課程名稱︰動力學 課程性質︰機械系必修 課程教師︰顏家鈺 開課學院：工學院 開課系所︰機械系 考試日期（年月日）︰2010/6/22 考試時限（分鐘）：120分鐘(助教延長30分鐘 共150分鐘) 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Choice (2 points each) 1. What is the assumption made when applying Newton's 2nd law to a system of particles ΣF_j = m_i a_i ,j=1,2,...,n. a) the measurements are based on a Newtonian frame, b) the particles are fixed together, c) the internal forces, f_ij does not act on the system particles, d) the particles does not interact among themselves. 2. A Newtonian frame refers to a frame that is a) moving at a constant acceleration, b) rotating at a constant angular velocity, c) moving at a constant speed, d) body fixed. 3. Consider a bug rests still on the disk rotating at angular speed ωk, were a is the vector point to B from the disk center and b is the vector pointing to P from the disk center. What is the velocity of the post, P, on the ground appear to the bug's eye, B? a) -ωk ×(b-a) b) -ωk ×b c) -ωk ×a d) ωk ×(b-a) 4. In problem 3, suppose the angular acceleration of the disk is αk, then what is the acceleration of the post, P, on the ground appear to the bug, B? a) αk ×a + ω^2 a b) αk ×b + ω^2 a - 2ωk ×(v_p)_rel c) αk × a + ω^2 a - 2ωk ×(v_p)_rel d) -2ωk ×(v_p)_rel 5. What is the difference between kinematics study and kinetic study a) kinematics study considers only the velocity of the motion, b) kinematics considers only the forces involved in the motion, c) kinetic study concerns the forces involved in the motion, d) kinetic study neglects the non-impulsive forces. 6. Consider applying a force F on the slide of mass m so that the slide is not moving. What can we say about the friction force, F_μ? a) F_μ = μ_k mg b) F_μ = F c) F_μ = μ_k N , N = -mg d) F_μ = μ_s mg 7. What is the assumption made on the forces acting on the ball, when applying conservation of angular momentum to the impact problem on the right? a) All the forces are parallel to the direction of motion, b) no particular assumption needed, c) there is no external forces other than the gravity, d) the ball sticks to the corner O after impact. 右圖: ─────┐(球被卡在這裡，O是接觸點"┐"，球半徑>階差) 　　　 　 ///////////└───── /////////////////////////// 8. Consider the four point masses m connected by rigid massless bars of length l as shown in the right. What is the resulting acceleration when the force F is applied? (PS.長度是小寫L，不是一) ○—○← l︱ ︱ F ○—○ a) F/4m b) F/2m c) F/2m + (l/2) ×(F/2m) d) none of the above. 9. In the above problem, what is the resultant angular acceleration α? a) F/2ml b) F/4ml c) Fl/4m d) none of the above. 10.To relate the applied moment ΣM_p with respect to point P in space with the change of angular momentum H_p for a system of particles, we can use . the relation ΣM_p = H_p when a) P is an arbitrary point b) P is any fixed point in space c) P is the location of the corner of the body. d) none of the above. 11.In the expression a_B = a_A + αk ×r_B/A - ω^2 r_B/A + (a_B)_rel + 2ωk ×(v_B)_rel , the term (a_B)_rel is commonly referred to as the a) Coriolis acceleration. b) the relative acceleration of point A to the body. c) the relative acceleration of point B to the body. d) the accelerationof point A. 12.Consider G is the mass center,ω is the angular velocity of the rigid body. For an arbitrary point P, which of the following statementsis true: _ a) H_P = H_G + r_G/P ×mv b) H_P = r_G/P ×m v_P + ∫r_/G ×(ω ×r_/G )dm c) H_P = r_G/P ×m v_P + ∫r_/P ×(ω ×r_/P )dm 13.Following the previous question, what is the assumption on P? a) P is the mass center b) P is a fixed point c) P is any arbitrary point d) P is an arbitrary point moving with the body. 14.Which on among the following quantity is not a vector? a) displacement, b) angular displacement, c) velocity, d) angular velocity. 15.What is the relationship between the moment of inertia of a body about its mass center, I^G and about another arbitrary point, I^P? a) I^P = I^G - mr^2, b) I^G = I^P - md^2, c) I^G = I^P + md^2, d) I^P = I^G Problems 16.(20%)The 1m-diameter disk shown in the figure has a mass of 20Kg. The mass center of the disk is located 250mm from the center of the disk, and its radious of gyration with respect to the fixed axis of rotation is 400mm. A cable wrapped around the circumference of the disk pass over a small pulley of neglible mass and is attached to a 25-Kg block B. If the disk has a counterclockwise angular velocity of 10 rad/s when θ= 0ﾟ. Write down the relation that determines the angle θ_m when the disk stops and begins to rotate clockwise. ┌───────────────────┬┬ │ ──────────────┤├╮ │ ↖此處與圓盤交 定滑輪位置→╰╯│ │ │ │ ■B │很難畫的圓盤位置(轉軸垂直紙面) ├─────╮ (質量分布不均) ├─────╯ │ │ ⊙ ←質心位置 │ │ ＼ 　 │ │ ＼ ╰ θ ╯ 17.(20%)The slender rod AB of length L forms an angle β with the vertical axis as it strikes the frictionless surface shown with a vertical velocity v_L and no angular velocity. Assuming that the impact is perfectly elastic, derive the expression for the angular velocity of the rod immediately after the impact. Moment of inertia of a slender rod about its mass center is (1/12)mL^2 . (本題試卷中L皆為小寫，使用大寫以方便與1區別) ╭β╮ ﹕ ∕B ﹕ ∕ ﹕ ∕ ﹕∕↓ v_L A∕ ──────────── 18.(30%)The 5kg uniform bar BDE is attached to the two rods AB and CD. Knowing that at the instant rod AB has an angular velocity of 6 rad/s clockwise and no angular acceleration, determine a) the velocity v_D,(10%) b) the acceleration a_D,(10%) c) the x-component of reaction force R_Bx at B.(10%) ─╮A ╭─╮ ◎╞════╪◎│B ─╯ 200mm │ │ │ │240mm │ │ ─╮C │ │ ◎╞══╪◎│D ─╯↑ │ │ 150mm │ │240mm │ │ │ │ │ │E ╰─╯ --

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