Download Gr 12 Physics Exam - Sample for Review

Gr 12 Physics Exam - Sample for Review
Modified True/False
Indicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the
sentence or statement true.
____
1. A car drives with constant speed around a corner. If it enters the corner travelling west and leaves travelling
south, its acceleration through the turn is directed south-west. _________________________
____
2. An object is thrown vertically upward. At the top of its flight, when its velocity is momentarily zero, its
acceleration is zero. _________________________
____
3. During the flight of a football from quarterback to receiver, the horizontal component of the ball’s velocity is
constantly changing. (Neglect the effect of air resistance.) ______________________________
____
4. To achieve maximum range across a horizontal surface, the angle at which a projectile must be launched is
90. _________________________
____
5. Provided that a boat always points perpendicular to the current in a river, the time it takes the boat to cross is
independent of the strength of the current. _______________________________
____
6. A plane’s destination is due east of its departure point. If a steady wind is blowing from the north-west, the
plane must point south-east to reach its destination. _________________________
____
7. A boat points directly across a river and gets carried 15 downstream by the current. To land at a position
directly across the river from its starting point, the boat must point at an angle slightly less than 15 upstream.
______________________________
____
8. The normal force
gravitational force
____
that acts on an object is always equal in magnitude and opposite in direction to the
that is acting on it. _________________________
9. Friction always acts against an object’s motion relative to the contact surface. _________________________
____ 10. When forces acting on an object are in equilibrium, the object can still be moving.
_________________________
____ 11. A car accelerates from rest when a traffic light turns green. A cup of coffee that was sitting on the dashboard
of the car falls into the driver’s lap. The driver could rightly argue that the cup’s apparent motion was due to
its inertia. It had a tendency to stay still and the car accelerated from beneath it.
_________________________
____ 12. A rock is tied to a string and whirled around in a circle that describes a vertical plane. The tension in the
string is greatest at the bottom of the circle and least at the top. ______________________________
____ 13. If Earth’s mass and radius were both one half their present values, the acceleration due to gravity on the
surface of the Earth would be four times its present value. __________________________________
____ 14. All geosynchronous satellites must have the same orbital radius. _________________________
____ 15. Work is done when the force and the displacement are perpendicular. _________________________
____ 16. The maximum work a force can do on an object occurs when the force is parallel to the direction of motion.
_________________________
____ 17. To raise a 2.3-kg mass from its resting place on a table, more work is done by lifting it diagonally than lifting
it straight up. ___________________________________
____ 18. A car speeds up as it descends a hill, gaining gravitational potential energy. _________________________
____ 19. As the altitude of a satellite increases, the speed of the satellite increases. _________________________
____ 20. Eg can never have a positive value. _________________________
____ 21. Light will travel at a faster speed when emitted from a forward-moving object.
_________________________
____ 22. At the speed of light, the moving object’s time will slow down to zero. _________________________
____ 23. The work function is the amount of energy required to remove an electron by light in the photoelectric effect.
____________________
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
____ 24. A football player successfully kicks a field goal through the uprights situated at the south end of the stadium.
What are the directions of the instantaneous velocity and acceleration, respectively, of the football at the peak
of its trajectory?
a. south, south
d. south, up
b. up, south
e. down, down
c. south, down
____ 25. Which of the following measurements is a scalar quantity?
a. the tension in an elevator cable
b. the acceleration of a car along a test track
c. the instantaneous velocity of a parachutist in free fall
d. the displacement of a hiker from her base station
e. the measured distance between Toronto and Montreal
____ 26. A race car completes exactly 10 laps around an oval track. Which of the following pairs of quantities
concerning its motion would both have values of zero?
a. displacement, average velocity
b. average speed, average acceleration
c. distance, average speed
d. average speed, average velocity
e. displacement, average speed
____ 27. A bus drives 40.0 km [E] from town A to town B, then another 30.0 km [S] to town C in a total time of 1.00
h. What are the values of its average speed and average velocity, respectively?
a. 70.0 km/h, 70.0 km/h [37º S of E]
d. 50.0 km/h, 70.0 km/h [37º S of E]
b. 70.0 km/h, 50.0 km/h [37º S of E]
e. 50.0 km/h [37º S of E], 70.0 km/h
c. 50.0 km/h, 50.0 km/h [37º S of E]
____ 28. Which of the following graphs does NOT depict uniform motion?
a. A and B
b. C only
d. B and D
e. A and E
c. D and E
____ 29. Which of the following graphs depicts uniform motion?
____ 30.
____ 31.
____ 32.
____ 33.
____ 34.
a. A and B
d. B and D
b. C and D
e. E only
c. A and C
Which of the following statements concerning motion graphs is correct?
a. The slope of a position-time graph gives acceleration.
b. The area under an acceleration-time graph gives instantaneous velocity.
c. The slope of a velocity-time graph gives displacement.
d. The area under a position-time graph gives velocity.
e. The area under a velocity-time graph gives displacement.
