108年 - 108 學士後西醫：物理#76808

1. The horizontal surface on which the objects slide is frictionless. If M = 5.0 kg, the tension in string 1 is 60 N. Determine F. (A) 20 N (B) 24 N (C) 30 N (D) 34 N (E) 48 N

2. The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m, and k2 = 450 N/m, what is approximate the frequency of oscillation (in Hz)? (A) 2 (B) 4 (C) 6 (D) 8 (E) 10

3. A pivoted bar has a weight of 10 kg and a length of 1 meter, and is supported by a cable, as shown below. What is the tension force of the cable when a 50 N box is hung at the end of the bar? (A) 150 N (B) 295 N (C) 410 N (D) 570 N (E) 775 N

4. A circular track of radius 1000 meters is banked at 30 degrees without any friction. What is required speed for a car to keep running on the circular track? (A) about 30 m/s (B) about 45 m/s (C) about 55 m/s (D) about 65 m/s (E) about 75 m/s

5. Two point masses 1 kg and 2 kg are on a massless bar with axis of rotation through the center of length 2 meters, and a sphere of radius 10 cm and of mass 100 kg is on the center of the bar, as shown below. What is the moment of inertia (kg∙m2 )? (A) 3.33 (B) 3.4 (C) 3.5 (D) 3.67 (E) 4

6. The disk A with moment of inertia I1 rotates with angular speed ω1 about a vertical frictionless axle. A second disk B with moment of inertia I2 rotates with angular speed ω2 drops on the disk A. Since two disks are rough and two disks eventually reach the same angler speed ω, what is the final angular speed ω? (A) (I_1ω1+ I_2ω2)/I₁ (B) (I_1ω1)/(I₁+ I₂) (C) (I_1ω1+ I_2ω2)/( I₁+ I₂) (D) (I_2ω2)/( I₁+ I₂) (E) (I_1ω1− I_2ω2)/( I₁+ I₂)

7. The same force F is applied horizontally to bodies 1, 2, 3, and 4, of masses m, 2m, 3m, and 4m, initially at rest and on a frictionless surface, until each body has traveled distance d. The correct listing of the magnitudes of the velocities of the bodies, are . (A) (B) (C) (D) (E)

8. What is the entropy change for one mole ideal gas that expands from volume V to 4V in a free expansion process? (A) 4 R (B) 2 R (C) (ln4) R (D) (ln2) R (E) R

9. The superposition of two wavesand

at the location x = 0 in space results in

(A) Beats at a beat frequency of 6 Hz in a 153 Hz tone.

(B) A tone at a frequency of 156 Hz, as well as beats at a beat frequency of 6 Hz in a 153 Hz tone.

(C) Beats at a beat frequency of 3 Hz.

(D) A pure tone at a frequency of 153 Hz.

(E) A pure tone at a frequency of 156 Hz.

10. A diver swims from 2 meters to 10 meters below the surface of a lake. What is the pressure difference? (A) 54.5 kPa (B) 62.1 kPa (C) 78.4 kPa (D) 82.8 kPa (E) 98.2 kPa

11. A Carnot engine takes 2000 J of heat from a reservoir at 500 K, does some work, and discards some heat to reservoir at 300 K. What is its efficiency? (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.5 (E) 0.6

12. A series of 3 uncharged concentric spherical conducting shells surround a small central charge q. The potential at a point outside the third shell, at distance r from the center, and relative to V = 0 at ∞, is (A) −3keq/r (B) +3keq/r (C) − (ln 3)keq/r (D) + (ln 3)keq/r (E) +keq/r

13. A conductor of radius r, length ℓ , and resistivity ρ has resistance R. It is melted down and formed into a new conductor, also cylindrical, with one fourth the length of the original conductor. The resistance of the new conductor is . (A) R (B) R (C) R (D) 4 R (E) 16 R

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14. There is an electric dipole in an electric field, as shown below. Which of the following statement is incorrect? (A) The dipole rotates clockwise. (B) The torque on +q points up. (C) The electric dipole moment is proportional to the distance from –q to +q. (D) The dipole has a max potential energy when it is perpendicular to E. (E) The electric dipole moment points from –q to +q.

15. A circuit contains a resistance and a charged capacitance. The resistance is 20 ohms, and the capacitance is 5 F. If the circuit is switched off, how long will it take when the current decreases to a half of initial value? (ln2 = 0.69) (A) 34 s (B) 50 s (C) 69 s (D) 100 s (E) 127 s

31. A uniform solid ball with mass M is supported by a massless rod. Derive the period of the pendulum with a small displacement. (A) T = 2π(1.1L/g)^1/2 (B) T = 2π(1.8L/g)^1/2 (C) T = 2π(1.5L/g)^1/2 (D) T = 2π(0.9L/g)^1/2 (E) T = 2π(0.7L/g)^1/2

