課程名稱︰普通物理學甲上 課程性質︰大一必修 課程教師︰李慶德 開課學院：電資學院 開課系所︰電機工程學系 考試日期（年月日）︰2014/11/20 考試時限（分鐘）：110分鐘 是否需發放獎勵金：是 試題 : 1. Multiple-choice Problems:{ 5 points each } 1. A Ferris wheel with a radius of 8.0 m makes 1 revolution every 10 s. When he is at the top, essentially a diameter above the ground, he releases a ball. How far from the point on the ground directly under the release point does the ball land? (A) 0 (B) 1.0 m (C) 8.0 m (D) 9.1 m (E) 16 m 2. A bureau rests on a rough horizontal surface ( s = 0.50, k = 0.40 ). A constant horizontal force, just sufficient to start the bureau in motion, is then applied. The acceleration of the bureau is: (A) 0 (B) 0.98 m/s^2 (C) 3.3 m/s^2 (D) 4.9 m/s^2 (E) 8.9 m/s^2 3. A man wishes to pull a crate 15 kg across a rough floor by exerting a force of 100 N. The coefficient of kinetic friction is 0.25. For the man to do the least work, the angle between the force and the horizontal should be: (A) 0 (B) 14°(C) 43°(D) 66°(E) 76° 4. Given a potential energy function U(x), the corresponding force is in the positive x direction if: (A) U is positive (B) U is negative (C) U is an increasing function of x (D) U is a decreasing function of x (E) it is impossible to obtain the direction of from U 5. A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane sliding down the incline. Then: (A) the sphere reaches the bottom first because it has the greater inertia (B) the cylinder reaches the bottom first because it picks up more rotational energy (C) the sphere reaches the bottom first because it picks up more rotational energy (D) they reaches the bottom together (E) none of the above is true 6. Object A strikes the stationary object B head-on in an elastic collision. The mass of A is fixed, you may choose the mass of B appropriately. Then: (A) for B to have the greatest recoil speed, choose M_B = M_A (B) for B to have the greatest recoil momentum, choose M_A >> M_B (C) for B to have the greatest recoil kinectic energy, choose M_B >> M_A (D) for B to have the least recoil speed, choose M_B = M_A (E) for B to have the greatest recoil kinetic energy, choose M_B = M_A 7. A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3 mm above its lowest position. The velocity of the bullet was: (A) unknown since the heat generated in the collision was not given (B) 8.0 * 10^2 m/s (C) 24.0 m/s (D) 8.0 m/s (E) 2.4 * 10^4 m/s 8. A 5.0-kg crate is resting on a horizontal plank. The coefficient of static friction is 0.50 and the coefficient of kinetic friction is 0.40. After one end of the plank is raised so the plank makes an angle of 30°with the horizontal, the force of friction is: (A) 0 (B) 18 N (C) 21 N (D) 22 N (E) 44 N 9. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 * 10 ^ -3 kg m^2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is: (A) 2.0 J (B) 4.0 J (C) 14 J (D) 22 J (E) 28 J 10. A cylinder of radius R = 6.0 cm is on a rough horizontal surface. The coefficient of kinetic friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation about the axis is given by MR^2/2, where M is its mass. Initially it is not rotating but its center of mass has a speed of 7.0 m/s. After 2.0 s the speed of its center of mass and its angular velocity about its center of mass, respectively, are: (A) 1.1 m/s , 0 (B) 1.1 m/s , 19 rad/s (C) 1.1 m/s , 98 rad/s (D) 1.1 m/s , 200 rad/s (E) 5.9 m/s , 98 rad/s 2. Calculation Problems: 1. {18 points} A disk-shaped pulley has mass M = 5 kg and radius R = 0.5 m. It rotates freely on a horizontal axis, as in the figure below. A block of mass m = 4 kg hangs by a string that is tightly wrapped around the pulley. Assume the system starts at rest. (a) Find the angular velocity of the pulley 4s after the block is released. (b) Find the speed of the block after it has fallen 2 m. (c) Repeat part(b) by using the principle of conservation of energy. 2. {16 points} On fast highways the outside edge of curve is raised. Such banking prevent vehicles from slipping sideways if there is not enought friction to provide the centripetal force. A car of mass 1500 kg rounds a circular curve of radius 20 m that is banked at 37°to the horizontal. The road is slippery, so the coefficient of static friction is only 0.15. (a) Find the maximum safe speed at which the car can travel without skidding. (b) Is it possible for a car to go around a banked curve even if there is no friction? 3. {16 points} A vertical chain has a length L and a mass M, which is supposed to be distributed uniformlt through the length. The chain is released with the bottom just touching a table. (a) Find the force on the table as a function of the distance fallen by the top end of the chain. (b) Find the maximum force on the table during the free-fall process of the chain to the table. 試題完 ============================================================================== 備註： (1) 試題皆是英文，如有不懂可以一直問助教 (2) 試題分A0, A1兩份，僅第一部分選擇題順序不同，本試題為A1卷 --

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