A car is travelling north when it enters a curve. It maintains a constant speed and leaves the curve travelling
east. The direction of the car’s acceleration is
a. south-east
d. south
b. north-east
e. the car does not accelerate
c. east
Ignoring air resistance, which of the following are exhibiting “free fall”?
a. an object, initially at rest, dropped out of a window
b. an object thrown vertically downward from a window
c. an object projected vertically upward from a window
d. an object thrown horizontally from a window
e. all of the above
A plane must fly to a destination located due north from its departure point. A gentle wind is blowing from
the south-west. What direction must the plane point to reach its destination?
a. north
d. west
b. north-west
e. east
c. north-east
The free-body diagram of a block being pushed up a rough ramp is best represented by
a. A
d. D
b. B
e. E
c. C
____ 35. A 24-kg traffic light is suspended from the midpoint of a cable suspended between two poles. The angle
between the cable and the pole is 80 at both poles. The net force acting on the traffic light has a value of
a. zero
d. 2.4  102 N
b. 47 N
e. 4.6  102 N
c. 82 N
____ 36. An elevator moves downward at a constant speed. What is the relationship between the gravitational force
acting on the elevator and the tension
a.
b.
in the cable?
d.
e.
c.
____ 37. An elevator accelerates downward. What is the relationship between the gravitational force
elevator and the tension
a.
b.
acting on the
in the cable that supports the elevator?
d.
e.
c.
____ 38. An elevator is moving upward at a constant velocity. What is the relationship between the gravitational force
acting on the elevator and the tension
in the cable that supports the elevator?
a.
d.
b.
e.
c.
____ 39. According to Newton’s third law, when you walk across a floor, the force that propels you forward is
a. the force applied by your feet on the floor
b. the force of friction of your feet on the floor
c. the force of the floor applied against your feet
d. exerted upward by the floor on your feet (i.e., the normal force)
e. the force acting on you working against gravity
____ 40. An airplane has three gliders in tow behind it (glider 1 in front of glider 2 which is in front of glider 3). If FT1
represents the force of the airplane on glider 1, FT2 represents the force of glider 1 on glider 2, and FT3
represents the force of glider 2 on glider 3, then which of the following statements correctly represents the
relationships among these three forces?
a.
d.
b.
e.
c.
____ 41. A 2.0-kg object is pulled horizontally by a force of 6.3 N along the floor where the coefficient of kinetic
friction is 0.24. What is the object’s acceleration?
a. 5.5 m/s2
d. 1.6 m/s2
b. 2.0 m/s2
e. 0.80 m/s2
2
c. 2.0 m/s
____ 42. A child whirls a ball around in circles on the end of a 48 cm long string at a frequency of 2.5 Hz. What is the
ball’s centripetal acceleration?
a. 1.2  104 m/s2
d. 38 m/s2
2
2
b. 1.2  10 m/s
e. 3.0 m/s2
c. 47 m/s2
____ 43. Imagine you are a passenger upside-down at the top of a vertical looping roller coaster. The centripetal force
acting on you at this position
a. is perhaps the least of anywhere in the loop
b. is supplied at least partly by gravity
c. is supplied partly by the seat of the roller coaster
d. is directed vertically downward
e. all of the above
____ 44. The orbital speed of a satellite at an altitude equivalent to Earth’s radius (rE = 6.38  106 m) is (mE = 5.98 
1024 kg, G = 6.67  10–11 N·m2/kg2)
a. 9.8  103 m/s
d. 4.9  103 m/s
3
b. 7.9  10 m/s
e. 2.5  103 m/s
3
c. 5.6  10 m/s
____ 45. Astronauts on board an orbiting space station appear to be “floating” because
a. they are in the vacuum of space
b. they are outside Earth’s gravitational influence
c. the force of gravity acting on them has been reduced to an insignificant level
d. they have become truly “weightless”
e. they are in free fall along with the space station itself
____ 46. In which situation is work not done?
a. a frozen turkey is carried upstairs
b. a frozen turkey is carried on level ground
c. a frozen turkey is dropped
d. a frozen turkey is carried downstairs
e. a frozen turkey is fired from a cannon
____ 47. When an object doubles its speed, the kinetic energy increases by a factor of
a. 1
d. 6
b. 2
e. 8
c. 4
____ 48. To maximize the gravitational potential energy of an object, you should
a. raise it as quickly as possible
d. get it as high as possible
b. maximize the total distance travelled
e. lower it in the vertical direction
c. avoid acceleration during lifting
____ 49. A cyclist reaches the bottom of a hill with a speed of 18 m/s. Neglecting air resistance and other friction, to
what maximum height can they coast up the hill without pedalling?
