《物理双语教学试题》Fundamentals of Physics - 大一 第2学期 Test 1 振动 热学 计算题

Fundamentals of Physics-Test 1

EXAMINEE NAME:

I. Solve the following 7 problems

1. Two identical blocks, each of mass M,

are connected by a massless string over a

pulley of radius R and rotational inertial I as

shown in the figure. The string does not slip

on the pulley; it is not known whether there

is friction between the table and the sliding

block; the pulley’s axis is frictionless. When this system is released, it is found that the pulley turns through an angular θ in time t and the acceleration of the blocks is constant. (a) What is the angular acceleration of the pulley? (b) What it the acceleration of the two blocks? (c) What are the tensions in the upper and lower section of the string? Express the answers in terms of M, I, R, θ, g, and t.

2. A string oscillates according to the equation

].)40cos[(])3)[sin(50.0('11t s x cm cm y --=ππ

What are the amplitude and speed of

the two waves (identical except for direction of travel) whose superposition gives this oscillation? (b) What is the distance between nodes?

3. One mole of a monatomic ideal gas is taken through the reversible cycle shown in the following Figure. Process bc is an adiabatic expansion, with atm p b 0.10= and 331000.1m V b -⨯=. Find (a) the heat added to the gas, (b) the heat leaving the gas, (c) the net work done by the gas, (d) the

efficiency of the cycle, and (e) the change in

entropy of the gas per cycle.

4. A non-conducting sphere shell, of inner radius

a and outer radius

b , has a volume charge

density r A /=ρ (within its thickness), where A is

a constant and r is the distance from the center of the shell. In addition, a point charge q is located at the center. What value should A have if the electric field in the shell (

b r a ≤≤) is to be uniform?

5. A rectangular loop of N close-packed turns

is positioned near a long straight wire. What

is the mutual inductance M for the loop-wire

combination?

6. A diffraction grating is made up of slits of

width 300nm with separation 900nm. The

grating is illuminated by monochromatic

plane waves of wavelength nm 600=λ at normal incidence. (a) How many diffraction maxima are there in the full pattern?

7. What is (a) the momentum and (b) the de Broglie wavelength of an electron whose kinetic energy is 120 eV (,1011.931kg m e -⨯= J eV 19106.11-⨯=)?