課程名稱︰普通物理學甲上
課程性質︰必修課程
課程教師︰趙治宇
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰2017/11/30
考試時限（分鐘）：170
試題 :
共12題
1. For a rigid body, exemplified by Fig.1, show that the angular momentum L_z=Iω where ω and I are the angular velocity and rotational inertia of the rigid body.
Fig.1:https://imgur.com/vJJ6ohD
2. Four identical unigorm bricks, each of length L, are put on top of one another(Fig.2)in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of (a)a1, (b)a2, (c)a3, and (d)a4, such that the stack is in equilibrium.
Fig.2:https://imgur.com/w1fuvkB
3. A rigid sculpture, consisting of a thin hoop (of mass m and radius R=0.15m)and two thin rods(each of mass m and length L=2R), is arranged as shown in Fig.3. The sculpture can pivot around a horizontal axis in the plane of the hoop, passing through its center.
(a)In terms of m and R, what is the sculpture's rotational inertia I about the rotational axis
(b)Starting grom rest, the sculpture rotates around the rotational axis from the initial upright orientation of Fig.3. What is its angular speed ω
about the axis when it is inverted?
Fig.3:https://imgur.com/lfQ4fsn
4. A mound is an incomplete right-circular cone (see Fig.4), with a flattened top of radius r_1, a base radius r_2, a height h, and a volume V. The sides of the cone make an angle θ with the horizontal. What is the center of mass of the mound?
Fig.4:https://imgur.com/S7gWGMh
5. Consider the air friction is proportioinal to object's velocity. Now, we throw ball 1 (mass m) up with initial velocity v_0, and simultaneously we drop ball 2 with mass m right on the top of ball 1, falling from rest at the height h. Find the meet time, and the height when two balls meet.
6. In Fig.5, a 2.0 kg block is placed on top of a 3.0 kg block, which lies on a frictionless surface. The coefficient of kinetic friction between the two blocks is 0.30; they are connected via a pulley and a string. A hanging block of mass 10 kg is connected to the 3.0kg block via another pulley and string. Both strings have negligible mass and both pulleys are frictionless and have negligible mass. When the assembly is released, what are
(a)the accleration magnitude of the blocks,
(b)the tension in string 1, and
(c)the tension in string 2?
Fig.5:https://imgur.com/w5s46G1
7. (a)Describe the principle of equivalence proposed by Einstein.
(b)Describe the cause of imaginary force proposed by Einstein.
8. In Fig.6, a 3.5kg block is acclerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction μ_k=0.25. The frictional force stops the block in distance D=7.8m.
What are (a)the increase in the thermal energy of the block-floor system,
(b)the maximum kinetic energy of the block, and
(c)the original compression distance of the spring?
Fig.6:https://imgur.com/71CAuPL
9. Fig.7 gives, as a function of time t, the force component F_x that acts on a 3.00 kg ice block that can move only along the x axis. At t=0, the block is moving in the positive direction of the axis, with a speed of 3.0m/s. What are its (a)speed and (b)direction of travel at t=11s?
Fig.7:https://imgur.com/3ZHdK4w
10: The uniform rod (length 0.60 m, mass 1.0kg) in Fig.8 rotates in the plane of the gigure about an axis through one end, with a rotational inertia of 0.12kg˙m^2. As the rod swings through its lowest position, it collides with a 0.20 kg putty wad that sticks to the end of the rod. If the rod's angular speed just before collision is 2.4 rad/s, what is the angular speed of the rod-putty system immediately after collision?
Fig.8:https://imgur.com/MbB4VUc
11. Fig. 9 shows an approximate plot of force magnitude F versus time t during the collision of a 58 g Superball with a wall. The initial velocity of the ball is 34m/s perpendicular to the wall;the ball rebounds directly back with approximately the same speed, also perpendicular to the wall. What is F_max, the maximum magnitude of the force on the ball from the wall during the collision?
Fig.9:https://imgur.com/2BSB8VA
12. A bowler holds a bowling ball with mass(M=6.8kg)in the palm of his hand(Fig.10).His upper arm is vertical; his lower are(1.9kg)is horizontal. What is the magnitude of
(a)the force of the biceps muscle on the lower arm and
(b)the force between the bony structures at the elbow contact point?
Fig.10:https://imgur.com/yl3IwY8