a. 17 m
d. 20 m
b. 18 m
e. 21 m
c. 19 m
____ 50. In the picture of a roller coaster track shown below, the point where the roller coaster car would be travelling
the fastest, under negligible friction is
a. A
d. D
b. B
e. E
c. C
____ 51. In the picture of a roller coaster track shown below, the point where the roller coaster car would be travelling
the slowest under negligible friction is
a. A
d. D
b. B
e. E
c. C
____ 52. Rubbing your hands together can quickly produce 45 J of thermal energy. If it is done with an average
frictional force of 8.4 N, the distance your hands have slid past each other is
a. 49 m
d. 3.7 m
b. 5.4 m
e. 1.2 m
c. 4.5 m
____ 53. A 0.25-kg apple is gently hung from a spring that stretches 4.6 cm. The force constant of the spring is
a. 0.054 N/m
d. 53 N/m
b. 6.1 N/m
e. 180 N/m
c. 18 N/m
____ 54. A horizontal spring, with a force constant of 39 N/m, is compressed 12.4 cm, and placed between a wall and a
0.17-kg box resting on a smooth floor. If the spring is released, the maximum speed of the box is
a. 1.9 m/s
d. 5.3 m/s
b. 2.7 m/s
e. 28 m/s
c. 3.5 m/s
____ 55. During an experiment carried out by an astronaut on the Moon (g = 1.6 N/kg), a 1.4-kg mass is dropped onto
a spring with a force constant of 49 N/m. The maximum compression in the spring is
a. 0.28 m
d. 4.8 m
b. 0.48 m
e. not enough information
c. 3.6 m
____ 56. You want to ride a bicycle to the house shown below. Neglecting friction, at which point should you start in
order to use the least amount of work to get there?
a. A
d. D
b. B
e. E
c. C
____ 57. A 2200 kg car starts from rest and speeds up to 12 m/s in 5.2 s. The net force acting on the car is
a. 1.8  102 N
d. 5.1  103 N
b. 4.2  102 N
e. 1.4  105 N
4
c. 1.1  10 N
____ 58. A car with a mass of 1800 kg slows from 42 km/h [E] to 28 km/h [E]. The impulse from the brakes is
a. 2.5  104 Ns [E]
d. 2.1  104 Ns [W]
b. 2.5  104 Ns [W]
e. 7.0  103 Ns [W]
4
c. 2.1 10 Ns [E]
____ 59. A boy throws a 15-kg ball at 4.7 m/s to a 65-kg girl who is stationary and standing on a skateboard. After
catching the ball, the girl is travelling at
a. 0 m/s
d. 3.2 m/s
b. 0.88 m/s
e. 4.7 m/s
c. 1.1 m/s
____ 60. A sabotaged curling stone explodes into three pieces as it travels across the ice. Neglecting the force of
friction,
a. all three pieces will travel at the same speed
b. the magnitudes of the momenta for each piece will be the same
c. an external net force had to act on the stone to accelerate the three pieces
d. the components perpendicular to the original motion must add up to zero
e. momentum is not conserved because of the small explosive charge
____ 61. A two-dimensional collision occurs as shown below.
Which vector below most closely represents the new velocity of P?
a. A
d. D
b. B
e. E
c. C
____ 62. If the mass of Earth is 5.98  1024 kg and the radius is 6.38  106 m, the gravitational potential energy of a 2.2
 103-kg vehicle located on the surface of Earth is
a. –1.4  104 J
d. –2.2  1012 J
4
b. –2.2  10 J
e. 0 J
c. –1.4  1011 J
____ 63. A satellite of mass m is in orbit around a planet of mass M at an altitude a above the planet’s surface. The
radius of the planet is r. The speed of the satellite is
a.
d.
b.
e.
c.
____ 64. Time is
a. dependent on the observer
d. simultaneous in all cases
b. absolute
e. never changing
c. the same for different observers
____ 65. The length of a horizontal metre stick moving at 0.75c is
a. 1.00 m
d. 0.56 m
b. 0.66 m
e. 1.51 m
c. 0.44 m
____ 66. The Lorentz contraction will apply to which of the following dimensions of an object:
a. height relative to direction
d. all dimensions equally
b. length relative to direction
e. no contraction occurs
c. width perpendicular to direction
____ 67. Flying in a fast rocket ship at a speed of 0.82c, you observe both your watch and a clock outside. Which of
the following statements is true?
a. Time will appear to be the same for you but slower outside.
b. Time will appear slower for you but normal outside.
c. Neither clock runs slow.
d. Both clocks run slow.
e. none of the above
____ 68. Two spaceships are heading toward each other at a mutual speed of 0.999c. Both ships shine a laser beam at
one another. How will each ship see the other light?
a. Both ships will see the light travelling at 2c.
b. Neither ship will see any light.
c. Both ships will see the light travelling at c.
d. One ship will see the light travelling at c, and the other will see it travelling at 2c.
e. none of the above
____ 69. An object is observed to be a length L with velocity v. Its proper length is given by the formula
a.
d.
b.
e.
c.
____ 70. A watch moving at speed v was observed to have a period t. Its proper time is given by the formula
a.
d.
b.
e.
c.
____ 71. An astronaut flying at 0.65c takes a 3-h sleep period. How long does mission control think that the astronaut
has slept?
a. 4.61 h
d. 3 h
b. 3.90 h
e. 2.28 h
c. 3.58 h
____ 72. The rest energy, in joules, of an electron of mass 9.11  10–31 kg is
a. 5.1  105 J
d. 3.0  10–39 J
b. 8.2  10–14 J
e. 1.0  10–47 J
–22
c. 2.7  10 J
____ 73. The momentum of a photon with a wavelength of 635 nm is
a. 4.21  10–40 kg·m/s
d. 1.04  10–36 kg·m/s
b. 1.04  10–27 kg·m/s
e. 4.21  10–31 kg·m/s
26
c. 9.57  10 kg·m/s
Short Answer
74. Describe a situation where an object is accelerating but its velocity is zero.
75. For an object sliding on a ramp, what is the most appropriate way of resolving the forces? Why is this method
superior to others?
