which of the following is a possible comparison of this
planet’s mass and radius with Earth’s?
August 04
26. The net force acting on a body in uniform circular motion is constant in:
(a) direction only
(b) magnitude only
(c) both magnitude and direction (d) neither magnitude nor direction
23. The force due to gravity between two masses (m1 and m2) is determined
for several separation distances. This data is then used to create the
graph below. What is the slope of this graph?
27. A 1200 kg car travels with a maximum speed of 24 m/s in a circular path
on a dry level road surface where μ=0.90 between the car tires and the
road. What is the radius of this circular path?
(a) 27 m
(b) 59 m
(c) 65 m
(d) 640 m
28. Two satellites, S1 and S2, are in circular orbits around a planet. Satellite
S2 has twice the mass and twice the orbital radius of satellite S1.
(a)
(c)
G
m1  m2
G
(b)
m1  m2
(d)
G  m1  m2
24. What is the speed of a 500 kg satellite orbiting the moon at a distance
of 2.5 x106 m from the moon’s centre?
(a) 0.89 m/s
(b) 20 m/s
(c) 1.4 x 103 m/s
(d) 3.1 x 104 m/s
What is the ratio of the centripetal force on S2 to that of S1? (S1:S2)?
(a) 1:1
(b) 1:2
(c) 1:4
(d) 1:8
29. Which of the following is a correct statement about gravity?
(a) An object falling freely has no gravitational force on it.
(b) The acceleration due to gravity, g, is a universal constant.
(c) The gravitational field of a body follows an inverse square law.
(d) The gravitational potential energy varies with the square of distance
of separation.
30. The mass of planet Neptune is 17 times more than that of the earth. It
has a radius 3.8 times that of the earth. Which of the following is the
best approximation of the acceleration due to gravity on the surface of
Neptune?
(a) 8.3 m/s2
(b) 12 m/s2
2
(c) 44 m/s
(d) 170 m/s2
31. How much work is required to raise a 4.0 x103 kg object to an altitude of
5.0 x 106 m above the earth’s surface?
(a) 1.1 x 1011 J
(b) 1.4 x 1011 J
11
(c) 2.0 x 10 J
(d) 2.5 x 1011 J
34. A small object of mass m is suspended from a fixed point by a light
cord.
The object is raised to an angle of 60º and released from rest. The
object moves in an arc of a circle as shown. When the object passes
through its lowest position at point P, what is the tension in the cord in
terms of the object’s weight (mg)?
(a) 0.5 mg
(b) 1.0 mg
(c) 1.5 mg
(d) 2.0 mg
35. The graph shows the gravitational force between the earth and an
object as a function of the distance of separation, r, from the centre of
the earth.
June 04
32. A 5.0 x 104 kg moonlet travels in a circular path around a planet. The
moonlet’s orbital radius is 2.5 x 107 m and the orbital period is 3.7 x 105
s. What is the mass of the planet?
(a) 1.1 x 108 kg
(b) 6.8 x 1022 kg
27
(c) 3.4 x 10 kg
(d) 2.5 x 1028 kg
33. A 0.15 kg toy airplane is suspended as shown. It travels in a horizontal
circle at a constant speed.
As the object is moved from r1 to r2, what is the work done?
(a) Q
(b) Q + S
(c) P + Q
(d) Q + S + T
36. A 200 kg object is released from rest at an altitude of 1.0 x 107 m.
What is its impact speed with the earth? Assume no air resistance.
(a) 7.0 x 103 m/s
(b) 8.7 x 103 m/s
(c) 1.1 x 104 m/s
(d) 1.4 x 104 m/s
January 04
What is the period of the motion of this airplane?
(a) 0.84 s
(b) 1.6 s
(c) 1.8 s
(d) 2.0 s
37. When an object is in uniform circular motion,
(a) its speed is constant
(b) its velocity is constant.
(c) its acceleration is constant
(d) the net force on the object is constant.
