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Name: ________________________ Class: ___________________ Date: __________
ID: A
Physics Quiz 1--Torque and Static Equillibrium
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Two children seat themselves on a seesaw. The one on the left has a weight of 400 N while the one on the right
weighs 300 N. The fulcrum is at the midpoint of the seesaw. If the child on the left is not at the end but is 1.50 m
from the fulcrum and the seesaw is balanced, what is the torque provided by the weight of the child on the right?
a. -600 N·m b. 450 N·m c. 600 N·m d. -450 N·m e. 0 N·m
2. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius
cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the
moment of inertia of cylinder and crank is 0.12 kg⋅m2. If the bucket is raised to the top of the well and released,
what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible,
that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)
a. 12 m/s2 b. 7.4 m/s2 c. 6.3 m/s2 d. 9.8 m/s2 e. 3.2 m/s2
3. Tasha has mass 20 kg and wants to use a 4.0-m board of mass 10 kg as a seesaw. Her friends are busy, so Tasha
seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.
How far is she from the support point?
a. 0.26 m b. 2.0 m c. 0.33 m d. 1.0 m e. 0.67 m
4. A vault is opened by applying a force of 300 N perpendicular to the plane of the door, 0.80 m from the hinges.
Find the torque due to this force about an axis through the hinges.
a. 120 N⋅m b. 240 N⋅m c. 420 N⋅m d. 300 N⋅m e. 360 N⋅m
5. A 100-N block, on a 30° incline, is being held motionless by friction. The coefficient of static friction between the
block and the plane is 0.60. The force due to friction is:
a. 0 N. b. 30 N. c. 61 N. d. 52 N. e. 50 N.
6. The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit. Compare the motion of
the satellite at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee). At
these two points:
a. the kinetic energies are the same. b. the angular velocities are the same. c. the angular momenta are the
same. d. the tangential velocities are the same. e. none of the above.
7. An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end. If the scaffold
weighs 500 N and the worker stands 1.0 m from one end, what is the tension in the rope nearest the worker?
a. 500 N b. 900 N c. 850 N d. 450 N e. 800 N
8. An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each
end. How far would the worker stand from one of the supporting ropes to produce a tension of 550 N in that rope?
a. 2.5 m b. 2.0 m c. 2.9 m d. 1.4 m e. 2.7 m
9. A string attached to an airborne kite is maintained at an angle of 40° with the horizontal. If a total of 120 m of
string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the
process? (Assume the kite string doesn't sag.)
a. 92 m b. 88 m c. 84 m d. 100 m e. 77 m
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Name: ________________________
ID: A
10. A bucket of water with total mass 23 kg is attached to a rope, which in turn, is wound around a 0.050-m radius
cylinder at the top of a well. A crank with a turning radius of 0.25 m is attached to the end of the cylinder. What
minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's
mass is negligible, that cylinder turns on frictionless bearings, and that g = 9.8 m/s2.)
a. 135 N b. 68 N c. 45 N d. 143 N e. 90 N
11. John throws a baseball from the outfield from shoulder height, at an initial velocity of 29.4 m/s at an initial angle
of 30.0° with respect to the horizontal. The ball is in its trajectory for a total interval of 3.00 s before the third
baseman catches it at an equal shoulder-height level. (Assume air resistance negligible.) What is the ball's
horizontal displacement?
a. 57.3 m b. 66.7 m c. 76.4 m d. 38.2 m e. zero
12. When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?
a. inertia b. centripetal force c. centripetal acceleration d. centrifugal force
13. Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0, 0.0) m, 4.0 kg at (2.0, 0.0) m, and 5.0 kg at (2.0,
3.0) m. What is the x-coordinate of the center of gravity of this system of masses?
a. 0.96 m b. 1.2 m c. 2.0 m d. 1.0 m e. 18 m
14. A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.050-m
radius cylinder at the top of a well. What torque does the weight of water and bucket produce on the cylinder if the
cylinder is not permitted to rotate? (g = 9.8 m/s2)
a. 23 N⋅m b. 11 N⋅m c. 34 N⋅m d. 17 N⋅m e. 28 N⋅m
15. An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth, frictionless wall. If the
ladder has a mass of 20 kg and it makes an angle of 60° with the ground, find the force of friction of the ground on
the foot of the ladder.
