課程名稱︰普通物理學甲上
課程性質︰資工系選修兼通識A7
課程教師︰傅昭銘
開課學院：電資學院
開課系所︰資工系
考試日期（年月日）︰2012/11/
考試時限（分鐘）: 120 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Part1 (30%) Single Choice (30points, 1.5 points each)
1. The position of a nanoparticle as a function of time is
x(t) = t^2-t-6, where x is measured in meters, t is measured
in seconds and t>0. When is the speed of the nanoparticle zero?
(A) when t = 0.5 s (B) when t = 2s
(C) when t = 3 s (D) The speed of the nanoparticle is never zero.
2. An object moves from a point with coordinates x = 0.0 m, y = -1.0 m,
to a point with coordinates x = 5.0m, y = -13.0 m in a time interval
of 4.0 seconds. The magnitude of its average velocity is
(A) 6.2m/s (B) 5.0m/s (C) 7.3m/s (D) 3.3 m/s
3. Tennis ball A is dropped from a height of 15 m. Tennis ball B is
thrown horizontally from a height of 15 m with a horizontal velocity
of 25 m/s. Which tennis ball hits the ground first?
(A) ball A
(B) ball B
(C) They both hit at the same time.
(D) Neither ball hits the ground.
4. The two blocks in the figure have masses M1 and M2 such that M1<M2
and they lay on a level, frictionless surface. We can apply a horizontal
force F either from the left or from the right, as depicted in the figure.
The contact force between masses M1 and M2 is
(A) the same in either case.
(B) larger when F is applied from the left.
(C) larger when F is applied from the right.
(D) zero newtons.
______
_____| |
F---->| M1 | M2 |
_________|____|_____|___________________
______
_____| |
| M1 | M2 |<-----F
_________|____|_____|___________________
5. A variable force of the form F = 3x^2 -2x +5 (N) acts
on a 2 kg object as it moves from x=2 m to x=3 m. How much
work is done by this force?
(A) 6J (B)13J (C)19J (D)24J
6. A spring with spring constant k is suspended from the ceiling .
When a mass of M is attached to the spring, it stretches d1. The
mass is then pulled down an additional d2 and let go. Which one
of the following statements about the resulting motion is true?
(A) The maximum kinetic energy is 0.5k(d1+d2)^2
(B) The maximum kinetic energy is 0.5k(d1)^2
(C) The maximum kinetic energy is 0.5k(d1-d2)^2
(D) The maximum kinetic energy is 0.5k(d2)^2
7. The potential energy of an object as a function of position is
U(x) = x^2-x-6, where U is measured in joules and x is measured in
meters. Where would the object be located if it was in stable equilibrium?
(A) x = -2m (B)x = 0m (C) x = 0.5m (D) x = 3m
8. A block of mass m is attached to a spring and sits on a table
with coefficient of friction μ, which is a height h above the floor.
The spring is compressed by d initially. If the spring constant is k,
what is the speed of the block when it reaches the ground?
(A) √ ( 2gh - 2μgd + k/m * d^2)
(B) √ ( 2gh + 2μgd + k/m * d^2)
(C) √ ( 2gh - 2μgd - k/m * d^2)
(D) √ ( 2gh + 2μgd - k/m * d^2)
9. Find the force acting on a 3.0 kg mass located at x=2.0 m inside
a potential U = -25x + 4x^3 (J).
(A)-18 N (B)+18 N (C)-23 N (D)+23 N
10. A block of mass M is sliding with velocity v along a horizontal
surface with coefficient of friction μ. How much heat produced in
bringing the block to rest?
(A) 0.5Mv^2
(B) 0.5μMv^2
(C) 1/(2μ) *Mv^2
(D) μMv^2
11. Two masses are attached to a R rope as shown such that half of the
rope hangs vertically below the frictionless table. M1 is set into
circular motion with speed v. What is the value of v if M2 is to
remain stationary?
(A) √( (M1/M2)*gR )
(B) √( (M1/M2)*2gR )
(C) √( (M2/M1)*gR )
(D) √( (M2/M1)*2gR )
12. What is the moment of inertia of a solid sphere of mass m and
radius r about a line parallel to another line passing through the
center of the sphere? The distance between the lines is half the
radius of the sphere.
(A) 2/3 * mr^2
(B) 2/5 * mr^2
(C) 11/12 * mr^2
(D) 13/20 * mr^2
13. A solid cylinder of mass m, radius r, and length L starts from
rest and rolls without slipping down an inclined plane. Its vertical
position decreases by a distance h. What is the final linear speed of
its center of mass?
(A) √ ( gh )
(B) √ ( (4/3)gh )
(C) √ ( (3/2)gh )
(D) √ ( 2gh )
14. Two weights are hanging on a 60 cm long, 100 g mass uniform
wooden bar as showm in the figure. Is this system in equilibrium?
(A) Yes
(B) No
(C) It cannot be determined.
(D) It depends on value of the normal force.
20cm 10cm 10cm
<--------><----><---->
_______________________________
| △ |
| |
| |
___|___ ___|___
| | | |
| 1kg | | 2kg |
|______| |______|
15. A physics processor is sitting on a rotating chair with his arms
outstretched, each holding a medium sized barbell. The frictionless
chair is originally rotating at a constant angular speed. He then
pulls his arms closer to his body. When he brings his arms in, his
angular velocity
(A) increases.
(B) remain constant.
(C) decreases.
(D) increases or decreases, due to depend on how he brings his arms in.
