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Wright State University Department of Mechanical and Materials Engineering Spring 2011 ME 213 DYNAMICS: MIDTERM EXAM 1 Open Book, Closed Notes, DO NOT Write on this Sheet Show All Work for Partial Credit Problem 1 (35 points): A projectile enters a resisting medium at x = 0 with an initial velocity v0 = 800 ft/s and travels 4 in. before coming to rest. Assuming that the velocity of the projectile is defined by the relation v = v0 – kx, where v is expressed in ft/s and x is in feet, determine (a) the initial acceleration of the projectile (at x = 0), (b) the time required for the projectile to penetrate 3.9 in. into the resisting medium. Problem 2 (15 points): From measurements of a photograph, it has been found that as the stream of water shown left the nozzle at A, it had a radius of curvature of 20 m. Determine (a) the initial velocity vA of the stream, (b) the radius of curvature of the stream as it reaches its maximum height at B. Problem 3 (35 points): A single wire ACB passes through a ring at C that is attached to an 11.5-lb sphere which revolves at a constant speed v in the horizontal circle shown. Knowing that θ1 = 50°, the tension in both portions of the wire is 7.6 lb, and the horizontal distance from the sphere to the pole is 18 in., determine (a) the angle θ2, (b) the speed v. Problem 4 (15 points): Rod OA oscillates about O in a horizontal plane. The motion of the collar of mass m is defined by the relations 𝜋𝑡 𝑟 = 𝑎 + 𝑏 cos ( 2 ); 𝜃 = 𝜋(𝑡 2 + 𝑐𝑡) Determine the radial and transverse components of the force exerted on the collar.