Physcis（A）
Department Grade Specialty Number Name Score
一．Fill in the blanks (40)
1. For the situation of figure, Barbara’s velocity relative to Alex is a constant vBA=52km/h and car P is moving in the negative direction of the x axis. If Alex measures a constant velocity vPA=-78km/h for car P, the velocity vPB measured by Barbara is ; If car P brakes to a stop relative to Alex (and thus the ground) in time t=10s at constant acceleration, the acceleration aPA relative to Alex is ; the acceleration aPB of car P relative to Barbara during the braking is .
2. In figure, three blocks are connected and pulled to the right on a horizontal frictionless table by a force with a magnitude of T3=65.0N. If m1=12.0kg, m2=24.0kg, and m3=31.0kg, calculate (a) the acceleration of the system is ;(b) the tensions in the interconnecting cords T1= ,T2= .
3．As shown in figure, a 1.34kg ball is connected by means of two massless strings to a vertical, rotating rod. The strings are tied to the rod and are taut. The tension in the upper string is 35N. (a) The tension in the lower string is ;(b) the net force on the ball is ;(c) the speed of the ball is .
T1 T2 T3 O’
P
o
4. A 1.50kg snowball is fired from a cliff 12.5m high with an initial velocity of 14.0m/s, directed 41.0° above the horizontal. (a)Work done on the snowball by the gravitational force during its flight to the flat ground below the cliff is ;(b) The change in the gravitational potential energy of the snowball-Earth system during the flight is ;(c) If the gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground .
5. In figure, two particles, each with mass m, are fastened to each other, and to a rotation axis at o, by two thin rods, each with length d and mass M. The combination rotates around the rotation axis with angular velocity ω. In terms of these symbols, and measured about o, (a) the combination’s rotational inertia is ;(b) the combination’s kinetic energy is .
ω 1.70m d M d o M 6. A wheel is rotating freely at angular speed 800 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with twice the rotational inertial of the first, is suddenly coupled to the same shaft. (a) The angular speed of the resultant combination of the shaft and two wheels is ;(b) What fraction of the original rotational kinetic energy is lost .
7. In figure, water flows through a horizontal pipe, and then out into the atmosphere at a speed of 15m/s. The diameters of the left and right sections of the pipe are 5.0cm and 3.0cm, respectively. (a) The volume of water flows into the atmosphere during a
10min period is ;(b) in the left section of the pipe, the speed v2 is ;(c) the gauge pressure is .
8. A wave traveling along a string is described by y(x,t)=0.00327sin(72.1x-2.72t), in which the numerical constants are in SI units (0.00327 m, 72.1 rad/m, and 2.72 rad/s). (a) The amplitude of this wave is ;(b) The wavelength of this wave is , the period is , the frequency is ;(c) the velocity of this wave is ;(d) the displacement y at x=22.5 cm and t=18.9 s is .
9. A cylinder contains 12 L of oxygen at 20°C and 15 atm. The temperature is raised to 35°C, and the volume is reduced to 8.5 L. The final pressure of the gas in atmospheres is . (Assume that the gas is ideal.) 10. Imagine a Carnot（卡诺） engine that operates between the temperatures TH=850 K and TL=300K. The engine performs 1200J of work each cycle, which takes 0.25s. (a) The efficiency of this engine is ;(b) The energy |QH| extracted as heat from the high-temperature reservoir every cycle is ;(c) The energy
|QL| delivered as heat to the low-temperature reservoir every cycle is (d) What is the entropy change of the working substance for the energy transfer to it from the high-temperature reservoir? From it to the low-temperature reservoir? , . 二．Problems (60)
1. A railroad flatcar of weight W can roll without friction along a straight horizontal track. Initially, a man of weight w is standing on the car, which is moving to the right with speed v0. What is the change in velocity of the car if the man runs to the left (in the figure) so that his speed relative to the car is vrel?
W V2 d2 d1 V1
2. A block of mass m1=2.0kg slides along a frictionless table with a speed of 10m/s. Directly in front of it, and moving in the same direction, is a block of mass m2=5.0kg moving at 3.0m/s. A massless spring with spring constant k=1120N/m is attached to the near side of m2, as shown in figure. When the blocks collide, what is the maximum compression of the spring? (Hint: At the moment of maximum compression of the spring, the two blocks move as one. Find the velocity by noting that the collision is completely inelastic at this point.)
m1
v1i
v2i
m2 3. In figure, one block has mass M=500g, the other has mass m=460g, and the pulley（滑轮）, which is mounted in horizontal frictionless bearing, has a radius of 5.00cm. When released from rest, the heavier block falls 75.0cm in 5.00s (without the cord slipping on the pulley). (a) What is the magnitude of the blocks’ acceleration? What is the tension in the part of the cord that supports (b) the heavier block and (c) the lighter block? (d) What is the magnitude of the pulley’s angular acceleration? (e) What is its rotational inertia?
4. In figure, a block weighing 14.0N. which slides without friction on a 40.0° incline, is connected to the top of unstretched length 0.450m and spring constant 120N/m. (a) How far from the top of the incline does the block stop? (b) If the block is pulled slightly down the incline and released, what is the period of the resulting oscillations?
m M