Download Exam 4 Spring 06

Exam 4 Phys. 124A Spring 2006
Name:
Time Allowed: 2 hours
Each question is worth 5 points.
Credits are given for numerical problems only if evidence of calculations is presented.
(Take g=10m/s2 unless otherwise stated)
1. Find the smallest angle a certain binocular can detect if the maximum distance in which it
can resolve the head and the feet of a 1.4 m tall person is 3 km.
(a) 0.055°
(b) 0.068°
(c) 0.043°
(d) 0.027°
2. What is the angular velocity in rad/s of a circular disk spinning at 150 rpm?
(a) 36.3 rad/s
(b) 24.8 rad/s
(c) 15.7 rad/s
(d) 9.2 rad/s
3. A flywheel speeds up in angular velocity from 100 rad/s to 400 rad/s in a 6 second interval.
How many complete revolutions has it gone through?
(a) 147
(b) 239
(c) 345
(d) 423
4. A bicycle wheel of diameter 0.8 m rotates with angular velocity 5.0 rad/s about a fixed axis.
What is the velocity of a point at the middle of a spoke?
(a) 1.0 m/s
(b) 2.0 m/s
(c) 3.0 m/s
(d) 4.0 m/s
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5. The drawing shows the same rod hinged at its left end being pulled by forces of equal
magnitude applied to its right end but in different directions. In which situation is the torque
about the hinge largest?
(a)
(b)
(c)
(d)
6. A uniform rod of length 1.2 m and mass 2.5-kg is loosely nailed to the wall at one end. It is
then pulled aside so that it makes an angle of 30º with the vertical. What is the magnitude of
the torque due to gravity?
(a) 22.5 N  m
(b) 18.5 N  m
(c) 15 N  m
(d) 7.5 N  m
7. Three forces act on a weightless rod 4m in length as shown. The 4 N force acts through the
point at a distance of 1 m from the 3 N force. Can the rod be in equilibrium? Give reason to
support your conclusion..
(a) Yes
(b) No
3N
1N
4N
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8. A 2m long horizontal massless plank is supported at the locations A and C as shown. An 8kg mass is placed at location B and a 2-kg mass is placed at location D. The following
distances are given: AB=1m, BC=0.5m, CD=0.5m. Find the support force at location A.
B
A
D
C
(A) 5 N
(B) 10 N
(C) 20 N
(D) 30 N
9. Find the spring constant of a spring that is stretched a length of 3 cm when it is pulled by 40N forces on each end.
(a) 285 N/m
(b) 648 N/m
(c) 1140 N/m
(d) 1330 N/m
10. The table shows the possible simultaneous values of the displacement, velocity, and
acceleration of an object moving in one dimension. Which case is possible if the motion is
simple harmonic?
Case
x
v
a
A
B
C
D
0
0
maximum
0
maximum
0
maximum
maximum
maximum
maximum
0
0
11. A vertically suspended spring is stretched a length of 0.03m when a mass of 6-kg hangs from
it in equilibrium. What is the period of the subsequent oscillations if the 6-kg mass is pulled
down a little from its equilibrium position and released.
(a) 0.25 s
(b) 0.34 s
(c) 0.48 s
(d) 0.59 s
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12. A spring-loaded gun is used to shoot a ball vertically up. The mass of the ball is 0.030 kg.
When the spring is compressed by 2 cm, the maximum height reached by the ball is 4 m.
Neglecting air resistance, find the spring constant.
(a) 4000 N/m
(b) 5000 N/m
(c) 6000 N/m
(d) 7000 N/m
13. Choose the correct expression for the displacement of a simple harmonic oscillator with a
period of 12s and amplitude of 0.5?
 
(A) x  1.0 cos t 
3 
 
(B) x  1.0 cos t 
6 
 
(C) x  0.5 cos t 
3 
 
(D) x  0.5 cos t 
6 
14. The diameter of a bowling ball is 16cm. It is made from a plastic with density 5200 kg/m3.
Find its weight is lb? (g=9.8 m/s2, 1 lb=4.445 N, V  4r 3 3 for a sphere)
(a) 15 lb
(b) 20 lb
(c) 25 lb
(d) 30 lb
15. The interior of a tightly sealed room is kept at a pressure of 0.94 ATM on a day when the
surrounding pressure is 1 ATM. What is minimum force to open on a door that measures
2m×1m? (1 ATM=1.013×105 Pa)
(a) 12 kN
(b) 24 kN
(c) 36 kN
(d) 48 kN
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16. The figure shows two fish tanks, each having sides of width 1 foot. Tank A is 3 feet long
while tank B is 6 feet long. Both tanks are filled with 1 foot of water. The water exerts forces
SA,SB on the sides of A and B and forces BA ,BB on the bottom of A and B. Which of the
following statements is correct?
A)
B)
C)
D)
SA = SB and BA = BB
SA = 2SB and BA = BB
2SA = SB and 2BA = BB
SA = SB and 2BA = BB
17. Two pistons of a hydraulic lift have radii 3cm and 15cm. The downward force on the 3cm
piston that is required to lift a 200 N weight is
(A) 4 N
(B) 8 N
(C) 40 N
(D) 80 N
18. A deep sea diver can withstand an external pressure of 5 ATM. What is the maximum depth
he can dive?
(a) 30 m
(b) 40 m
(c) 50 m
(d) 60 m
19. One fourth of the volume of a 20-kg block of steel is immersed in a pool of hydraulic oil.
Find the buoyant force. (Densities of steel and oil are 7860 kg/m3 and 800 kg/m3
respectively)
(a) 25 N
(b) 12 N
(c) 5 N
(d) 2 N
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20. A metallic sample weighs 29.0 N in air and 23.0 N in water. The buoyant force on the object
and the density of the metal are
(a) 4 N and 4.8×103 kg/m3
(b) 4 N and 3.4×103 kg/m3
(c) 6 N and 4.8×103 kg/m3
(d) 6 N and 3.4×103 kg/m3
21. (Bonus) A long glass tube with one closed end is first filled with mercury and then inverted
on a pool of mercury exposed to the atmosphere. It is found that the tip of the tube is 50 cm
above the surface of the pool, and the tube is completely filled with mercury. What is the
pressure of mercury at the tip of the tube? (Atmospheric pressure is 1.01×105 Pa, and the
density of mercury is 13600 kg/m3.)
50cm
(A) 3.4×104 Pa
(B) 2.5×104 Pa
(C) 1.0×105 Pa
(D) 3.2×105 Pa
22. (Bonus) A block of wood of volume 0.02 m3 is held under water at a depth of 30 m. It is then
released with zero velocity. The density of the wood is 600 kg/m3. Find how long it takes to
float to the surface.
(a) 1 s
(b) 2 s
(c) 3 s
(d) 4 s
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