76. Why does the centripetal force not appear on any free-body diagrams.
77. Why do roller coasters use clothoid loops instead of circular loops?
78. How much work is done to speed up a 2200-kg car from 12 m/s to 24 m/s?
79. A battery-powered toy travelling at 2.2 m/s drives off a diving board at a height of 1.2 m above the water.
What is the impact speed of the toy?
80. A small spring with a force constant of 83 N/m is held vertically and then stretched 18 cm. A 1.8-kg mass is
attached to it and then released. Calculate the acceleration of the mass at the moment of release.
81. A 57-g tennis ball travelling at 28 m/s is hit straight back with the same velocity. Determine the average force
on the tennis ball if the racket is in contact with the ball for 4.9 ms.
82. During an elastic collision between a superball and the ground, the superball comes to rest for a brief instant.
Where is the energy stored?
83. A 0.25-kg snowball moving at 15 m/s [E] collides and sticks with a 1.9-kg toy truck travelling at 2.8 m/s [W].
Neglecting friction, calculate the velocity of the snowball–truck system after the collision.
84. A plane is dropping medical supplies to a village. Describe the path of the supplies relative to an observer on
the ground watching the plane travel from left to right.
85. If a scientist looks out the window while flying by a clock on Earth at nearly the speed of light, how would
she perceived time on Earth?
86. A spacecraft is travelling between two stars at 0.9c. Would the pilot of the ship notice any changes to the
shape or length of the ship?
Problem
87. A ball is thrown vertically upward from a window that is 3.6 m above the ground. Its initial speed is 2.8 m/s.
(a) With what speed does the ball hit the ground?
(b) How long after the first ball is thrown should a second ball be simply dropped from the same window so
that both balls hit the ground at the same time?
88. An object is pushed along a rough horizontal surface and released. It slides for 10.0 s before coming to rest
and travels a distance of 20.0 cm during the last 1.0 s of its slide. Assuming the acceleration to be uniform
throughout
(a) How fast was the object travelling upon release?
(b) How fast was the object travelling when it reached the halfway position in its slide?
89. A pedestrian is running at his maximum speed of 6.0 m/s trying to catch a bus that is stopped at a traffic light.
When he is 16 m from the bus, the light changes and the bus pulls away from the pedestrian with an
acceleration of 1.0 m/s2.
(a) Does the pedestrian catch the bus and, if so, how far does he have to run? (If not, what is the pedestrian’s
distance of closest approach?)
(b) How fast is the bus moving when the pedestrian catches it? (or at the distance of closest approach)
(c) On a single set of axes, plot the corresponding position-time graphs of both the bus and pedestrian to
confirm your answer in (a).
90. Two planes fly from Toronto to Philadelphia. Plane A flies via Pittsburgh whereas passengers on plane B
have a direct flight. Pittsburgh is 350 km due south of Toronto and 390 km due west of Philadelphia. The
airspeed of both planes is 400.0 km/h and a steady wind is blowing from the east at 60.0 km/h.
(a) What direction must the pilot point the plane flying from Toronto to Pittsburgh? Include a vector diagram
of velocities.
(b) How long will the entire flight take for plane A assuming a 0.50-h layover in Pittsburgh?
(c) How much time must the pilot of plane B wait before leaving Toronto if she is to arrive in Philadelphia at
the same time plane A arrives?
91. The graph below represents the motion of an object over a recorded time interval. Using methods of graphical
analysis wherever possible, determine
(a) the object’s displacement relative to its starting position at t = 6.0 s.
(b) the object’s average velocity between t = 0.0 s and t = 6.0 s.
(c) the object’s average speed between t = 0.0 s and t = 6.0 s.
(d) Including t = 0.0 s, how many times during the entire recorded time interval is the object at its starting
position?
(e) During which interval is the object’s acceleration the greatest? What is the value of the acceleration during
this interval?
(f) Plot the corresponding position-time graph.
(g) Plot the corresponding acceleration-time graph.
92. A shell is fired from a cliff that is 36 m above a horizontal plane. The muzzle speed of the shell is 80.0 m/s
and it is fired at an elevation of 25 above the horizontal.
(a) Determine the horizontal range of the shell.
(b) Determine the velocity of the shell as it strikes the ground.
93. A force of 3.5 N [60E of N] and a force of 2.8 N [40W of S] act on the same object. Find the net force
acting on the object using (a) a trigonometric method and (b) a component method.
94. A pulley device is used to hurl projectiles from a ramp (k = 0.26) as illustrated in the diagram. The 5.0-kg
mass is accelerated from rest at the bottom of the 4.0 m long ramp by a falling 20.0-kg mass suspended over a
frictionless pulley. Just as the 5.0-kg mass reaches the top of the ramp, it detaches from the rope (neglect the
mass of the rope) and becomes projected from the ramp.
(a) Determine the acceleration of the 5.0-kg mass along the ramp. (Provide free-body diagrams for both
masses.)
(b) Determine the tension in the rope during the acceleration of the 5.0-kg mass along the ramp.
(c) Determine the speed of projection of the 5.0-kg mass from the top of the ramp.
(d) Determine the horizontal range of the 5.0-kg mass from the base of the ramp.
