A) Find the Tension in the Cable
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I. The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of 60 with the horizontal. A person (mass = 60 kg) stands 3.0 m from the pivot.
a) Find the tension in the cable.
Tension = b) Determine the horizontal and vertical forces exerted on the beam by the pivot.
Rx =
Ry = c) If the maximum tension that the cable can sustain without breaking is 500 N, how far can the man safely walk out on the beam?
x = II. A 1.0 kg mass is attached to a spring with a force constant k=16 N/m. It oscillates on a horizontal, frictionless track. At the time t=0, the mass is released from rest at x=- 7.0 cm (that is, the spring is compressed by 7 cm). a) Find the period of the motion.
Period = b) Find the maximum values of the velocity and the acceleration.
vmax=
amax= c) Write expressions for the position, velocity and accelerations as a function of time. Use all the numeric values that you are able to calculate (time is the only variable that should appear in your solutions).
x(t)=
v(t)=
a(t)= 3. A skater extends her arms horizontally, her moment of inertia is about 10 kgm2 . She then picks up a 5-kg mass in each hand. Then she rotates about a vertical axis with an angular velocity of one revolution per second. If she pulls the weights in to her shoulders, what will the final angular velocity be if the moment of inertia of her body (without the weights) remains approximately constant at 10 kgm2, and the distance of the masses from the axis changes from 1 m to .1 m?
a) 6 rev/s
b) 3 rev/s
c) 9 rev/s
d) 4 rev/s
e) 2 rev/s
4. Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. The angular velocity of a star increases as it shrinks because of
a) conservation of energy
b) conservation of linear momentum
c) conservation of angular momentum
d) the law of universal gravitation
e) conservation of mass
5. Write the equation of a wave, traveling along the +x axis with an amplitude of .02 m, a frequency of 440 Hz, and a speed of 330 m/sec.
a) y = .02 cos [880 x/330 – 440t]
b) y = .02 sin [880 (x/330) – t)]
c) y = .02 sin [880(x/330 + t)]
d)y = .02 sin [2(x/330 + 440t)]
e) y = .02 cos [2(x/330 + 440t)] 6. The figure below shows a sine wave at one point of a string as a function of time.
7. How much louder is the intensity of sound of a jet in comparison with that of a whisper, if the two intensity levels (in dB) are 130 and 20, respectively?
a) 1012
b) 108
c) 106
d) 1010
e) 1011
8. A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 Hz. What is the difference (approximately) between the frequency the observer hears as she approaches the police car and the frequency she hears as she moves away from the police car (let the speed of sound in air be 340 m/s)?
a) 110 Hz
b) 210 Hz
c) 410 Hz
d)50 Hz
e) 550 Hz