Download Physics Exam: Problems on Waves, Mechanics, and Ideal Gases and more Exams Physics in PDF only on Docsity!
First Name: ____________________ Last Name:_____________________ Section: ________
May 18, 2007 Physics 207
Final EXAM
Please print your name and section number (or TA’s name) clearly on all pages. Show all
your work in the space immediately below each problem. Problems will be graded on reasoning and
intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the
direction of vectors. Each problem is worth 20 points. Try to be neat! Check your answers to see
that they have the correct dimensions (units) and are the right order of magnitude. You are allowed
two sheets of notes (8.5” x 11”, 4 sides), a calculator, and the constants in this exam booklet. The
exam lasts exactly 120 minutes.
Constants:
Avogadro’s Number: NA = 6.02 x 10^23 molecules/mole
Mathematics:
trigonometric identity: sinA + sinB = 2cos[(A-B)/2]sin[(A+B)/2]
small angle approximations: sinθ = θ - θ^3 /3 + O (θ^5 )
cosθ = 1- θ^2 /2 + O (θ^4 )
SCORE:
Problem 1: __________
Problem 2: __________
Problem 3: __________
Problem 4: __________
Problem 5: __________
TOTAL: ___________
Don't open the exam until you are instructed to start.
“Imagination is more important than knowledge.” A. Einstein
First Name: ____________________ Last Name:_____________________ Section: ________
PROBLEM 1
Part I
a. A mass m = 20 kg is attached to a steel wire of length L = 1 m and cross-sectional area 10-^6 m^2. The
Young's Modulus of the steel is 2 x 10^11 N/m^2. Suppose the mass is spun with speed v in a horizontal
circle on a frictionless surface. If the steel wire is horizontal and stretches to 1.01 m in length, what is
the speed v? (10 pts)
First Name: ____________________ Last Name:_____________________ Section: ________
PROBLEM 2
Part I
A traveling wave on a string is shown below at times t = 0 s and t = 0.1 s. Between these times, the
peak labeled “A” smoothly moves between the two marked locations.
a. For this traveling wave, give numerical values for each of the following quantities: (4 pts)
b. Circle the equation that best describes this wave ( k and ω are positive): (2 pts)
y = Asin(kx + ωt)
y = Asin(kx - ωt)
y = Acos(kx + ωt)
y = Acos(kx - ωt)
c. What is the maximum transverse speed of a piece of the string (i.e. the maximum speed in the y
direction)? (4 pts)
Wavelength λ =
Period T =
Wave speed v =
Amplitude =
First Name: ____________________ Last Name:_____________________ Section: ________
Part II
d. Two loudspeakers emit identical sound waves. A listener at the center position hears the loudest
sound. At a point 0.65 m away from the center the listener hears the least sound. What is the sound's
wavelength and frequency? The speed of sound in air is 340 m/s. (10 pts)
7.5 m
loudest
least sound
0.65 m
4.0 m
loudspeakers listener
wavelength=
center line
frequency =
First Name: ____________________ Last Name:_____________________ Section: ________
d. A ball of mass m = 1.0 kg is thrown downward and bounces off the floor. The approximate force
exerted by the floor on the ball during the bounce is shown in the graph. If the ball’s speed just
before it hits the floor is 5.0 m/s, what is its speed just after it comes off the floor? (3 pts)
i. 2.0 m/s. ii. 3.0 m/s. iii. 4.0 m/s. iv. 5.0 m/s. v. None of the preceding choices is correct.
First Name: Last Name: Section:
Multiple Choice
A heat engine absorbs heat Q from a hot reservoir. The amount of work done by the engine a) is Q b) must be greater than Q c) must be less than Q d) could be greater than Q e) is zero
A particle of mass m moves in one dimension x with simple harmonic motion according to the equation
d^2 x dt^2
= −Ax
where A > 0. What is its period? a) √πmA b) 2 √πmA c) 2 π
√ (^) m A d)^ √^2 π A e) none of the above
mb
mw
A block of mass mb rests on a horizontal surface and is accelerated by means of a horizontal cord that passes over a frictionless peg to a hanging weight of mass mW. The coe cient of kinetic friction between the block and the horizontal surface is μ. If you are given that the mass mW is accelerating downward, the acceleration is a) g m mWb^ +−mμmWb b) g m mb−b+μmmwW c) g mW m^ (1b−+μm)w− mbd) g (^) μmmbb−+mmwW e) none of the above
First Name: Last Name: Section:
d) If the answer to part c) is ∆tm, what is the time necessary to hit the target in terms of ∆tm? (2 pt)
e) What is the angle θ at which the ball should be launched such that the target is reached (express your answer in terms of {g, d, ϕ, v^20 }? (5 pt)
f ) If the ball has mass M and moment of intertia 25 M R^2 and is rolling without slipping (instead of sliding frictionlessly), and assuming again that θ is known, what distance up the board (measured in distance from the bottom edge of the board) does the ball go before rolling back down (express your answer in terms of {v 0 , θ, g, ϕ}). (The initial speed is taken to be the speed of the center of mass of the ball.) [Hint: One way to solve this is through energy conservation.] (5 pt)
First Name: Last Name: Section: (extra space for work)
First Name: Last Name: Section: (c continued if necessary)
d) If the answer to part c) is W 0 , what is the minimum heat is required for the process described in part b). (Neglect any changes in bulk mechanical energy.) Assume that the answer to part b) was
Vf Vi
= c 1 (
Tf Ti
)α
(where Vf is the nal volume) for a particular constant α and c 1 , and express your answer in terms of {W 0 , Tf , Ti, Vi, A, c 1 , α, Mp}. (7 pt)