a. 1.7 × 102 N b. 7.8 × 102 N c. 50 N d. 100 N e. 2.0 × 102 N
16. A woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N. The board is supported at each
end. The support force at the right end is 3 times the support force at the left end. How far from the right end is the
woman standing?
a. 2.7 m b. 2.0 m c. 4.0 m d. 1.4 m e. 1.6 m
17. Which type of quantity is characterized by both magnitude and direction?
a. scalar b. trigonometric c. vector d. dimensional e. algebraic variable
18. A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F
is now removed and another force F' is applied at the midpoint of the rod. If F' is at an angle of 30o with respect to
the rod, what is its magnitude if the resulting torque is the same as when F was applied?
a. F b. 5F c. 3F d. 4F e. 2F
19. What term describes a change in the speed of an object in circular motion?
a. tangential speed b. centripetal acceleration c. centripetal force d. tangential acceleration
20. Arvin the Ant travels 30 cm eastward, then 25 cm northward, and finally 15 cm westward. What is Arvin's
direction of displacement with respect to his original position?
a. 59° N of E b. 29° N of E c. 15° N of W d. 29° N of W e. 77° N of E
21. A 3.0-m rod is pivoted about its left end. A force of 6.0 N is applied perpendicular to the rod at a distance of 1.2 m
from the pivot causing a ccw torque, and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot. The
5.2 N is at an angle of 30o to the rod and causes a cw torque. What is the net torque about the pivot?
a. 6.3 N·m b. 0 N·m c. -6.3 N·m d. 15 N·m e. -0.6 N·m
2
Name: ________________________
ID: A
22. A meter stick is supported by a knife-edge at the 50-cm mark. Doug hangs masses of 0.40 and 0.60 kg from the
20-cm and 80-cm marks, respectively. Where should Doug hang a third mass of 0.30 kg to keep the stick
balanced?
a. 20 cm b. 40 cm c. 30 cm d. 70 cm e. 25 cm
A child rides a bicycle in a circular path with a radius of 2.0 m. The tangential speed of the bicycle is 2.0 m/s. The
combined mass of the bicycle and the child is 43 kg.
23. What kind of force provides the centripetal force on the bicycle?
a. gravitational force b. air resistance c. normal force d. friction
24. Vector ä
A is 3.0 units in length and points along the positive x-axis; vector ä
B is 4.0 units in length and points along
A and ä
B are added?
a direction 150° from the positive x-axis. What is the magnitude of the resultant when vectors ä
a. 7.0 b. 1.8 c. 6.7 d. 2.1 e. 4.7
25. A 100-N uniform ladder, 8.0 m long, rests against a smooth vertical wall. The coefficient of static friction between
ladder and floor is 0.40. What minimum angle can the ladder make with the floor before it slips?
a. 18° b. 51° c. 42° d. 58° e. 22°
Problem
26. Two trucks with equal mass are attracted to each other with a gravitational force of 6.7 × 10 −4 N. The trucks are
separated by a distance of 3.0 m. What is the mass of one of the trucks? (G = 6.673 × 10 −11 N•m 2 /kg 2 )
27. A force of 4.0 N is applied to a door at an angle of 60.0° and a distance of 0.30 m from the hinge. What is the
torque produced?
A car on a roller coaster loaded with passengers has a mass of 2.0 × 10 3 kg. At the lowest point of the track, the
radius of curvature of the track is 24 m and the roller car has a tangential speed of 17 m/s.
28. What is the centripetal acceleration of the roller car at the lowest point on the track?
29. To warm up before a game, a baseball pitcher tosses a 0.15 kg ball by rotating his forearm, which is 0.32 m in
length, to accelerate the ball. The ball starts at rest and is thrown at a speed of 12 m/s in 0.40 s. While the ball is in
the pitcher’s hand, what torque is applied to the ball to produce the final tangential speed?
A 35 kg child moves with uniform circular motion while riding a horse on a carousel. The horse is 3.2 m from the
carousel’s axis of rotation and has a tangential speed of 2.6 m/s.
