A 1.0 kg collar attached to a spring and slides without friction along a circular rod which lies in a vertical plane. The spring has a constant k=250N/m and is un-deformed when collar is at B. Knowing that the collar passes through point D with a speed of 3.0 m/s, determine: a) The speed of collar as it passes through C. b) The speed of collar as it passes through B.

A spring is used to stop a 50-kg package which is moving down a 20° incline. The spring has a constant k =34 kN/m and is held by cables so that it is initially compressed 50 mm. Knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest. Assume that the kinetic coefficient of friction between the package and the incline is 0.2. 2 m/s 50 kg 8m Cable 20° The maximum additional deformation of the spring in bringing the package to rest is 0.574 x m.

(2) A 5 lb ball is attached to a 3 ft long rope and it rotates in a vertical circular path at a constant tangent velocity of 30 ft/s. (a) Determine the tension in the rope when the ball is at point A. (b) Determine the tension in the rope when the ball is at point B. B 3 ft A