True/False
Indicate whether the
sentence or statement is true or false.
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For
questions 1 to 6, consider a ball of mass m, thrown at an angle
above the horizontal and undergoing projectile motion under negligible
air resistance.
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1. |
The time for the ball to rise equals the time for
the ball to fall to the same horizontal level.
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2. |
The net force on the ball at the top of its flight
is zero.
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3. |
The
acceleration of the ball on the way up equals the acceleration on the
way down.
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4. |
After
leaving your hand and before landing, the speed of the ball is at a
minimum at the top of its trajectory.
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5. |
The magnitude of the horizontal
component of the velocity of the ball just before impact exceeds the
magnitude of the horizontal component of the velocity just after the
ball leaves your hand.
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6. |
The
magnitude of the acceleration of the ball at the top of its trajectory
equals the ratio of the weight of the ball to its mass.
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or questions 7 to 12, assume that you are twirling
a small rubber stopper of mass m (at a constant speed v)
tied to a string in a vertical circle as shown in Figure 1.
Figure
1
For questions 7 to 12
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7. |
At
position 3, the direction of the instantaneous acceleration is westward
and the direction of the instantaneous velocity is upward.
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8. |
The
vector quantity 
is closest to the instantaneous acceleration as the stopper moves
from position 6 to position 1.
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9. |
The
magnitude of the tension in the string at position 1 exceeds the magnitude
of the tension at position 4 by an amount equal to mg.
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10. |
At
position 5, the force that causes the stopper to accelerate toward the
centre of the circle is the sum of the force of tension in the string
and a component of the force of gravity on the stopper.
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11. |
If
you release the ball at the instant it reaches position 1, the instantaneous
velocity of the stopper just after the release will have a small upward
component and a large eastward component.
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12. |
For
a constant radius and frequency of revolution of the stopper, the magnitude
of the centripetal acceleration is directly proportional to m.
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Multiple Choice
Identify
the letter of the choice that best completes the statement or answers
the question.
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Questions 13 to 18 relate to the situation in Figure 2,
in which a child on a toboggan (a system of total mass m) accelerates
down a hill of length L inclined at an angle q
to the horizontal in a time interval  t.
The +x and +y directions are labelled on the diagram.
Assume that friction is negligible unless indicated.
Figure 2
For questions 13 to 18
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13. |
The
magnitude of the child’s acceleration down the hill is
a. |
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b. |
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c. |
g
sin  |
d. |
g cos  |
e. |
g
tan  |
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14. |
The
magnitude of the child’s average velocity is
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15. |
The
magnitude of the force exerted by the toboggan on the hill is
a. |
mg |
b. |
mg cos  |
c. |
mg
sin  |
d. |
mg tan  |
e. |
 mg sin  |
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16. |
If
the child starts from rest and accelerates uniformly down the hill,
the time required to reach the bottom of the hill is
a. |
Lg
sin  |
b. |
2Lg sin  |
c. |
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d. |
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e. |
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17. |
If
 av is the average velocity and 
is the instantaneous velocity, then at the halfway point in the journey
down the hill
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18. |
If
the situation in Figure 2 is changed so that there is a coefficient
of kinetic friction mK
between the toboggan and the hill, then the magnitude of the child’s
acceleration down the hill is
a. |
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b. |
g(sin
 + mK
cos  ) |
c. |
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d. |
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e. |
none
of these |
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