95. A planet has a mass of 2.5 times that of Earth and a radius 1.2 times Earth’s radius. How much would a
60.0-kg person weigh at the planet’s surface?
96. A satellite orbits Earth at an altitude of 325 km above the planet’s surface. What is its orbital period? Express
your answer in minutes. (rE = 6.38  106 m, ME = 5.98  1024 kg)
97. An 87-g box is attached to a spring with a force constant of 82 N/m. The spring is compressed 11 cm and the
system is released.
(a) What is the speed of the box when the spring is stretched by 7.0 cm?
(b) What is the maximum speed of the box?
98. A spring is suspended from a ceiling and a 256-g mass is attached to it and pulled down to stretch the spring
by 18.2 cm. The mass is released and travels through the equilibrium position with a speed of 0.746 m/s.
Calculate the force constant of the spring.
99. A spring with a force constant of 89 N/m is compressed 8.7 cm and placed between two stationary dynamics
carts of mass 1.0 kg and 1.5 kg. If friction is negligible, determine the final speed of the more massive cart
when the spring is released.
100. A small explosive charge is placed in a rubber block resting on a smooth surface. When the charge is
detonated, the block breaks into three pieces. A 200-g piece travels at 1.4 m/s, and a 300-g piece travels at
0.90 m/s. The third piece flies off at a speed of 1.8 m/s. If the angle between the first two pieces is 80º,
calculate the mass and direction of the third piece. Assume two significant digits for each value.
101. How much work is done against gravity to fire a 7.2  102-kg weather monitor 120 km into the air? (rE = 6.38
 106 m, ME = 5.98  1024 kg)
102. How fast must a satellite leave Earth’s surface to reach an orbit with an altitude of 895 km?
103. A pilot on a distant voyage to a star is placed in suspended animation for the journey. The ship’s clock
recorded that he aged 15 years but the trip had lasted 132 years relative to Earth. How fast was the ship
travelling?
104. The distance between two planets was measured by an alien spacecraft to be 4.53 light-years. If the alien pilot
was travelling at 0.93c, how far away was the planet in proper distance?
105. Calculate the energy of light with wavelength 486 nm. Give your answer in joules and in electron volts.
106. Would 449-nm blue light eject electrons from silver metal with a work function of 4.74 eV?
107. With what speed would an electron be ejected from sodium that has a work function of 2.36 eV when it is
illuminated by 442-nm light?
Essay
108. Amusement parks often make use of the centrifugal forces that people apparently feel when travelling in
uniform (and nonuniform) circular motion. Provide three distinct examples and examine the physics
associated with each.
109. A car is moving at a rapid pace. It is approaching a garage with doors at either end. The proper length of the
car is longer than the length of the garage. As the car travels through the garage, describe what the driver
would observe. Describe what would be seen by a stationary observer inside the garage.
Gr 12 Physics Exam - Sample for Review
Answer Section
MODIFIED TRUE/FALSE
1. ANS:
LOC:
2. ANS:
LOC:
3. ANS:
LOC:
4. ANS:
LOC:
5. ANS:
LOC:
6. ANS:
LOC:
7. ANS:
LOC:
8. ANS:
LOC:
9. ANS:
LOC:
10. ANS:
LOC:
11. ANS:
LOC:
12. ANS:
LOC:
13. ANS:
LOC:
14. ANS:
LOC:
15. ANS:
LOC:
16. ANS:
LOC:
17. ANS:
F, south-east
FM1.05
F, 9.8 m/s2 [down]
FM1.05
F, vertical component
FM1.03
F, 45
FM1.03
T
FM1.02
F, north-east
FM1.02
F, slightly greater than 15
FM1.02
F, not always equal
FM1.01
T
FM1.01
T
FM1.01
T
FM1.05
T
FM1.04
F, two times its present value
FM1.06
T
FM1.04
F, parallel
EM1.01
T
EM1.01
F, the same amount of work is done
REF: K/U
OBJ: 1.2
REF: K/U
OBJ: 1.3
REF: K/U
OBJ: 1.3
REF: K/U
OBJ: 1.4
REF: K/U
OBJ: 1.5
REF: K/U
OBJ: 1.5
REF: K/U
OBJ: 1.5
REF: K/U
OBJ: 2.1
REF: K/U
OBJ: 2.1
REF: K/U
OBJ: 2.1
REF: K/U
OBJ: 2.5
REF: K/U
OBJ: 3.2
REF: K/U
OBJ: 3.3
REF: MC
OBJ: 3.4
REF: K/U
OBJ: 4.1
REF: K/U
OBJ: 4.1
REF:
18. ANS:
LOC:
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21. ANS:
LOC:
K/U
OBJ: 4.3
F, losing
EM1.01
F, decreases
EM1.06
T
EM1.07
F, at a constant speed
ME1.05
LOC: EM1.01
REF: K/U
OBJ: 4.3
REF: K/U
OBJ: 6.2
REF: K/U
OBJ: 6.3
REF: K/U
OBJ: 11.1
22. ANS:
LOC:
23. ANS:
LOC:
T
ME1.05
T
ME1.03
REF: K/U
OBJ: 11.2
REF: K/U
OBJ: 12.1
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MULTIPLE CHOICE
24.
