110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所機械設計組:靜力學#100593

(a) Draw the free-body diagram of the man. (3%)

(b)Draw the frce-body diagram of the bar. (3%)

(c)Find the smallest force the man can exert on the cable if the bar is to remain horizontal. (14%)

(a) Without loading, its maximum working force FRI, max and its spring constant krI of the piezoelement Ri, as shown in Fig2(a).(3%)

(b) When the piezoelement R₁ rks against a weight of W, how large is its weight-loaded deflection AlRiw of the piezoelement R₁? as shown in Fig2(b). (5%)

(c) When the piezoelement R₁works against a spring with a spring constant of k, how large is its spring-loaded deflection AlRis of the piezoelement Ri ? as shown in Fig2(c). (5%)

(a) Please write down and proof the conditions for stable equilibrium for systems with one degree of freedom. (20% total, 5% for the conditions, 15% for proof of the conditions)

(b)Figure 3 shows a W(kg) hemisphere supports a cylinder having a specific weight of p kg/m?. If the radi of the cylinder and the hemisphere are both r, please determine the height h of the cylinder which will produce neutral equilibrium in the position shown. (20%)

(a) The acting force F_ainduced by the pedal force F_pthrough the pedal lever and the hydraulic piston with different piston area Ain and A_a (5%)

(b) The firee body diagram for the actuating lever with the braking block. (2%)

(c) The normal force N between the lining and the drum (5%)

(d) The horizontal and vertical reaction forces, R_h and R_y, at the pin location C (2%)

(e) The braking torque T_b on the drum (3%)

5. An 80 kg man tries to stay on a tree using a rope only. The diaeter of the tree is 30 cm. The center of gravity of the man is as indicated. The coefficient of friction between the rope and the tree is the same as that between the feet and the tree. The rope is kept horizontally. Please find the minimum coefficient of friction at which the man can be supported. (10%)

110年 - 110 國立臺灣大學_碩士班招生考試_機械工程研究所機械設計組:靜力學#100593

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