A spring with spring constant 35 N/m is vertically suspended with a 5.0-cm- diameter, 1.0 kg metal cylinder attached to its lower end. The cylinder is located above an empty tank. To fill the tank with water you use a garden hose. You know that the hose normally can fill a 1 gallon bucket in 8 s but to speed things up you place your thumb over the end of the hose, covering half of the opening. From your childhood water fights, you recall that this seems to speed the water up. a. Assuming all else is equal, how long in seconds will it take you to fill up the 5 gallon tank with water using your thumb trick? Explain.
b. What is the speed (in meters per second) of the water normally at the end of your hose (with no thumb covering it)? To the naked eye your hose appears to be 1 in in diameter.
c. With this estimate you are now intrigued by the physics of the situation. Estimating that the end of your hose is 1.5 m above the pressurized, underground city water lines and that they have 10 times the cross sectional area of your hose, what is the gauge pressure in psi of those city lines? With the tank finally filled, the surface of the water just touches the bottom of the linder if you hold it o avoid e spring. When released, t cylinder oscillates a few times before quickly coming to rest (being damped by the water)
d. How deep in centimeters does the cylinder sit in the water?
e. Does the spring potential energy gained equal the gravitational potential energy that the cylinder lost? If so, how many Joules were transferred? If not, where did the energy go?