109年 - 109 台灣綜合大學系統_學士班轉學招生考試︰普通物理B#138484

1. In a circular motion, the radius r = 20 m, and the tangential speed v = t² + 1, where t is in unit s and v is in unit m/s. What are magnitudes of the instantaneous tangential acceleration and centripetal acceleration at t=3 s?

2. A car of mass m moves on a frictionless road. At t = 0, the driver shuts the engine off, and the car has speed v₀. After that, the only force acting on the car is the air drag force: , where A is a constant, and v̄ is the velocity. For t ≥ 0, find the speed of the car as a function time t.

3. A bullet of mass m is fired into a suspended block of mass 4m with speed u. The bullet then embeds in the block and raises the block. What is the maximum raised height H?

4. An object of mass m is initially at rest on a frictionless horizontal plane. If a constant power P acts on this object for t duration, how far will it travel during this interval?

5. A thin ring of mass M and radius R rotates about an axis through its edge. The ring starts at its highest point and is given a very small push to start its rotation. What is the angular velocity at the lowest point?

6. A uniform spherical planet has mass M and radius R. A very thin tunnel passes from one end of the planet, through the planet center, and then out from the other end of the planet. A particle of mass m fell into one end of the tunnel and then performed simple harmonic motion. Find the angular frequency of the simple harmonic motion.

7. One mole of an ideal monatomic gas is taken around the reversible cycle as shown in the figure . Find the efficiency of the heat engine.

8. (True of False?) An irreversible engine works in cycles. When the engine returns to its initial state, the entropy change of the engine is zero.

9. A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field as shown in the right figure. When E = A i + B j, where A and B are positive quantities, the ball is in equilibrium at the angle θ. The tension in the string is ________.

10. A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar², where A is a constant and r ＜ R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r ＞ R) the sphere is ________

11. A particle with charge q is located at x = 2R, and a particle with charge −2q is located at the origin. The equipotential surface that has zero potential is a sphere centered at (−4R/3, 0, 0) and having a radius ________.

12. Consider two long, parallel, and oppositely charged wires of radius r with their centers separated by a distance D that is much larger than r. Assuming the charge is distributed uniformly on the surface of each wire, show that the capacitance per unit length of this pair of wires is ________

13. The switch in the following figure a closes when ΔV_C ＞ 2/3 ΔV and opens when ΔV_C ＜ 1/3 ΔV. The ideal voltmeter reads a potential difference as plotted in following figure b. What is the period T of the waveform in terms of R₁, R₂, and C?

14. A bar of mass m and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in the following figure. The rails are separated by a distance d. A battery that maintains a constant emf ε is connected between the rails, and a constant magnetic field B is directed perpendicularly out of the page. Assuming the bar starts from rest at time t = 0, show that at time t it moves with a speed

15. High-power lasers in factories are used to cut through cloth and metal. One such laser has a beam diameter of 1.00 mm and generates an electric field having an amplitude of 0.700 MV/m at the target. Find the power delivered by the laser.

16. The rest energy of a proton is 938 MeV, and the total energy of a proton is twice its rest energy. Find the momentum of the proton in MeV/c units, c is the speed of light.

(a) If the solid cylinder unwinds on the vertical string without spinning, what is the tension of the string?

(b) If the string is pulled to have the cylinder spin but not fall, what is the angular acceleration of the cylinder?

 (a) When the speed of the light source is equal to 0.280 c, photoelectrons just begin to be ejected from the metal. What is the work function of the metal?

(b) When the speed of the light source is increased to 0.900 c, determine the maximum kinetic energy of the photoelectrons.