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Torque and Static Equilibrium

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Physics 12 Practice Test – Torque and Static Equilibrium
Multiple Choice Section
1. A 45 N block is suspended as shown in the diagram.
65º
T=?
45 N
What is the tension, T, in the horizontal cable?
A.
B.
C.
D.
19 N
21 N
23 N
97 N
2. What are the tensions T 1 and T2 in the two ropes holding the 36 kg mass as shown?
60º

T1 ?
T2 ?
50º




m 36 kg
TENSION T1
TENSION T2
A.
180 N
180 N
B.
180 N
270 N
C.
350 N
180 N
D.
350 N
350 N
3. A mass is suspended by two ropes from a ceiling and a wall.
57°
T 250 N
m ?
Determine the mass m.
A.
B.
C.
D.
13 kg
17 kg
26 kg
39 kg
4. A 25 kg block is shown suspended by two ropes. What is the tension in rope 2?
65°
Rope 1
55°
Rope 2
25 kg
A.
B.
C.
D.
110 N
120 N
260 N
430 N
5. Three horizontal forces are acting at the same point on a puck lying on a level frictionless table.
The puck is in translational equilibrium.
Two of these forces are:
F1  10.2 N, east
F2  15.4 N, 30E of N
What is the magnitude of the third force?
A. 5.2 N
B. 15.6 N
C. 18.5 N
D. 22.3 N
6. Which of the following is a torque expression?
A.
B.
C.
D.
 = ma
 = mv
 = v sin
 = F sin d
7. A uniform 2.4 m long beam with a mass of 25 kg is kept horizontal by a force F.
F
30º
25 kg
2.4 m
What is the magnitude of the force F?
A.
B.
C.
D.
1.2 x 102 N
1.4 x 102 N
2.5 x 102 N
4.9 x 102 N
8. A uniform plank, 5.0 m long and with a mass of 15 kg, rests on two supports as shown.
5.0 m
3.0 m
What force does the left-hand support exert on the plank?
A.
B.
C.
D.
74 N
88 N
123 N
147 N
9. Which of the following demonstrates the application of torque?
A.
B.
C.
D.
Pulling a block across a floor
Pushing a block up an incline
Using a screwdriver to turn a screw
Stopping a block from sliding down an incline
10. Two cables are used to support a 24 kg mass on a 1.6 m long 8.0 kg uniform horizontal
beam as shown.
m = 8.0 kg
m = 24 kg
right cable
1.0 m
0.60 m
What is the tension T in the right cable?
A.
B.
C.
D.
130 N
150 N
190 N
300 N
11. A 1.6 kg ball is held in the hand of a fully extended 11.2 kg arm as
shown. (cg = centre of gravity)
Shoulder joint
cg of
arm 25



m 1.6 kg
What is the total torque about the shoulder joint due to the ball and to this arm?
A.
B.
C.
D.
17 N-m
19 N-m
35 N-m
38 N-m
12. A force is used to rotate a beam. As the beam rotates, the direction of the force changes
but its magnitude does not.
F
4
F
3
F
2
1
F
What happens to the torque on the beam due to this force as the beam is rotated from position 1 to
position 4?
A.
B.
C.
D.
always increases
always decreases
increases then decreases
decreases then increases
13. Two young children are playing on a seesaw.
m 42 kg
m 36 kg
17°
What is the magnitude of the net torque, due to the two children, about the seesaw pivot in the
position shown?
A. 220 Nm
B. 230 Nm
C. 1400 Nm
D. 1500 Nm
14. Two cables support a vertical tower. The tension in each cable is shown.
2500 N
5300 N




What is the angle ?
A.
B.
C.
D.
25º
28º
62º
65º
15. If the load on the uniform beam shown below is moved to the right, how do the tension force FT
in the cable and the horizontal forceF x that the hinge exerts on the beam change?
wall
cable with
tension FT
load moved to right
beam
Fx
hinge
TENSION FORCE FT
HORIZONTAL FORCE Fx
A.
Decrease
Decrease
B.
Decrease
Increase
C.
Increase
Decrease
D.
Increase
Increase
16. A uniform 3.0 m long beam is supported by a cable as shown. The tension in the cable is 530 N.
cable
37°
beam
What is the mass of the beam?
A.
B.
C.
D.
33 kg
43 kg
65 kg
86 kg
17. A uniform 3.5 m beam of mass 54 kg is supported by a cord attached at the 3.0 m position and
at an angle as shown in the diagram. The tension in the cord is 730 N.
65º
hinge
3.0 m
What is the magnitude of the torque produced by the cord about the hinge?
A.
B.
C.
D.
310 N-m
930 N-m
2000 N-m
2200 N-m
18. The horizontal uniform beam shown below is 4.0 m long and has a mass of 120 kg.
cord
55º
3.0 m
load
If the maximum tension allowed in the cord is 2.7 x 103 N, what is the maximum load that can be
hung from the end of the beam?
A.
B.
C.
D.
59 kg
110 kg
150 kg
230 kg
19. A post of negligible mass is supported by two cables as shown.
X
2200 N
Post
58°
75°
What is the force exerted by the post on point X?
A.
B.
C.
D.
1100 N
2600 N
2900 N
5100 N
Written Section
1. A uniform 50.0 kg beam with a length of 2.4 m supports a 200 kg load.
a) What is the tension in the horizontal cable attached to the beam as shown below?
2.4 m beam
50 kg
cable
hinge
50°
200 kg
b) Using principles of physics, explain how this tension will change if the beam is lowered to a
more horizontal orientation (i.e., greater angle) as shown below. The cable remains
horizontal and connected to the same point on the beam.
cable
Page 4
Physics 12 – 0801 Response Booklet
2. An 80 kg, 12 m uniform diving board in static equilibrium is shown below. Support A
is providing a 3000 N force directed downward on the board.
12 m
L
70 kg
diver
A
B
Determine the force provided by support B and the distance L.
3. A 65 kg man is 3.0 m up a 5.0 m, 16 kg ladder leaning against a smooth wall at an angle of
72ºas shown below.


72º

What minimum force of friction between the ladder and the floor is required to keep the ladder
from sliding?
4. A 4.0 m long steel beam is supported 3.0 m from a hinge by a cable attached as shown.
FT 150 N
65°
40°
If the tension in the cable is 150 N what is the mass of the steel beam?
5. Two vertical wires with tensions as indicated support a uniform 14 kg, 3.0 m-long beam
carrying an object of mass M as shown.
TL 625 N
TR 348 N
Object M
l
At what distance l from the right-hand wire is the object located?
6. A 1.5 m-long uniform beam supports a 120 kg load. The beam is suspended by a wire
connected as shown. This wire is under a tension of 3700 N.
Wire
FT 3700 N
70°
18°
1.5 m beam
120 kg
What is the mass of the beam?
Answers
MC: 1 B 2 B 3 D 4 A 5 D 6 D 7 C 8 C 9 C 10 C 11 C 12 C 13 A 14 C 15 D 16 C 17 B 18 B 19 B
Written: 1 a) FT = 3.15 x 103 N b) Perp. component of Fg increases so ccw also increases; this increases perp. component of FT in
cable needed, and since cable is nearly // with beam, overall FT must be greater 2. FB = 4.47 x 103 N, L = 9.1 m 3. Ff = 150 N
4. m = 16 kg 5. l = 2.0 m
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