Physics 2 Practise Final - UC Santa Barbara
Physics 2 Practise Final
1. A mechanist is using a wrench to loosen a nut. The wrench is 25 cm long, and he exerts a 17-N force at the end of the handle.
a) What torque does the mechanist exert about the center of the nut?
b) What is the maximum torque he could exert with this force?
2. A solid wood door 1 m wide and 2 m high is hinged along one side and has a total mass of 40 kg. Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 5 kg, traveling perpendicular to the door at 12 m/s just before the impact. Find the final angular speed of the door. Does the mud make a significant contribution to the moment of inertia?
3. A solid, uniform ball roll without slipping up a hill, as shown. At the top of the hill it is moving horizontally, and then it goes over the vertical cliff.
a) How far from the foot of the hill does the ball land? And how fast was it moving just before it lands?
b) Notice when the ball lands, it has a larger translational velocity than when it started from the foot of the hill. Does this mean that the ball somehow gained energy? Explain.
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4. A 1.05 m long rod of negligible weight is supported at its ends by wires A and B of equal length. The cross sectional area of A is 2 mm2 and the cross sectional area of B is 4 mm2. Young’s modulus for wire A is 1.8*1011 Pa; and for wire B is 1.2*1011 Pa. At point along the rod should weight W be suspended to produce
a) equal stresses in A and B?
b) equal strains in A and B?
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5. A landing craft with mass 12,500 kg is in a circular orbit 5.75*105 m above the surface of a planet. The period of the orbit is 5800 sec. The astronauts in the lander measure the diameter of the planet to be 9.6*106 m. The lander sets down at the north pole of the planet. What is the weight of a 85.6 kg astronaut as he steps out onto the planet’s surface?
6. As Mars orbits around the sun in its elliptical orbit, its distance of closest approach to the sun (at perihelion) is 2.067*1011 m, and its maximum distance from the sun (at aphelion) is 2.492*1011 m. If the orbital speed of Mars at aphelion is 2,198*104 m/s, what is the orbital speed at perihelion?
7. A uniform beam is suspended from the horizontally by two identical vertical springs that are attached between the ceiling and each end of the beam. The beam has mass 225 kg, and a 175 kg sack of gravel sits on the middle of it. The beam is oscillating in SHM, with am amplitude of 40 cm and a frequency of 0.6 Hz.
a) The sack of gravel falls off the beam when the beam has its maximum upward displacement. What are the frequency and amplitude of the subsequent SHM of the beam?
b) If the gravel instead falls off when the beam has its maximum speed, what are the and amplitude of the subsequent SHM of the beam?
8. A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15 cm.
a) What is the gauge pressure at the water-mercury interface?
b) Calculate the vertical distance h from the top of the mercury in the right-hand arm of the tube to the top of the water in the left-hand arm.
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9. A Styrofoam bucket of negligible mass contains 1.75 kg of water and 0.45 kg of ice. More ice, from a refrigerator of -15◦C, is added to the mixture in the bucket, and when thermal equilibrium has been reached, the total mass of ice in the bucket is 0.778 kg. Assuming no heat is exchanged with the surroundings, what mass of ice is added?
10. A large tank of water has a hose connected to it, as shown the figure. The tank is sealed on the top and has compressed air between the water surface and the top. When h = 3.50 m, the absolute pressure p of the compressed air is 4.20*105 Pa. Assume that the air above the water expands at a constant temperature, and take the atmospheric pressure to be 1.00*105 Pa.
a) What is the speed which water flows out of the hose when h = 3.50 m?
b) As water flows out of the tank, h decreases. Calculate the speed of the flow for h = 3.00 m and for h = 2.00 m.
c) At what value of h does the flow stop?
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11. Three moles of ideal gas are in a rigid cubical box with sides of length 0.2 m.
a) What is the force that the gas exerts on each of the six sides of the box when the gas temperature is 20 ◦C?
b) What is the force when the temperature is increased to 100 ◦C?
12. A Carnot engine takes heat in from a reservoir at 400K and discards heat to a reservoir at 300K. If the engine does 1200 J of work per cycle, how much heat does it take in per cycle?
13. A copper pot at room temperature is filled with room temperature water. Imagine a process whereby water spontaneously freezes and the pot becomes hot. Which thermodynamics law does such a process violate?
A. 1st Law B. 2nd Law C. Both the 1st and the 2nd Law D. Neither
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