課程名稱︰普通物理學甲上
課程性質︰系定必修
課程教師︰趙治宇
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰96.11.23
考試時限（分鐘）：180分鐘(之後延10分鐘)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Derive the moment inertia of a uniform sphere shell of inner radius R1 and
outer radius R2.(10%)
2.The x-component of the initial velocity of particle 1 is 25m/s, and that of
particle 2 is -25m/s. The mass of these two particles are identical. Assume
the collision coefficient is 0.6, find the final velocity of particle 1 and 2.
(4%,4%)
3.A rocket whose initial mass Mi is 850kg consumes fuel at rate R=2.3kg/s. The
speed u of the exhaust gases relative to rocket engine is 3000m/s. (a) What
thrust(effective force) does the rocket engine provide; (b) What is the initial
acceleration of the rocket; and (c) What is its final speed when its fuel is
exhausted down to 250kg?(3%,2%,5%)
4.A ball with mass m is launched vertically from the ground with an initial
velocity v0. Consider the air friction is proportional to the velocity square
(f=μv^2). Find the velocity of this ball when it hits back to ground again.
(8%)
5.(a) Briefly describe the physical principle of He-Ne gas laser. (b) Briefly
describe the principle of the time-of-flight mass spectroscopy.(4%,4%)
6.Describe the working principle of Scan Tunneling Microscope.(8%)
7.In Fig.1, a tin of antioxidants(m1=1.0kg) on a frictionless inclined surface
is connected to a tin of corned beef(m2=2.0kg). The pulley is massless and
frictionless. An upward force of magnitude F=6.0N acts on the corned beef tin,
which has a downward acceleration of 5.5m/s^2. What are (a) the tension in the
connecting cord and (b) angle β?(4%,4%)
8.A projectile is fired with an initial speed v0=30.0m/s from level ground at a
target that is on the ground, at distance R=20.0m, as shown in Fig.2. What are
the (a) least and (b) greatest launch angles that will allow the projectile
to hit the target?(4%,4%)
9.In Fig.3, a slab of mass m1=40kg rests on a frictionless floor, and a block
of mass m2=10kg rests on top of the slab. Between block and slab, the
coefficient of static friction is 0.60, and the coefficient of kinetic friction
is 0.40. The block is pulled by a horizontal force F of magnitude 100N. In
unit-vector notation, what are the resulting acceleration of (a) the block and
(b) the slab?(4%,4%)
10.A 1.5kg block is initially at rest on a horizontal frictionless surface when
a horizontal force along an x axis is applied to the block. The force is given
→ ^
by F(x)=(2.5-x^2)i N, where x is in meters and the initial position of the
block is x=0. (a) What is the kinetic energy of the block as it pass through
x=2.0m? (b) What is the maximum kinetic energy of the block between x=0 and
x=2.0m?(4%,4%)
11.The potential energy of a diatomic molecule(a two-atom system like H2 or O2)
is given by U=A*r^-12－B*r^-6, where r is the separation of the two atoms of
the molecule and A and B are positive constants. This potential energy is
associated with the force that binds the two atoms together. (a) Find the
equilibrium separation-that is, the distance between the atoms at which the
force each atom is zero. (b) Is the force repulsive(the atom are pushed apart)
or attractive(they are pulled together) if their separation is smaller and
larger than the equilibrium separation?(6%,2%)
12.A single conservative force F(x) acts on a 1.0kg particle that moves along
an x axis. The potential energy U(x) associated with F(x) is given by
U(x)=-4xe^(-x/4) J, where x is in meters. At x=5.0m the particle has a kinetic
energy of 2.0J. (a) The maximum kinetic energy of the particle? (b) Determine
an expression in newtons and meters for F(x) as a function of x?(5%,3%)
Fig.1 Fig.2 Fig.3
◢◣m1
＼◥◤
＼ ＼ ╴╴ →
＼ ＼ ╱ ╲ F
β╭＼○ High trajectory ←──□m2
￣￣￣￣|｜ → ∕ Low trajectory μ=0 ￣╲█████m1 x
|｜ v0∕╱ ╲ ￣￣￣￣￣￣￣￣￣
|█m2 █████████
|↑→ |←───Ｒ──→|
|｜F
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※ 編輯: tiesto1114 來自: 218.169.59.241 (11/24 22:06)