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C
E
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C
E
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K/U
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MC
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I
K/U
1.4
1.1
1.1
1.1
1.1
1.1
1.1
1.2
1.4
1.5
2.1
2.1
2.2
2.1
2.1
2.2
2.3
2.4
3.1
3.2
3.4
3.4
4.1
4.2
4.3
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4.5
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4.4
5.1
5.1
5.2
5.4
5.4
6.3
FM1.03
FM1.02
FM1.01
FM1.02
FM1.02
FM1.02
FM1.02
FM1.01
FM1.02
FM1.02
FM1.01
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FM1.01
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FM1.01
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FM1.05
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EM1.01
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E
A
B
B
A
C
A
B
B
B
B
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K/U
K/U
I
K/U
K/U
MC
I
I
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I
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6.3
11.1
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11.3
12.1
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EM1.07
ME1.01
ME1.05
ME1.05
ME1.05
ME2.02
ME2.02
ME2.02
ME2.02
ME1.06
ME1.03
SHORT ANSWER
74. ANS:
This would occur at the instant when an object is reversing direction. For example, when an object is thrown
vertically upward its acceleration during the entire trip is 9.8 m/s2 [down], including its acceleration at the
peak of its flight when its velocity is momentarily zero.
REF: C
OBJ: 1.2
LOC: FM1.02
75. ANS:
For an object sliding along a ramp, it is best to resolve the forces both parallel and perpendicular to the ramp.
If the object is to accelerate, it will be parallel to the ramp, whereas there will be no acceleration
perpendicular to the ramp. The forces acting perpendicular to the ramp will be in equilibrium, whereas the
forces acting parallel to the ramp may or may not be in equilibrium.
REF: C
OBJ: 2.1
LOC: FM1.01
76. ANS:
The centripetal force is the net force in every case. As such, it is comprised of the sum of all the forces that act
on the object. This being the case, as in any free-body diagram, it does not appear on the diagram itself.
REF: K/U
OBJ: 3.2
LOC: FM1.04
77. ANS:
The speed of a roller coaster will decrease as it moves up a loop and increase on the way down. For a circular
loop (of constant radius), the centripetal acceleration will decrease steadily as the roller coaster climbs the
loop and increase steadily as it descends. The resulting centripetal force acting on passengers changes
accordingly. The apparent centrifugal force that passengers feel changes as well. Designers of roller coasters
have found that this results in an unpleasant ride for many passengers and may even lead to injury. When the
clothoid loop is used (changing radius), the radius of the loop steadily decreases as the roller coaster ascends
and increases as it descends. When this is combined with the changing speed, the result is a relatively constant
centripetal acceleration (and force), making for a better ride for the passengers.
REF: K/U, C
78. ANS:
OBJ: 3.2
LOC: FM1.04
The work done to speed up the car is 4.8  105 J.
REF: K/U
79. ANS:
OBJ: 4.2
LOC: EM1.01
The impact speed of the toy is 5.3 m/s.
REF: K/U
80. ANS:
OBJ: 4.4
LOC: EM1.03
The acceleration of the mass is 1.5 m/s2 [down].
REF: K/U
OBJ: 4.5
LOC: EM1.08
81. ANS:
We can neglect the force of gravity because it is so small.
The average force acting on the ball is 6.5  102 N.
REF: K/U
OBJ: 5.1
LOC: EM1.01
82. ANS:
The energy is stored as elastic potential energy in the deformed shape of the ball.
REF: K/U
OBJ: 5.3
83. ANS:
Choose east as the +x direction.
LOC: EM1.04
The final velocity is 0.73 m/s [W].
REF: K/U
OBJ: 5.2
LOC: EM1.02
84. ANS:
The medical supplies would travel in a parabolic arch down and to the right relative to an observer on the
ground.
REF: MC
OBJ: 11.1
LOC: ME1.01
85. ANS:
She would see that time on Earth would be moving slower.
REF: K/U
OBJ: 11.2
LOC: ME2.02
86. ANS:
No, the pilot would not notice any length or other changes.
REF:
K/U
OBJ: 11.2
LOC: ME2.02
PROBLEM
87. ANS:
(a)
Using a sign convention of “down” as (+) and “up” as (–).
The speed of the object when it hits the ground is 8.9 m/s.
(b)
Time of flight for the first ball:
Time of flight for the second ball:
The difference in flight times is 1.19 s – 0.86 s = 0.33 s.
The second ball should be dropped 0.33 s after the first one is thrown so that both hit the ground at the
same time.
REF: K/U
OBJ: 1.3
LOC: FM1.02
88. ANS:
(a)
The object’s acceleration during the last 1.0 s:
t = 1.0 s
v1 = 40 cm/s
v2 = 0.0 cm/s
a=?
This is also the acceleration for the entire trip.
The speed upon release:
The object was travelling at 4.0 m/s upon release.
(b)
The distance travelled:
t = 10.0 s
v2 = 0.0 cm/s
a = –40 cm/s2
d = ?
At the halfway position:
d = 1.0  103 cm
v2 = 0.0 cm/s
a = –40 cm/s2
v1 = ?
The object is travelling at 2.8 m/s at the halfway position in its slide.