32. A rocket moving in space, far from all other objects, has a speed of vi relative to the Earth. Its engines are turned on, and fuel is ejected in a direction opposite to the rocket’s motion at a speed of vrel relative to the rocket. What is the speed of the rocket, vf relative to the earth once the rocket’s mass is reduced to half its mass before ignition? (A) v_i+ v_rel ln2 (B) v_i+ v_rel ln(1/2) (C) v_i+ 2_vrel(D) (v_i+ v_rel) / 2 (E) v_i+ v_rel/ 2

33. A satellite is in a circular orbit and has a total mechanical energy of U. If the satellite lost half of its weight and doubled its radius of the circular orbit, what will be its total mechanical energy? (A) 1/4 U (B) 1/2 U (C) U (D) 2 U (E) 4 U

34. A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision? (A) 2.0 (B) 4.2 (C) 6.1 (D) 8.1 (E) 10

35. A set of pulleys is used for supporting the calf (100 N). Please determine the weight of the subject in the right hand side. (A) 50 N (B) 73 N (C) 100 N (D) 141 N (E) 173 N

36. Nadal received a shot with the tennis ball (60 g) travelling horizontally at 50 m/s, and returned the shot at 60 m/s horizontally in the opposite direction in 0.02 sec, what is the average force that Nadal suffered during this stroke? (A) 22 N (B) 30N (C) 180 N (D) 330 N (E) 550 N

37. The aluminum cylinder is 0.10 m² (cross-sectional area) and 0.35 m long. What is the force exerted on its ends if the elongation is0.20 mm? (Young’s modulus of aluminum is 7.0 × 10¹⁰ Pa) (A) 2.00 × 106 N (B) 4.00 × 10⁶ N (C) 8.00 × 10⁶ N (D) 4.00 × 10³ N (E) 2.00 × 10³ N

38. The wing of an airplane has an area of 1 m² , and its wing thickness is 0.5 m. Air flows over the top at 20 m/s and under the wing at 10 m/s. The density of air is 1.2 kg/m³ . What is the net force on the wing due to Bernoulli effect? (Gravitational acceleration g = 10 m/s² ) (A) 12 N (B) 15 N (C) 18 N (D) 183 N (E) 186 N

39. A large tank of water has a hose connected to it. The tank is sealed at the top and has compressed air between the water surface and the top. When the water height h is 3.5 m the pressure of the compressed air is 4.0 x 10⁵ Pa. Take the atmospheric pressure to be 1.0 x10⁵ Pa. What is the speed of the water when it flows out of the hose if h is 3.5 m? (A) 30.8 m/s (B) 28.4 m/s (C) 26.8 m/s (D) 25.5 m/s (E) 23.4 m/s

40. A stainless steel container has a surface area of 0.5 m² and thickness of 2 cm. If the container is fully filled with 57°C hot-water and the temperature in the room is 27°C, what is the rate of energy loss through the container? (The thermal conductivity of stainless steel is 80 W/m/K) (A) 30 kW (B) 60 kW (C) 120 kW (D) 180 kW (E) 210 kW

41. A jack could lift a very heavy object like a car. It compressed air and exerts a force on a small piston of area 10 cm² and the pressure is transmitted by an incompressible liquid to a second piston of area 30 cm² . If we want to lift a car weighting 1300 kg, what force must be exerted in the small area piston? (A) 43.3 N (B) 424.6 N (C) 433.3 N (D) 1300.0 N (E) 4247.7 N

42. An ambulance moves at a speed of 50 km/hr, and its siren emitting sound at a frequency of 5.0x10² Hz. What frequency of sound is heard by a runner who is running at 4 m/s approaching each other in the opposite direction (the speed of sound in air is 345 m/s)? (A) 47 Hz (B) 475 Hz (C) 506 Hz (D) 527 Hz (E) 555 Hz

43. One rope is wiggled with frequency f = 2.0 Hz, amplitude A = 1.0 m, and wave speed v = 4.0 m/s. What is the mathematical description of this wave? (A) y(x,t) = cosπ (2x − t) (B) y(x,t) = cosπ (2x + t) (C) y(x,t) = cosπ (x − 2t) (D) y(x,t) = cosπ (x + 2t) (E) y(x,t) = cosπ (x − 4t)

44. There is a 1 kg gallium block and its melting point is around 30°C. What is the change of entropy when it was melted from solid to liquid at 30°C? (The fusion heat of gallium is Lf = 80.18 kJ/kg) (A) 0 (B) 0.265 kJ/K (C) 0.374 kJ/K (D) 2.673 kJ/K (E) 3.779 kJ/K

45. Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40 m length. Determine the net electric flux through the surface of the cube. (εo= 8.85 x 10^-12 C² / N•m² ) (A) 2.8 N•m² /C (B) −2.8 N•m² /C (C) 1.1 N•m² /C (D) −1.1 N•m² /C (E) −0.47 N•m² /C

46. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on its surface. If point A is located at the center of the sphere and point B is 15 cm from the center, what is the magnitude of the electric potential difference between these two points? (k_e = 9 x 109 N•m² /C2 ) (A) 15 V (B) 23 V (C) 30 V (D) 45 V (E) 60 V

47. A segment of wire of total length 2.0 m is formed into a circular loop having 5.0 turns. If the wire carries a 1.2-A current, determine the magnitude of the magnetic field at the center of the loop. (μ₀ = 4π• 10^-7 T∙m/A) (A) 59 μT (B) 69 μT (C) 79 μT (D) 89 μT (E) 94 μT

48. A circuit consists of a capacitor and an inductor that are sequentially connected. If the capacitance is 0.5 mF and the inductance is1 H, what is the resonance frequency of this circuit? (A) 23.4 rad/s (B) 44.7 rad/s (C) 50.5 rad/s (D) 76.8 rad/s (E) 87.6 rad/s

49. Three thin lenses with focal lengths 0.1 m, 0.2 m, and 0.3 m are placed next to each other. What is the equivalent focal length of a single lens? (A) 0.05 m (B) 0.15 m (C) 0.25 m (D) 0.33 m (E) 0.45 m

50. A cloud layer is 1000 m above the planet, with the area of 1x10⁶ m² , considered as the plates of a parallel-plate capacitor. If an electric field strength is greater than 3.0x10⁶ N/C, it causes lightning, what is the maximum charge the cloud can hold? (εo= 8.85 x 10^-12 C² /N•m2 ) (A) 28.55 C (B) 26.55 C (C) 24.55 C (D) 22.55 C (E) 20.55 C

51. Two isotopes leave the slit at point S and into a magnetic field of magnitude 0.100 T pointing into the page, each has speed of 1.00 x 10⁶ m/s. The first one contain one proton and has a mass of 1.67 x 10^-27 kg and the other contains a proton and a neutron and has a mass of 3.34 x 10^-27 kg. What is the distance that they could be separated when they strike a photographic plate? (e = 1.6 x 10^-19C) (A) 0.520 m (B) 0.313 m (C) 0.210 m (D) 0.105 m (E) 0.104 m

52. If a farsighted patient’s near point of eyes is 40 cm, what kinds of lens and focal length of a corrective lens have to enable the eye to see clearly an object 20 cm away? (A) converging lens, f = 13.3 cm (B) diverging lens, f = 13.3 cm (C) converging lens, f = 40 cm (D) diverging lens, f = 40 cm (E) converging lens, f = 20 cm

53. There are two point-charges −Q, and 2Q located at the distance 2d, and 4d from the origin O, respectively. What is the electric field at the origin O? (Vacuum permittivity is ε0) (A) 0 (B)E= (C)E= (D)E= (E)E=

54. There is a cylindrical conductor with radius R which carries current I. Which diagram is correct for the magnetic field of this conductor?

(A) (B) (C) (D) (E)

55. There are two parallel, straight current-carrying conductors with current I1 = 10 A and length I2 = 2 A. Both of these two conductors are 1 m length, and the distance between them is 2 m. What is the force between these two parallel conductors? (Permeability constant is μ0) (A) (B) (C) (D) (E)

56. A medical blue light therapy laser treatment pen emits a blue light with wavelength of 415 nm in the visible light. The index of refraction for air and cornea is 1.00 and 1.34, respectively. What is the wavelength of this blue light when that enters into cornea from air? (Speed of light in vacuum is 3 × 10⁸ m/s) (A) 185 nm (B) 310 nm (C) 486 nm (D) 556 nm (E) 693 nm

57. There is an ideal polarizer with the angle of ϕ = 60° between the polarizing axis and the vertical axis, and there is an ideal analyzer with the angle of ϕ = 0° between the polarizing axis and the vertical axis.When an unpolarized light with intensity I is incident on this ideal polarizer, what is its transmitted intensity? (A) 0.125 I (B) 0.250 I (C) 0.750 I (D) 0.866 I (E) 1.000 I

58. There is thin converging lens with focal length f = 140 mm. When an object is placed at the distance of 210 mm from the lens, what is the lateral magnification? (A) 0.3 (B) 0.5 (C) 1.0 (D) 2.0 (E) 3.0

59. The X-ray typically operate at a potential difference of 1.00 x 10⁵ V. What is the minimum wavelength the X-ray tubes produce when electrons are accelerated through this potential difference? ( The Planck’s constant is 6.63 x 10^-34 J•s) (A) 1.24 x 10⁻⁷ m (B) 1.24 x 10⁻⁹ m (C) 1.24 x 10⁻¹¹ m (D) 1.24 x 10⁻¹³ m (E) 1.24 x 10⁻¹⁵ m

60. In process ab, 20 J of heat is added to the system. In process bd, 80 J of heat is added to the system. Find the internal energy change ΔU in process abd. (A) 21 J (B) 59 J (C) 79 J (D) 101 J (E) 121 J

108年 - 108 學士後西醫：物理#76808

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