Question

3. As part of a packaging process, cans roll along a ramp from one location to another. In one section, the cans 1) go through a curve and make a 90 degree turn and then 2) go down a ramp from one level to another. The cans have a diameter of 4 inches, a height of 4", and a weight of 1.61 lbs. The upper level is 4 feet above the lower level. The cans roll onto into the curve with an initial linear speed of 2 ft/sec. Answers are to be given in the system of units used in the problem. Work is to be done in these units as well. a) What is the initial angular speed of the cans in (rad/sec) when the linear speed is 2 ft/sec? Also calculate the mass of the can in (slugs) from the weight and find the mass moment of inertia about the axis of the can in [slugs ft?). (15 pts) The minimum radius of curvature is 2.3 feet. Assuming no losses due to friction, so the speed is the same as the initial value. (Note: this is not realistic). b) Find the lateral (sideways) acceleration in [ft/sec) and force (in lbs] acting to keep the can on the curve at this point. Assuming no losses, v = 2 ft/sec. (10 pts) In practice the cans are only moving at a linear speed of after going through the curve and down 4 feet. If there were no losses, the speed would be higher. c) Find I. ... the initial system energy at the start of the ramp (linear speed of 2 ft/sec; elevation of 4 feet above the lower level). ii. ... the final angular speed and system energy for a linear speed on the lower level of 10 ft/sec. iii. ... Given that the length of this section of ramp is 16 feet, find the average force acting to resist motion (the force dissipating - removing - energy from the system). (15 pts)