REF: K/U
OBJ: 1.2
89. ANS:
(a)
Bus: v1B = 0.0 m/s, aB = 1.0 m/s2
Pedestrian: vP = 6.0 m/s
Bus:
LOC: FM1.02
Pedestrian: dP = vPt
dP = 6.0 t
dP = dB + 16 m
6.0 t = 0.5(t)2 + 16
solving the quadratic: t = 4.0 s, 8.0 s
The pedestrian does catch the bus after running for 4.0 s.
d
= 6.0 m/s(t)
= 6.0 m/s(4.0 s)
d = 24 m
The pedestrian runs 24 m to catch the bus.
(b)
v1B = 0.0 m/s
aB = 1.0 m/s2
t = 4.0 s
v2B = ?
v2B = v1B + aBt
= (1.0 m/s2)(4.0 s)
v2B = 4.0 m/s
The bus is travelling at 4.0 m/s when the pedestrian catches it.
(c) The position-time graph of the motion of the pedestrian is a straight diagonal line that begins at the origin.
The line that represents the motion of the bus is a curved line that begins at the 8.0 m mark and crosses that
pedestrian’s line twice, at 4.0 s and at 8.0 s.
REF: K/U
OBJ: 1.3
LOC: FM1.02
90. ANS:
(a) The triangle of velocity vectors appears as:
The plane must point [8.6 E of S].
(b) For the first leg of the trip of plane A:
time to fly from Toronto to Pittsburgh:


Layover time in Pittsburgh is 0.5 h.
Pittsburgh to Philadelphia:
Time to fly:
Total time Toronto to Philadelphia: 0.885 h + 0.5 h + 1.15 h = 2.5 h
The total time for plane A is 2.5 h.
(c) Distance from Toronto to Philadelphia:
Vector triangle of velocities:
Using sine law:  = 5.8, then  = 180 – 138 – 5.8 = 36
Using cosine law:
353 km/h
Time for plane B to fly from Toronto to Philadelphia:
Plane B must wait 2.5 h – 1.48 h = 1.0 h.
REF: K/U
91. ANS:
(a)
displacement
displacement
OBJ: 1.5
LOC: FM1.05
= area under graph
= 23.75 m [S] + 18.75 m [N]
= 5.0 m [S]
(b)
The object’s average velocity during the first 6.0 s is 0.83 m/s [S].
(c)
The object’s average speed during the first 6.0 s is 7.1 m/s.
(d) The object is at its starting location 3 times throughout the motion.
(e) The object’s acceleration is greatest between t = 6.5 s and 7.0 s. (the greatest slope) acceleration = slope of
graph = 30 m/s2 [N]
(f)
(g)
REF: K/U
OBJ: 1.2
LOC: FM1.02
92. ANS:
(a)
Time of flight: let “up” be (–) and “down” be (+)
v1 = –80.0 m/s(sin 25) = –33.8 m/s
a = 9.8 m/s2
d = 36 m
t = ?
36 = (–33.8)t + 4.9(t)2
Solving the quadratic: t = 7.84 s
Horizontal range: d = vt = 80.0 m/s(cos 25)(7.84 s) = 5.7  102 m
The horizontal range of the shell is 5.7  102 m.
(b) Horizontal component of final velocity: 80.0 m/s(cos 25) = 72.5 m/s
Vertical component of final velocity: v2 = v1 + at = –33.8 m/s + 9.8 m/s2(7.84 s)
v2 = 43.0 m/s
Using Pythagoras:
=
The shell lands with a velocity of 84 m/s at an angle of 31 below the horizontal.
REF: K/U
OBJ: 1.4
93. ANS:
(a) Trigonometric Method
LOC: FM1.03
Looking at the vector triangle:  = 20.
Using cosine law:
= 1.3 N
Using sine law:  = 18.
As a result:
.
(b) Component Method
F1X = 3.5 N(cos 30) [E] = 3.03 N [E]
F2X = 2.8 N(sin 40) [W] = 1.80 N [W]
FX = 3.03 N [E] + 1.80 N [W] = 1.23 N [E]
F1Y = 3.5 N(sin 30) [N] = 1.75 N [N]
F2Y = 2.8 N(cos 40) [S] = 2.14 N [S]
FY = 1.75 N [N] + 2.14 N [S] = 0.39 N [S]
Using Pythagoras:
Using a trigonometric ratio:  = tan–1
As a result:
= 18.
.
The two methods give equivalent results.
REF: C
94. ANS:
(a)
For the 5.0-kg mass:
Free-body diagram:
OBJ: 2.3
LOC: FM1.01
FN acting perpendicular to ramp and up
Fg acting down
FT acting up along the ramp (this is the positive direction)
FK acting down along the ramp (this is the negative direction)
5.0 kg(a) = FT – mg(cos ) – mg(sin )
5.0 kg(a) = FT – 35.5 N
For the 20.0-kg mass:
Free-body diagram:
FT acting up (this is the negative direction)
Fg acting down (this is the positive direction)
20.0 kg(a) – 196 N – FT
Solving the system of equations:
a = 6.4 m/s2
The acceleration of the 5.0-kg mass along the ramp is 6.4 m/s2.
(b)
The tension in the cable is 68 N.
