Fundamentals of Physics-Test 3
EXAMINEE NAME:
I. Fill in each of the following blanks with an appropriate expression or quantity.
(40)
1. The position of an electron is given by k j t i t r 0.20.40.32+-= (where t is in
seconds and the coefficients have the proper units for r to be in meters). (a) The
velocity )(t v and the acceleration )(t a are (1) and (2) respectively for
the electron. (b) In unit-vector notation, The velocity v and the acceleration a are, at
t=2.0s, (3) and (4) .
2. A wheel rotates with an angular acceleration given by 2334bt at -=α, where t is the time and a and b are constant. If the wheel has an initial angular speed 0ω, then (a) the equation for the angular speed is (5) , and (b) the angular displacement of the wheel is (6) as functions of time.
3. An oscillator consists of a block attached to a spring (k = 400 N/m). At some time t, the position (measured from the system’s equilibrium location), velocity, and acceleration of the block are ,/6.13,100.0s m v m x -== and 2/123s m a -=. Then (a) the frequency of the oscillation is (7) , (b) the mass of the block is (8) , and the amplitude of the motion is (9) .
4. The equation of a transverse wave traveling along a very long string is given by ),0.402.0sin(0.6t x y ππ+= where x and y are expressed in centimeters and t is in seconds. So (a) the amplitude is (10) , (b) the wavelength is (11) , (c) the frequency is (12) , (d) the speed is (13) , (e) the maximum transverse speed of a particle in the string is (14) , (f) the maximum rate of energy transfer along the string is (15) , and (g) the minimum rate of energy transfer along the string is
(16) .
5. Suppose 4.00 mol of an ideal diatomic gas, with molecular rotation but not oscillation, experiences a temperature increase of 60.0 K under constant-pressure conditions. (a) The heat added to the gas is (17) . (b) The increase in internal the kinetic energy is
(20) .
II. Solve the following problems. (60)
1．Force j N i xN F )4()3(+=, with x in meters, acts on a particle, changing only the
kinetic energy of the particle. (a) How much work is done on the particle as it moves from coordinates (2m, 3m) to (3m, 0m)? (b) How much the kinetic energy of the particle is changed during the motion? (6)
2. A steel ball whose mass m is 5.2 g is fired vertically downward from a height 1h of 18 m with an initial seed 0v of 14 m/s. It buries itself in sand to a depth 2h of 21 cm. (a) What is the change in the mechanical energy of the ball? (b) What is the magnitude of the average force F exerted the ball by the sand? (8)
3. A
4.0 kg mass sliding on a frictionless surface explodes into two 2.0 kg masses. After the explosion the velocities of the 2.0 kg masses are 3.0 m/s, due north, and
5.0 m/s, 030 north of east. What was the original speed of the 4.0 kg mass? (8)
4. 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 left 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. (12)
5. A string oscillates according to the equation
].)40cos[(])3)[sin(50.0('11t s x cm cm y --=ππ
(a) 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? (c) What is the speed of a particle of the string at the position x = 1.5 cm when t = 9s/8? (12)
6. 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. (14)