16. A small circular object with mass m and radius r has a moment of
inertia given by I=cmr^2. The object rolls without slipping along
the track shown in the figure. The track ends with a ramp of height
R that launches the object vertically. The object starts from a height
H. To what maximum height will it rise after leaving the ramp?
(A) I c
----- H + -----R
I+c I+c
(B) I c
----- H + -----R ●
I-c I-c ↑\
(C) c I | \
----- H + -----R H | \ ○
I+c I+c | \ / ↑ R
(D) c I ______↓____\__/___↓_____
----- H + -----R ↑
I-c I-c 此處為圓滑弧形
17. A demenstration gyroscope consists of a uniform disk with a
41.3 cm radius, mounted at the midpoint of a light axle with 79.5 cm
length. The axle is supported at one end while in a horizontal
position. How fast is the gyroscope precessing, in units of rad/s,
if the disk is spinning aroung the axle at 18.9 revolution/s?
(g=9.8m/s^2)
(A)0.192 rad/s (B)0.385 rad/s (C)1.21 rad/s (D)2.42 rad/s
18. Consider a simple harmonic motion; its equation of motion is
d^2 x
formed as ------- + ω^2 x =0. Which soluiton satisfies the equation
d t^2
of motion and is most reasonable? (α,φ: constant)
(A) x(t) = x*e^(-αt)
(B) x(t) = x*cos(αt+φ)
(C) x(t) = x*cosh(αt+φ)
(D) x(t) = x*e^(-αt)*cos(αt+φ)
19. Which following statement is true about the damping system?
(A) Curve a is an overdamped oscillation.
(B) Curve b is a critically damped oscillation.
(C) Curve a is an underdamped oscillation.
(D) For underdamped there is no angular frequency.
20. Which following item of simple harmonic motion (SHM) is true?
(θ<0.5 rad)
(A) The simple pendulum : |\
d^2 θ | \ L
g + ------- + Lθ = 0 , ω = √(L/g) |θ\
dt^2 ↓ | \
g | ● m
| --->
<---
(B) The spring-loaded system :
d^2 x
m ------- + kx^2 = 0, ω = √(k/m)
d t^2
-->
<--
| k --------
|^ ^ ^ ___| | m
|_\/_\/_\/___|______|_____
(C) The physical pendulum :
d^2 θ
I -------- + mgdθ = 0, ω = √ (I/mgd)
d t^2
(D) The torsional oscillator :
d^2 θ
I -------- + kθ = 0, ω = √ (k/I)
d t^2
Part 2 (40%) Calculation Problems and Essay Questions.
(Answer the question systematically and describe the relevant
physical principles in detail. Simple formulas or too short
descriptions are NOT acceptable.)
1. Consider a small sphere of mass m released from rest in a
liquid. Assuming the only force acting on the sphere are the
resistive force F = -bv , buoyant force F1 = -ρVg (ρ:the density of
the liquid, V:the volume of the small sphere) and the gravitational
force F2 = mg. Please derive the equation of motion v(t) of the sphere.
(5 pts)
2. The achilles tendon connects the calf muscles to the calcaneus
at the back of the heel. Please calculate the force exerted by this
tendon on the calcaneus when a person is standing on the ball of
one foot, assume that the entire foot can be regarded as a rigid body.
(This mean that interal forces within the foot are being ignored.)
The right figure shows the force exerted by the tendon on the foot
Ft, the force of the leg bones(tibia) and the fibula on the foot Fb,
and the force on the floor upward, which is equal to the weight of
the body W. The weight of the foot itself is small compared to these
forces and will be neglected. (5%)
<抱歉圖太難畫了，此題只要求用"合力為零"和"合力矩為零"列式即可>
3. A uniform solid cylinder has a radius R, mass M, and the length L.
Please derive the moment of inertia about its central axis. (3pts)
4.
(a) Using mathematical approach to describe the Simple Harmonic Motion
of a spring-mass system. (3pts)
(b) Describe the physical behavior of a Damped Oscillations. (6pts)
(c) Describe the physical behavior of a Forced Oscillations. (3pts)
5. A solid sphere of radius r is released from rest and rolls
down an incline without slipping and then into a circular loop of
radius R. What is the minimum height h from which the solid sphere
has to be released so that it does not fall off the track when in the
loop? (5pts)
6. Describe the physical behavior of soft tissues.
(a) What is stress relaxation(應力鬆弛)? (2pts)
(b) What is creep(蠕變)? (2pts)
(c) What is hysteresis(滯後效應)? (1pt)
7. (蘋果日報) 新北市一名男子，開著1.9公尺寬的BMW740i轎車，停進自家僅2.2公尺寬
車庫後，未熄火即下車，加上他當時疑似未打停車檔、忘記按電子式停駐煞車鈕，轎
車順著車庫5度斜坡向下滑動，重達1825公斤的車體將他夾困在車身與牆壁間，
後經警消破壞車體才將他拉出。他腹部因長時間重壓，還印著壁磁磚痕跡，
送醫不治。請用物理學的原理解釋死亡的原因。(5pts)
(The Apple Daily) A man who lived in New Taipei city drove a car
(BMW740i) of width 1.9 m and weight 1825 kg. After parking the car
into his garage (having the width 2.2 m), he did not shut off the
engine and probably forgot to pull up to a parking stall as well
as to push down the electronic parking brake. Then the car slid
down a gentle slope (5 degree) and caused him to be sandwiched
between the car body and the wall. Unfortunately, he died in the
accident because his abdomen was heavily pressed for too long.
Please explain the cause of death from the physical principle.
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