(c)
The speed of projection of the mass off the top of the ramp is 7.2 m/s.
(d)
Vertically: Let “up” be (–) and “down” be (+).
a = 9.8 m/s2
d = 6.0 m
Horizontal range:
The horizontal range for the projected mass is 9.5 m.
REF: K/U
OBJ: 2.3
LOC: FM1.01
95. ANS:
The weight of a 60.0-kg person at Earth’s surface:
Fg = mg
= 60.0 kg(9.8 N/kg)
Fg = 588 N
Since
Earth: FE = 588 N
m1 = 60.0 kg
m2 = mE
r = rE
, the two planets can be compared.
Planet: FP = ?
m1 = 60.0 kg
m2 = 2.5 mE
rP = 1.2rE
The person would weigh 1.0  103 N at the planet’s surface.
REF: K/U
OBJ: 3.3
LOC: FM1.06
96. ANS:
The orbital radius is 6.38  106 m + 3.25 105 m = 6.705  106 m
The centripetal force acting on the satellite is supplied by gravity.
FC = Fg
The orbital period is 91.0 min.
REF: K/U
OBJ: 3.4
LOC: FM1.06
97. ANS:
(a) The total energy is conserved, so
Noting that all the original energy is elastic potential,
The speed at a stretch of 7.0 cm is 2.6 m/s.
(b) The total energy is conserved.
All of the original energy is elastic potential, and all of the final energy will be kinetic,
The maximum speed is 3.4 m/s.
REF: K/U
OBJ: 4.5
98. ANS:
Using conservation of energy,
LOC: EM1.08
The spring constant is 31.9 N/m
REF: K/U
OBJ: 4.5
99. ANS:
Using conservation of momentum:
LOC: EM1.03
Now use conservation of energy:
The final speed of the more massive cart is 0.42 m/s.
REF: K/U
OBJ: 5.3
LOC: EM1.02
100. ANS:
The momentum of the 200-g piece, p2, is 0.20  1.4 = 0.28 kgm/s.
The momentum of the 300-g piece, p3, is 0.30  0.90 = 0.27 kgm/s.
The momentum of the unknown piece, pm, is m  1.8 = 1.8m kgm/s.
Choose the +x direction to be the direction of the 200-g piece.
 is the angle between the unknown momentum vector and opposite to the 200-g momentum vector.
Now divide Equation 1 by Equation 2:
Substitute this value into Equation 1:
The angle measured from the 200-g piece is 180º – 39º = 141º.
The mass of the third piece is 0.23 kg and it is moving 141º from the 200-g piece. (It is 139º from the
300-g piece.)
REF: K/U
101. ANS:
OBJ: 5.4
LOC: EM1.03
The work
done against gravity is 8.3  108 J.
REF: K/U
102. ANS:
OBJ: 6.3
LOC: EM1.07
The launch speed would need to be 8.38  103 m/s.
REF: K/U
103. ANS:
OBJ: 6.3
LOC: EM1.07
The ship was travelling at 0.99 the speed of light.
REF: I
104. ANS:
v = 0.93c
Lm = 4.53 ly
OBJ: 11.2
LOC: ME2.02
The proper length between the planets was 12.2 ly.
REF: I
105. ANS:
E=?
OBJ: 11.2
LOC: ME2.02
The energy of the light is 4.09  10–19 J or 2.56 eV.
REF: I, C
106. ANS:
OBJ: 12.1
LOC: ME1.03
No, an electron would not be ejected because the kinetic energy is not a positive value.
REF: I
107. ANS:
v=?
OBJ: 12.1
LOC: ME1.03
The electron would be ejected from the sodium with a speed of 3.98  105 m/s.
REF:
I, C
OBJ: 12.1
LOC: ME1.03
ESSAY
108. ANS:
(a) Clothoid loop roller coaster:
Vertical (clothoid) loops on roller coasters have a radius of curvature that decreases as the coaster ascends
into the loop and increases as it descends. The change in radius compensates for the coaster’s change in speed
through the loop, keeping the centripetal acceleration and the force
acting on the patrons
relatively constant. The centrifugal force experienced by the patrons is relatively constant.
(b) Rotating swings:
Swings are suspended and then rotated around a central point. The angle of the suspended swing becomes
more vertical with the speed of rotation. The centripetal force acting on the swing is supplied by the
horizontal component of the tension. As the speed (and centripetal acceleration) increases so must the angle to
the vertical. At a given speed, a rider feels a constant centrifugal force.
(c) Pendulum ride:
Passengers sit in a multi-seat vehicle that is suspended and swung back and forth repeatedly like a giant
pendulum, eventually “going over the top.” Since their speed increases as the passengers swing downward, an
ever-increasing centrifugal force is experienced. As they swing upward, the sensation of being pushed
outward lessens as the vehicle climbs higher and slows down.
REF: C
OBJ: 3.2
LOC: FM1.04
109. ANS:
As the car is moving through the garage, the driver sees the car as unchanged. The garage will appear to have
decreased in length. As the car goes through the garage the driver would see that the car would stick out from
both ends of the garage. The stationary observer would see the car as having a decreased length. As the car
went through the garage, it would appear that the car would actually fit inside the garage.
REF:
C
OBJ: 11.2
LOC: ME2.06