1.  

A momentum transfer enthusiast goes ice skating on a cold 20 oF day. While skating, they notice that their skates are gliding across a very thin layer of water on top of the ice. Assume the ice and water surfaces are perfectly flat and that this water layer thickness is a constant t = 1.50 m, as pictured above (not to scale). a. What is the shear stress the water experiences as you pass over the water with a velocity of 4.0 m/s? b. Each single ice skate blade has a width of 0.50 cm and a length of 15 cm. What net acceleration does this person feel, and in what direction, if traveling at 4.0 m/s, with both skate blades flat on the ice? Assume they weigh 75 kg 2) This tube is used to carry the same aluminum cylinder a fixed vertical distance every day. Over the past few weeks, the total time it takes for the aluminum cylinder to travel this distance has continued to increase. Which of the following scenarios could explain the behavior of the slowing aluminum cylinder? a. A high pressure weather pattern settled over the area, increasing Patm. b. Dirt has gotten into the tube and mixed with the oil, resulting in a higher viscosity. c. The cylinder, being roughly handled. has been scratched so that its mass is now less than 1.0 kg but still has roughly the same shape. d. The pneumatic tube has bent and stretched such that it now has a larger diameter, resulting in a thicker layer of lubricating oil between the cylinder and the tube wall 3) A block, connected to a bag of sand, is initially stationary near the interface between fluids 1 and 2, as depicted in the figure. The bag of sand (initial volume = 5 m 3 ) hangs below the block from a massless chain. At time = 0 a hole forms in the bag, out of which sand leaks at a constant rate of r = 0.169 m3 min-1. As the block rises without friction through the fluids it eventually is only submerged in fluid 1 (or h= 0). At what time, in minutes, does this occur? Hint: the sand leak is slow enough that the sand and block system is always in mechanical equilibrium, or the sum of forces is equal to zero.