110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所固體力學、系統控制組:動力學(A)#100865

科目：研究所、轉學考(插大)◆動力學 | 年份：110年 | 選擇題數：0 | 申論題數：8

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所屬科目：研究所、轉學考(插大)◆動力學

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申論題 (8)

1.1:請推導腳踏車車輪傳動系統動態方程式dynamic equations(共兩條方程式):

1.2:假設是在逆風模式·是一個常數·但是(風阻)是一個随速度上升的負載,其數值如下為、Ri為34齒、Ro為14齒、Kc為∞(剛性鍊條)、ρ為 1.2258、A 為0.645m²,

請推導解析解(包含變数與數值)及劃出縱軸與時間的示意圖

2.1假設左腳踩踏力與右踩踏力如圖4表示,不考慮上題的車輪負載請用數學式說明踏板軸力矩與踩踏力關係,並且畫出踏板軸力矩與踏板角度大概關係圖(至少制出一個週期0~360度)

2.2假設踏板軸力矩與踏板角度。的為一常數如圖5,請用數學式回推左右牌腳踏踩力與踏板角度關係式·並且畫出與踏板角度大概關係圖(至少劃出一個週期0-360度)

B. You are requested to participate in a court case as an expert witness. As illustrated in Fig. 6, a spacecraft is known to have unfortunately exploded into three pieces, A, B, and C. ma - 1000 kg, ma = 500 kg, and mc = 500 kg. Telemetry data showed that the positions of the satellitc with respect to a know wn reference ce position O at a particular tim ime were Rwo = (400 i - 1000 ) m, Ro = 1000 j m, and Reo = (800 i + 1000 j) m. The respective velocities were V, = -500j m/s, VB = (-4001 + 500) m/s, and Vc = (400i + 500) m/s. The engineer of the spacecraft company claims that a single explosion caused the described configuration, whereas the lawyer representing the insurance ce company contends that at least two separate explosions were responsible. Who is correct? (You have to describe detailed reasons and calculation results to support your answer. O point will be given if no explanation is provided.)

1. What assumption is needed so that the system depicted in Fig. 7 can be treated as a conservative system?

2. Draw the free-body diagram for the system with the assum mption stated above.

3. Determine the velocity of A and the total kinetic energy of the system when B contacts the horizontal guide.