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

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.