112年 - 112 臺灣綜合大學系統_學士班轉學生聯合招生考試：普通物理B#125308

1. The position of a particle moving in circular motion in the xy plane is = 3cos(2t) î + 3sin(2t)j, where r is in meters and t is in seconds. What is the period of the circular motion?_____

2. An object with mass m is hanging from a wire attached to the ceiling of an elevator. The elevator is moving downward and has a downward acceleration of magnitude a. The gravitational acceleration is g. Find the magnitude of the tension of the wire. _____

3. The position of a particle of mass m kg is given by x(t)=At³+B, where A and B are constants, and the unit of x is in meter, and t is in second. Find the instantaneous net power done on this particle at t=2 s._____

4. A bullet of mass m strikes a stationary block of mass M from below with a speed u. The mass of M is three times of m (M=3 m). After the collision, the bullet embeds in the block. The gravitational acceleration is g. To what height does the block rise? Express your answer by u and g. _____

5. A mass m is connected to two springs, with spring constants k₁ and k₂, as shown in the figure. Find the oscillation period for this configuration. _____

6. The maximum oscillation speed of a string carrying a sinusoidal wave is . When the displacement of a point on the string is half its maximum, what is the oscillation speed of the point?_____

7. The ideal Diesel cycle is shown in the figure, where a to b and c to d are adiabatic processes, b to c is constant pressure compression, and d to a is constant volume process. The temperature at a, b, c, d points are , and , respectively. The ratio of molar specific heat at constant pressure to that at constant volume is γ = Cp/Cv = 5/3. Find the entropy change (ΔS) of the engine after a complete cycle: a → b → c → d →a._____

8. Same conditions as the ideal Diesel cycle mentioned in above question, find the efficiency of the engine._____

9. Four electrons move from point A to point B in a uniform electric field as shown below. Rank the electrons in diagrams I through IV by the changes in potential from most positive to most negative when traveling from A to B._____

10. Addition of a metal slab of thickness a between the plates of a parallel-plate capacitor of plate separation d is equivalent to introducing a dielectric with dielectric constant k between the plates. The value of k is:_____

11. The circuit below shows three resistors in parallel. R₃ ＞ R₂ ＞ R₁. The resistors are all made of the same wire with the same diameter but have different lengths. Rank the magnitudes of the electric fields in the resistors from least to greatest._____

12. Using the electric constant (permittivity) ε0 and magnetic constant (permeability) μ0, the speed of light is given by the value of _____

13. The segment of wire (total length including portions of incoming and outgoing wire = 6R) is formed into the shape shown and carries a current I. What is the magnitude of the resulting magnetic field at the point P?_____

14. There is no current in the circuit shown in the figure below until the switch is closed. The current through the 20-Ω resistor the instant after the switch is closed is either [1] 15 A or [2] 5.0 A, and the current through the 20-Ω resistor after the switch has been closed a long time is either [3] 5.0 A or [4] 15 A. Which combination of the above choices is correct?_____

15. The centers of two slits of width a are a distance d apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light of wavelength λ, the ratio a/d is equal to _____

16. The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV. The light intensity is doubled. Determine the maximum kinetic energy of the photoelectrons (in eV)._____

 (a) Find the tension of the rope；

(b) After the Yo-Yo falls a distance h starting form rest (vo=0), find the speed of center of the mass of the Yo-Yo.

(a) Assuming Cooper was 160 km above the Earth in a circular orbit, determine the difference in elapsed time between someone on the Earth and the orbiting astronaut for the 22 orbits. You may use the approximation , for small x.

(b) Did the press report accurate information? Please explain.