30. What is the centripetal force on the child?
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ID: A
Physics Quiz 1--Torque and Static Equillibrium
Answer Section
MULTIPLE CHOICE
1. ANS: A
PTS: 1
DIF: 2
TOP: 8.1 Torque
2. ANS: E
PTS: 1
DIF: 3
TOP: 8.5 Relationship Between Torque and Angular Acceleration
3. ANS: E
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
4. ANS: B
PTS: 1
DIF: 1
TOP: 8.1 Torque
5. ANS: E
PTS: 1
DIF: 2
TOP: 4.6 Forces of Friction
6. ANS: C
PTS: 1
DIF: 2
TOP: 8.7 Angular Momentum
7. ANS: C
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
8. ANS: A
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
9. ANS: A
PTS: 1
DIF: 2
TOP: 3.2 Components of a Vector
10. ANS: C
PTS: 1
DIF: 3
TOP: 8.1 Torque
11. ANS: C
PTS: 1
DIF: 2
TOP: 3.4 Motion in Two Dimensions
12. ANS: A
PTS: 1
DIF: I
OBJ: 7-1.3
13. ANS: B
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
14. ANS: B
PTS: 1
DIF: 2
TOP: 8.1 Torque
15. ANS: A
PTS: 1
DIF: 3
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
16. ANS: E
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
17. ANS: C
PTS: 1
DIF: 1
TOP: 3.1 Vectors and Their Properties
18. ANS: D
PTS: 1
DIF: 2
TOP: 8.1 Torque
19. ANS: D
PTS: 1
DIF: I
OBJ: 7-1.1
20. ANS: A
PTS: 1
DIF: 2
TOP: 3.2 Components of a Vector
21. ANS: E
PTS: 1
DIF: 2
TOP: 8.1 Torque
22. ANS: C
PTS: 1
DIF: 2
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
23. ANS: D
PTS: 1
DIF: II
OBJ: 7-1.2
24. ANS: D
PTS: 1
DIF: 2
TOP: 3.2 Components of a Vector
1
ID: A
25. ANS: B
PTS: 1
DIF: 3
TOP: 8.2 Torque and the Two Conditions for Equilibrium | 8.3 The Center of Gravity | 8.4 Examples of Objects
in Equilibrium
PROBLEM
26. ANS:
9.5 × 10 3 kg
Given
m1 = m2
r = 3.0 m
F g = 6.7 × 10 −4 N
G = 6.673 × 10 −11 Nm2 / kg2
Solution
m1 = m2
Fg = G
m1 2 =
m1 m2
r2
Fg r2
m1 =
=G
m1 2
r2
G
Fg r2
G
PTS: 1
27. ANS:
1.0 N•m
=
ÁÊÁ 6.7 × 10 −4 N ˜ˆ˜ (3.0 m) 2
Ë
¯
= 9.5 × 10 3 kg
−11
2
2
6.673 × 10 Nm / kg
DIF:
IIIC
OBJ: 7-2.2
Given
F = 4.0 N
d = 0.30 m
θ = 60.0°
Solution
τ = Fd sin θ = (4.0 N) (0.30 m) (sin60.0°) = 1.0 N •m
PTS: 1
DIF:
IIIB
OBJ: 7-4.2
2
ID: A
28. ANS:
12 m/s 2
Given
v t = 17 m/s
r = 24 m
Solution
2
vt 2
(17 m/s)
ac =
=
= 12 m/s 2
r
24 m
PTS: 1
29. ANS:
1.4 N•m
DIF:
IIIA
OBJ: 7-1.1
Given
m = 0.15 kg
v i = 0 m/s
v f = 12 m/s
∆t = 0.40 s
d = 0.32 m
Solution
ÊÁ v − v ˆ˜
i¯
(12 m/s − 0 m/s)
Ë f
F = ma = m
= ÊÁË 0.15 kg ˆ˜¯
= 4.5 N
∆t
0.40 s
τ = Fd = (4.5 N) (0.32 m) = 1.4 Nm
PTS: 1
30. ANS:
74 N
DIF:
IIIB
OBJ: 7-4.2
Given
m = 35 kg
v t = 2.6 m/s
r = 3.2 m
Solution
ÊÁ 35 kg ˆ˜ (2.6 m/s) 2
mv t 2
Ë
¯
Fc =
=
= 74 N
r
3.2 m
PTS: 1
DIF:
IIIA
OBJ: 7-1.2
3