1. (15%) Determine by direct integration the location of the centroid of a parabolic spandrel.

2.(20%) A worker slowly moves a 50-kg crate to the left along a loading dock by applying a force P at comner B as shown. Knowing that the crate starts to tip about the edge E of the loading dock when a = 200 mm, determine (a) the coefficient of kinetic friction between the crate and the loading dock, (b) the corresponding magnitude P of the force.

3. (15%) A thin plate of the shape (A square plate of side b) indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant (a) of Point A, (b) of Point B.

4.(15%) Linkage DBEF is part of a windshield wiper mechanism, where points O, F and D are fixed pinned connections. At the position shown, θ = 60° and link EB is horizontal. Knowing that link EF has a counterclockwise angular velocity of 4 rad/s at the instant shown, determine the angular velocity of links EB and DB.

5. (15%) A 30-kg block rests on top of a 20-Kg block supported by, but not attached to, a spring of constant 40 N/m. The upper block is suddenly removed. Determine (a) the maximum speed reached by the 20-kg block, (b) the maximum height reached by the 20-kg block.

6.(20%) A projectile enters a resisting medium at x = 0 with an initial velocity vo = 270 m/s and travels 100 mm before coming to rest. Assuming that the velocity of the projectile is defined by the relation v = vo - kx, where v is expressed in m/s and x is in m, determine (a) the initial acceleration of the projectile. (b) the time required for the projectile to penetrate 97.5 mm into the resisting medium.

(b) (10%) Determine the angular velocity of Rand the velocity of C (the mass center of C) when the collar leaves the rod.

(a) (10%) Determine the angular velocity of C when the string breaks.

4. (20%) As shown in Fig. 4, force P is applied to a plate that rests on a smooth surface with the friction coefficient μ2equal to 0. The friction coefficient between the Mass m and Mass M is given as μ1. Find the largest force P for which the pipe will not slip on the plate.

3. (20%) Collar Cin Fig. 3 is pined to rod Rat P and is free to slide along rod B. The angular velocity of Ris 0.2 rad/s in clockwise direction. Find the angular velocity of B at this time. Determine the velocity of P relative to B.

2. (20%) At the instant shown in Fig. 2, the velocity of point A is 0.2 m/s to the right. Find the angular velocity of rod B, and determine the velocity of its other end (point B) which is constraint to move in the circular slot.

110年 - 110 國立中山大學碩士暨碩士專班招生考試_機電系碩士班/乙組:應用力學(含靜力學及動力學)#104258

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