38. A toy airplane, suspended by a light thread, is moving in a circular path
at a constant speed as shown.
Which of the following is the correct free body diagram for the toy
airplane?
39. A 1400 kg car is travelling at 25 m/s on a circular hill of radius 210 m.
What is the normal force on this car at the top of the hill?
2
(a) 4.2 x 10 N
(c) 1.4 x 104 N
3
(b) 9.6 x 10 N
(d) 2.3 x 104 N
41. Which of the following is a correct statement about gravitational force?
(a) It is applicable only to our solar system.
(b) It is both an attractive and repulsive force.
(c) It is directly proportional to the product of the masses involved.
(d) It is directly proportional to both the mass and radius of the earth.
August 03
42. Which of the following correctly shows the velocity vector, v, for an
object in uniform circular motion?
43. An airplane is flying in a horizontal circle at a speed of 86 m/s. The 72
kg pilot does not want his centripetal acceleration to exceed 68.6 m/s2.
What is the minimum radius of the circular path?
(a) 90 m
(b) 110 m
(c) 750 m
(d) 7700 m
44. A roller coaster car is moving past the top of a loop of diameter 14 m as
shown below. The normal force (directed downwards) provided by the
track at the top of the loop is equal to one-half the weight of the car.
40. In amusement park, a 2.8 m radius “drum” rotates such that a person
does not fall when the “floor” drops away.
What is the speed of the coaster car at this point?
(a) 5.9 m/s
(b) 8.3 m/s
(c) 10 m/s
(d) 14 m/s
If the coefficient of friction between the person and the wall is 0.35,
what is the maximum period of the rotation so that a person will not
fall?
(a) 2.0 s
(b) 3.4 s
(c) 5.7 s
(d) 18 s
45. The earth pulls an apple towards its centre with a force of 4.9 N. Which
of the following is correct?
(a) The apple attracts the earth with a force of 4.9 N.
(b) The apple does not exert an attractive force on the earth.
(c) The apple attracts the earth with a force that is less than 4.9 N.
(d) The apple attracts the earth with a force that is more than 4.9 N.
46. A 2500 kg space probe is sitting on the surface of an asteroid of mass
4.8 x 1014 kg. The asteroid has a radius of 3.5 x 104 m. What is the
force of attraction between the space probe and the asteroid?
(a) 2.6 x 10-5 N
(b) 6.5 x 10-2 N
-1
(c) 9.1 x 10 N
(d) 2.3 x 103 N
47. A satellite circling the earth completes each orbit in 5.10 x 10 3 s. What
is the gravitational field strength at the location of the satellite’s
orbit?
(a) 3.08 m/s2
(b) 9.68 m/s2
2
(c) 9.72 m/s
(d) 9.80 m/s2
51. Which of the following best represents the gravitational force of
attraction between two people one metre apart?
(a) 10-17 N
(b) 10-12 N
-7
(c) 10 N
(d) 10-2 N
January 03
52. A ball moves at a constant speed in a vertical circle when the string
breaks at the position shown.
June 03
48. A car is travelling in uniform circular motion. Which of the following
correctly describes the speed, velocity, and acceleration of the car?
49. A 45 kg child stands on the rim of a merry-go-round of radius 2.3 m.
The child completes 5 rotations in 72 s. What is the centripetal force
acting on the child?
(a) 0.44 N
(b) 0.79 N
(c) 20 N
(d) 280 N
50. Which of the following represents the graph of gravitational field
strength g as a function of the distance d from the centre of a planet?
The ball would then move along which the indicated paths?
(a) P
(b) Q
(c) R
(d) S
53. A 0.090 m diameter computer floppy disk spins at a constant speed of
1.40 m/s measured at its rim. What is the centripetal acceleration at
the rim of this floppy disk?
(a) 16 m/s2
(b) 22 m/s2
2
(c) 31 m/s
(d) 44 m/s2
54. A 960 kg car is travelling on a 65 m radius horizontal circular track. The
coefficient of friction between the tires and the track surface is 0.57.
