課程名稱︰普通物理上 課程性質︰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）︰2008/11/21 考試時限（分鐘）：180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 (mass = M) 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 is -25m/s. The mass of these two particles is identical. Assume the collision coefficient is 0.6,find the final velocity of particle 1 and 2 (4%,4%) 3.A rocket (Vo=0) whose initial mass Mi is 850kg consumes fuel at the rate R=2.3kg/s. The speed u of the exhaust gases relative to the 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 250 kg? (3%,2%,5%) 4.A ball with mass m is launched vertically from the ground with an initial velocity Vo. Consider the air friction is proportional to the velocity square (f=μv^2). Find the velocity of this ball when it hits back to the 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.A force acts on a 3.00kg ice block that can move only along the x-axis. The force is a function of t: ┌ 2+2t 0≦t≦2 │ 6 2≦t≦5 │ 36-6t 5≦t≦6 Fx= │ 24-4t 6≦t≦7 │ -4 7≦t≦9 └ -22+2t 9≦t≦11 where the unit of force Fx is Newton and time t is second. At t=0, the block is moving in the positive direction of the axis, with the speed of 3.0m/s. What are its (a) speed and (b) direction of travel at t=11s ? (4%,4%) 8.A football kicker can give the ball an initial speed of 25m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball t to score a field goal from a point 50m in front of goalposts whose horizontal bar is 3.44m above the ground? (4%,4%) 9.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 the slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. The block is puled by horizontal force F of magnitude 100N. In unit-vector notation, what are the resulting accelerations of (a)the block and (b)the slab? (4%,4%) ← F ┌───┐ ←───┤ m2 │ ┌───┴───┴─┐ μ=0 │ m1 │ ↙ ───┴─────────┴─── 10.A 1.5kg block 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 kinectic energy of the block as it passes through x=2.0m? (b) What is the maximum kinectic energy of the block between x=0 and x=2.0m? (3%,5%) 11.At a certain factory, 300kg crates are dropped vertically from a packing machine onto a conveyor belt moving at 1.20m/s. (A motor maintains the belts constant speed.) The coefficient of kinetic friction between the belt and each crate is 0.400. After a short tme, slipping between the belt and the crate ceases, and the crate then moves along with the belt. For the period of time during which the crate is being brought to rest relative to the belt, calculate, for a coordinate system at rest in the factory,(a) the kinetic energy supplied to the crate, and (b) the energy supplied by the motor. (c) Explain why answers (a) and (b) differ. (2%,2%,4%) ┌──┐ └──┘ ↓ ← ┌──┐ ┌─┴──┴───────┐ ◎ ◎ └────────────┘ 12.A single consrevation 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^(-4/x) J, where x is in meters. At x=5.0m the particle has a kinetic energy of 2.0J. (a) What's the maximum kinetic energy of the particle and the value of x at which it occurs? (b) Determine an expression for F(x) as a function of x and for what value of x does F(x)=0? (4%,4%) --

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