113年 - 113 台灣聯合大學系統_碩士班招生考試_物理類：普通物理#125301

(a) What is the angular velocity of the object when it reaches the bottom of the incline?

(b) How much tim does it take to reach the bottome

(c) What is the instantaneous power the object received from the gravitation field? Suppose the gravitational acceleration is g.

(a) What is the magnitude of l?

(b) When the rod is lifted a distance d from equilibrium and then released, it undergoes simple harmonic motion. Determine the angular frequency of the oscillation.

(c) What is the total energy of the rod during the oscillation?

 (a) the work during B→C,

(b) the change of entropy during B→C,

(c) the temperature at A,

(d) the change of internal energy during C → A,

(e) the work during A → B, and

(f) the efficiency of the engine. Keep notation e in your calculations and do not substitute it by 2.71828 ....

(a) Given the permittivity of free space ε₀, use Gauss's law to derive the capacitance of a capacitor formed by two parallel plates with a large area A separated by a narrow distance d.

(b) Determine the work required to transfer a total charge Q from one plate to the other in such a capacitor when it is initially charge-free.

(c) Connect two capacitors of this type in parallel (upper figure), each with capacitance C and charge Q. If the plate separation is increased from d to 3d in one capacitor and decreased from d to d/3 in the other (bottom figure), express the potential difference on each capacitor in terms of C and Q.

(d) In this case, what is the total energy stored in the two capacitors in terms of C and Q?

(a) A conducting bar of length L has one end connected to a pivot, and the other end is connected to a conducting ring around the pivot. A magnetic field is directed perpendicular into the ring and varies with the distance r to the pivot by B(r) = 2r. If the rod rotates with a constant angular speed ω about the pivot, what is the induced motional electromotive force between the ring and the pivot?

(b) If the rod is absent, and the magnetic field changes with both r and time t as B(r,t) = 2rt, what is the induced electromotive force along the ring?

(a) Calculate the apparent depth of the tank when viewed from directly above the water.

(b) If a glass plate, 10 cm thick, is placed on the bottom of the tank, what is the apparent thickness of the plate when viewed from directly above the water? The indices of refraction for air, water, and glass are = 1, = 4/3, and = 5/3, respectively. Express your calculations using fractional numbers (such as 4/3) instead of decimal numbers (such as 1.33...).