What is the minimum time for the car to complete one lap of the track?
(a) 0.69 s
(b) 12 s
(c) 21 s
(d) 67 s
55. A satellite is brought from a higher circular orbit to a lower circular
orbit around the earth. Which of the following describes what has
happened to the satellite’s period?
(a) The satellite’s period decreased.
(b) The satellite’s period increased.
(c) The satellite’s period did not change.
(d) You cannot determine this without more information.
56. A 2500 kg satellite is placed into a circular orbit at an altitude of
1.2 x 105 m above the earth’s surface. What is the period of this
satellite?
(a) 13 s
(b) 700 s
(c) 5100 s
(d) 5200 s
57. A 3500 kg piece of space debris is brought from an altitude of
2.1 x 105 m back to the earth’s surface. What is the change in potential
energy of this space debris?
(a) -7.0 x 109 J
(b) -7.2 x 109 J
11
(c) -2.1 x 10 J
(d) -2.2 x 1011 J
(b)
(c)
From your straight line graph, determine the slope. (Include
units). (1 mark)
What is the acceleration due to gravity on this asteroid?
(2 marks).
60. A 7.5 x 104 kg space vehicle leaves the surface of the earth with a
speed of 1.3 x 104 m/s. What will its speed be when it is infinitely far
from the earth? (August 04) (7 marks).
61. A 4.20 x 104 kg satellite orbits the earth at an altitude of 700 km
(7.00 x 105 m). (June 04)
Written
58. A blue ball is swung in a horizontal circle and completes a single rotation
in 1.2 s. The 0.44 m long cord makes an angle of 35º with the vertical
during the ball’s motion as shown. (Release 07/08)
(a) What is the satellite’s orbital speed at this altitude? (4 marks)
(b) What is the satellite’s total energy at this altitude? (3 marks)
62. A stationary 1.60 x 103 kg vehicle is taken from the surface of the moon
and placed into a circular orbit at a height of 2.0 x 106 m above the
surface of the moon. Its speed in this orbit is 1.15 x 10 3 m/s. How much
work is required for this process? (January 04) (7 marks)
What is the centripetal acceleration of the ball? (5 marks)
59. An experiment was performed on the surface of an asteroid. A mass was
dropped from various heights and the time taken to fall was recorded.
(Release 04/05)
63. An object is dropped from a significant height above the surface of the
Moon. It is observed to fall with increasing acceleration. Using principles
of physics, give an explanation for this observation. (January 04)
(4 marks).
(a)
Plot a straight line graph of d vs. t2.
64. A 1500 kg satellite orbits the moon at an altitude of 2.3 x 10 6 m.
66. A 12 000 kg spaceship is 7.2 x 108 m from the centre of a planet that
has a mass of 5.1 x 1025 kg.
The spaceship gains 9.0 x 1011 J of kinetic energy as it falls to the
planet’s surface. What is the radius of this planet? (January 03)
(7 marks)
What is the period of the satellite? (August 03) (7 marks)
65. A 3.2 x 104 kg spacecraft is in a circular orbit of radius 6.68 x 106 m
around the earth. (June 03)
(a) Calculate the period of this spacecraft? (5 marks)
(b) If this spacecraft is then placed into an orbit of the same radius
around the moon,
explain how and why the period of this spacecraft would be
different than when it was orbiting the earth. (4 marks)
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B
C
B
C
C
C
A
A
A
C
B
A
C
B
C
A
C
A
A
D
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
A
A
D
C
A
B
C
B
C
B
A
B
C
D
B
B
A
B
B
A
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
C
D
B
C
A
B
C
B
C
D
C
D
D
C
A
D
A
58.
59.
60.
61.
62.
63.
64.
65.
66.
6.9 m/s2
0.28 m/s2; 0.56 m/s2
6.6 x 103 m/s
7.51 x 103 m/s; -1.18 x 1012 m/s
3.5 x 109 J
words
23 000 s
5400 s; words
4.3 x 107 m