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Unformatted text preview: Physics 8A Fall 2003
Final Exam (Section 2) Useful data:
Speciﬁc heat capacity of water = 4190 J/kgK 1 atm = 1.01 x 105 Pa
Latent heat of fusion for water = 3.33 x 105 J/kg Freezing point of water = 273 K Latent heat of vaporization for water = 2.256 x 106 J/kg R = 8.31 J/molK 1. (10 pts) A 2.0 kg particle traveling along the x axis has a position given by x(t) = 2.0!3  4.01
+ 3.0, where x is in meters and tis in seconds. Find the (a) instantaneous velocity and (b)
instantaneous acceleration at t = 1.0 s, and the (c) average velocity and (d) average
acceleration between t = 1.0 s and t: 2.0 s. (e) Use the workkinetic energy theorem to ﬁnd
the work done by the net force on the particle between t: 1.0 s and t = 2.0 s. 2. (15 pts) A block of mass m is attached to a rope wound around a Q~
pulley with a moment of inertia l and radius r. The block is on an ~
incline that is at an angle 0 with respect to the horizontal. A
coefﬁcient of kinetic friction it exists between the block and the
incline. Find the acceleration of the block as it slides down the incline, in terms of the given quantities and g, the acceleration due
to gravity. 3. (15 pts) Two cars of mass 1.0 kg and 2.0 have an elastic spring 1  r ”/J between them, and are also connected by a string. The spring i E? l is compressed, but the string keeps the cars from ﬂying apart. The cars move at 2.5 m/s. Now the string breaks, and the cars ﬂy apart. The 1.0 kg cart is now moving backward at 1.5 m/s. _____> (a) What is the speed of the other cart? (b) How much energy 1. y n I I V : ?
was stored in the spring before the string broke? J‘PI‘JAJ no [anjev +DULLCI o‘i‘ker c‘r (10 pts) A block of mass m is attached to a horizontal spring with
spring constant k. Resting on top of this block is another block of
mass m. A coefﬁcient of static friction u exists between the two
blocks. Now suppose that the spring is initially at equilibrium length,
and someone comes along and gives the blocks a shove. The blocks
move in response, beginning to undergo simple harmonic motion.
But at a certain distance x from equilibrium, the top block starts
sliding off the bottom one. Find x in terms of the given quantities and
g, the acceleration due to gravity. (Hint: This problem actually has a
fairly short solution. First ﬁnd what acceleration the masses would be
undergoing if the top one is just about to slip. Then you can
determine at what point the masses will have that acceleration.) M (15 pts) Suppose 1.0 kg of ice at 0° C is Combined with 1.0 kg of water vapor at 100° C. The
mixture is allowed to come to equilibrium. (a) What will be the ﬁnal temperature? (b) How much ice will be present? How much water? How much vapor? (10 pts) A string has a length of 0.50 m, a tension of 600 N, and a mass of 0.050 kg. A
second string has a length of 0.125 m and a mass of 0.040 kg. What tension should the second
string be set to in order that its mird harmonic is at the same frequency as the second harmonic of the ﬁrst string? during this process. (10 pts) Suppose we wanted a Camot refrigerator to take 1500 J out of a
themal reservoir at 10° C and transfer it to another reservoir at 50° C. (a)
How much work would need to be put in? (b) How much heat would be
added to the reservoir at 50° C? (c) For an engine operating between these
temperatures, what is the best possible efﬁciency? (d) Suppose we use an
engine with an efﬁciency of 0.30 times that of the most efﬁcient engine to
power our refrigerator. Over a cycle, what would be the net heat ﬂow
between the reservoirs created by the combined operation of the engine and
refrigerator, and in which direction would it ﬂow? (15 pts) In the PV diagram, the process a =>b is isochoric, and the P 5
process b => 0 is adiabatic. The gas is monatornic. Suppose that the
pressure, volume and temperature at point a are 1.0 atm, 1.0 m3, and
250 K. The pressure at point b is 3.0 atm, and the volume at point c is
1.5 m3. (a) How many moles of gas are present? (b) What is the L
temperature of the gas at point c? (c) Consider the direct process a => 6:
c, as shown. If 131,500 J of heat are absorbed, ﬁnd the work done
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