DG-Nov. 17-2021 - DGD PDF

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PHY1121 DISCUSSION GROUP NOVEMBER 17, 2021 1. The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length of the rod. Such a rod is hung vertically from one end and set into a small-amplitude oscillation. If L = 1.0 m and M = 200 g, then this rod will have the same period as a simple pendulum of length A) 33 cm. B) 50 cm. C) 67 cm. D) 100 cm. E) 150 cm. Answer: C)

2. A disk (radius R = 1.0 m and mass M = 2.0 kg) is suspended from a pivot. The pivot is at a distance d = 0.25 m from the center of mass of the disk. The rotational inertia of such a disk about its central axis is MR2/2. The angular frequency (in rad/s) of this disk for small oscillations is A) 3.0. B) 0.48. C) 2.1. D) 13. E) 4.2. Answer: C)

3.

A torsional pendulum consists of a solid disk (mass = 2 kg and radius = 1 m) suspended by a wire attached to a rigid support. The disk oscillates about the support wire. If the torsion constant is 16 N⋅m, what is the angular frequency (in rad/s)? A) 2 B) 6 C) 8 D) 3 E) None of the above. Answer: E

4. A car’s front suspension has a natural frequency of 0.45 Hz. The car’s front shock absorbers are worn out, so they no longer provide critical damping. The car is driving on a bumpy road with bumps 40 m apart. At a certain speed, the driver notices that the car begins to shake violently. What speed? Answer: 64.8 km/h

5. What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the earth, where R is the radius of the earth? A) 4.8 m/s2 B) 1.1 m/s2 C) 3.3 m/s2 D) 2.5 m/s2 E) None of the above. Answer: 1.1 m/s2

6. At what height is the object’s weight n times smaller that its weight at the surface of the Earth? Calculate this height for n = 5 and 9. Answers: 7870 km, 12700 km

7.. A 150-kg object is released from rest at an altitude of 1000 km above the north pole of the earth. Ignoring atmospheric friction, the speed (in km/s) of the object as it strikes the surface of the earth is closest to A) 2.9. B) 3.3. C) 3.7. D) 4.1. E) 4.4. Answer: D)

8. A projectile is launched from the surface of a planet of mass M and radius R. What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere. A)

4GM . 3R

8GM . 5R 3GM C) . 2R 5GM D) . 3R E) None of the above is correct. B)

Answer: A)

9. A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet? A) B) C) D) E)

GmM 24 R GmM 15 R GmM 12 R 2 GmM 21R None of the above is correct.

Answer: A)...