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Unformatted text preview: Physics 171.101 Final Exam May 12, 2003
Prof. Barnett Take 7T : 3, g : 10 meters/secondsg, sin(37°) : 0.6, cos(37") : 0.8., R : 8 Joule/(mole—OK) Use a pen. No “snow paint”. Explain your work clearly for maximum partial credit.
You are allowed to use material written on the front and back of four 3” x 5” index cards. 1. [\I) You walk 2 km North with a speed of 6 km/hour, then 3 km East with a speed of 5 km/hour,
and, ﬁnally, 5 km at an angle of 37" South of East with a speed of 4 km/hour. A) (15 pts) What is your displacement vector, 1?, for the entire trip?
B) (10 pts) What is your average speed for the entire trip?
C) (10 pts) What is your average velocity for the entire trip? Steady state automobile trafﬁc can be analyzed as a ﬂuid flowing in a two-dimensional space.
Suppose the traﬁic velocity is 100 km/hour when the highway is 4 lanes wide but only 25
km/hour when it narrows to only 2 lanes wide. The number of cars passing a certain point
on the two lane highway, i.e. the sum of the cars in the two lanes, is 1 car per 5 seconds. A) (15 pts) Find the distance between the cars in a single lane on the two lane highway. B) (20 pts) Find the distance between the cars in a single lane on the four lane highway. A car of mass 2000 kg is traveling on a circular,
banked, icy, frictionless racetrack. The angle, 6’, of
the banked racetrack is 37° relative to the horizontal.
The car’s speed is 180 km/hour; A) (10 pts) Draw a picture showing all the forces acting on the car. Deﬁne a coordinate system (i, j, k) and write out each force in terms of its (2,}, k) components and 6.
B) (10 pts) Find the magnitude of the Normal Force on the car. C) (10 pts) Find the radius of the car’s path on the circular racetrack. D) (10 pts) Given the figure showing that the car is driving “out of the page” “towards you”, ﬁnd the angular velocity vector, (3, in terms of your coordinate system. Two metal bars are placed in contact with two walls,
one held at 1000 C and the other held at 0° C. One
bar is made of lead and the other is silver. Both are 5 cm long and they have rectangular cross sections.
The dimensions of the lead bar’s cross section are 5 cm x 5 cm. The dimensions of the silver bar’s cross section are 4 cm x 3 cm. The coefficients of
thermal conductivity are 350 W/m-K for lead and 450 W'/m-K for silver. The heat ﬂow from one wall to the other is stable, i.e. it is not changing with time. A) (25 pts) What is the total heat flow per second from the hot wall to the cold wall?
B) (15 pts) \Vhat is the change in entropy for the total system per second? 5. A steel wire having a mass of 0.5 grams and a length of 2.0 meters is ﬁxed at both ends in a
piano. It has a tension of 250 Newtons. A) (10 pts) What is the speed of a transverse wave on this wire?
B) (10 pts) What is the frequency of the fundamental standing wave? C) (20 pts) Write the formula describing the ﬁrst overtone (second harmonic) standing wave
if the maximum displacement of the wire is 3 mm. 6. Three blocks are connected by massless strings looped
over massless pulleys on a table as shown. The masses
are M1 : 5 kg, M2 : 10 kg and M3 = 15 kg. The table’s
coefficient of kinetic friction is ,uk 2 0.1. The blocks are
initially at rest. At t = 0 they are released and can move. g = 10 771/32 Mg : 10 kg A) (20 pts) Find the acceleration, 53, of M3.
B) (10 pts) Find the tension in the right string.
C) (10 pts) Find the tension in the left string. 7. A cannon is attached to the outer rim of a horizontal uniform disk with radius 25 meters
that is free to rotate about an axle at its center. The cannon contains one cannonball. The cannonball has a mass, MB, of 20 kg, the cannon has a mass, MC, of 600 kg, and the disk has
a mass, MD, of 2000 kg. The entire system is initially at rest. The cannon ﬁres the cannonball horizontally with a speed relative to the ground of 200 km/sec. The cannon and disk recoil
from the shot and rotate about the axle. [disk : 0.5MDRZ. A) (10 pts) What impulse was applied to the cannonball? é—o B) (25 pts) What is the rotational angular speed of the cannon ball
and disk about the axle after the cannonball was shot? C) (15 pts) What is the ﬁnal kinetic energy of the ENTIRE
system after the cannonball was shot? 8. Two moles of an ideal gas are used in an engine with
a three process cycle. One process, A —+ B, is isobaric,
one process, B —> C, is adiabatic, one process, C —> A,
is isothermal, as shown in the diagram. The maximum F '
pressure is 2 x 105 Pascals and the minimum pressure is A_ B 2 105 Pascals
105 Pascals. The temperature during the isothermal X
compression, 0 —> A, is 500" K. The speciﬁc heat per
mole at constant pressure is Op 2 3R and the speciﬁc 5000 K ~ heat per mole at constant volume is 0V : 2R where R is 5 P 1
the “Gas Constant”. Use R = 8 Joule/(mole—OK) C 10 asca S A) (5 pts) What is the vo1ume at point A? B) (5 pts) What is the volume at point C? -
(15 pts) What are the volume and temperature at point B? V
(15 pts) How much heat ENTERS the engine during each process? (20 pts) How much work is done BY the engine during each process? C) D) E) F) (10 pts) What is the efﬁciency of this engine? ...
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