課程名稱︰普通物理學乙
課程性質︰牙醫系大二必修
課程教師︰董成淵
開課學院：理學院
開課系所︰物理系
考試日期（年月日） 2008/11/26
考試時限（分鐘）：兩堂課
是否需發放獎勵金：yes
（如未明確表示，則不予發放）
試題 :
1.Independent measurements (with errors) were made on the length(l±△l) and
radius (r±△r) of a cylinder.
Please derive the formula for the volume V±△V. Derive the errors for the
volume measurements assuming that the errors for length and radios are
independent. (14%)
2.A small block, mass m, slides down a frictionless surface through height h
and then stricks to a uniform rod of mass M and length l. The rod pivots
about point O through angle θ before momentarily stopping. Find θ.
3.A funny car accelerates from rest through a measured track distance in time
T with the engine operating at a constant power P. If the track crew can
increase the engine power by a differential amount dP, what is the change in
the time required for the run? (14%)
4.Two speakers aeparated by distance d1=2.00m are in phase. Assume the
amplitudes of the sound waves from the speakers are approximately the same at
the listener's ear at distance d2=3.75m directly in front of one speakers.
Consider the full audible range for normal hearing, 20Hz to 20kHz. (a)What is
the lowest frequency f(min,1) that gives minimum signal (destructive
interference) at the listener's ear? By what number must f(min,1) be
multiplied to get (b)the second lowest frequency f(min,2) that gives minimum
signal? (c)What is the lowest frequency f(max,1) that gives maximum signal
(constructive interfeerence) at the listener's ear? By what number must
f(max,1) be multiplied to get (d)the second lowest frequency f(max,2) that
gives maximum signal? (12%)
5.A baseball is hit at a height h=1.00m and then caught at the same height. It
travels alongside a wall, moving up past the top of the wall 1.00s after it
is hit and then down past the top of the wall 4.00s later, at distance
D=50.0m farther along the wall. (a)What horizontal distance is traveled by
the ball from hit to catch? What are the (b)magnitude and (c)angle (relative
to the horiaontal) of the ball's velocity just after being hit? (d)How high
is the wall? (16%)
∣← D →∣
█████████
█████████h=1.00m
6.A uniform thin rod of length L, mass m, is lying on the usual smooth
horizontal table. A horizontal impulse, P, is suddenly applied perpendicular
to the rod at one end.
(a)How far does the rod travel during the time it takes to make one complete
revolution?
(b)What are the translational, rotational, and total kinetic energies of the
rod after the impulse?
(15%)
7.A solid cylinder rolls, mass m, from the rest on an incline angled at θ.
(a)What is the acceleration at the center of mass?
(b)Please proof the cylinder will slip when the coefficient of static
friction μs＜ (tanθ/3).
(15%)
------- 附可能用到的值 -----------
The following formulas may be useful:
(1)The rotational inertia of thin rod, length L, about axis through center
perpendicular to length is (1/12)ML^2
(2)The rotational inertia of solid cylinder, tadius R, length L, abort central
is (1/2)MR^2.
(3)Sounds velocity 343m/s
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