Homework 7Physics 1310, Fall 2021

Read Chapter 7. Reminder: The second exam is on Monday October 11th.

Complete the following problems:

1. Toni Matt won the 1939 Mt. Washington "Inferno" by schussing Tuck-erman�s Ravine, a feat that was never again performed. Passing over the lip,shown in the photo, the slope makes an angle of 50 degrees above the horizon-tal. (a) Assuming that Matt�s terminal velocity would have been 180 mph ina straight vertical fall, what would have been his terminal velocity on the 50degree slope? Assume that the coe¢ cient of sliding friction between his skis andthe snow was 0.10, and assume that the slope was smooth. (b) At this speed,at what rate (Watts) is energy dissipated by air friction if Matt weighs 190 lbs?At what rate is energy dissipated by snow friction if Matt weighs 190 lbs?

2. Water balloons are launched in the parking lot of the CEC each year asan educational activity in Ray Tokuda�s physics class. They are shot using aslingshot made of a long piece of surgical hose. The sti¤ness constant k of thehose is 60 N/m, and the hose attaches to the sling from both sides, and it isdoubled up on each side (see photo). (a) How far must the sling be pulled backto launch a 1 lbs water balloon 150 meters at an angle of 25 degrees? Neglectair friction. (b) What will be the initial acceleration (in g�s)?

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3. Water drops 167 feet as it �ows over Niagra Falls. It is estimated that ifthe �ow over the scenic part of the falls were harnessed to generate electricity,in a typical year it would be equivalent to having a 0.75 GW power plant (GWis giga-Watt). Assuming 100% conversion of potential energy into electricalenergy, what �ow rate does this correspond to (in cubic feet per second)?

4. A 2.5 kg block of wood is to be launched across a slippery �oor by acompresssed spring. The sti¤ness constant of the spring is 150 N/m, and thespring is initially compressed by 0.17 meters. If the block slides 10 meters beforecoming to rest, what is the coe¢ cient of sliding friction? If the block were toslide 0.17 meters - the very same distance the spring was compressed - whatwould be the coe¢ cient of sliding friction?

5. A skier stands on the top of a giant frictionless snowball with radius R:She is initially at rest, but a slight perturbation starts her sliding o¤ to the side.(a) At what angle � with respect to the vertical will she lose contact with thesnow? (b) What is the velocity at this point if R = 75 m, and how fast willshe be traveling when she hits the ground? The snowball is �xed in place, anddoesn�t roll.

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6. The latest contraption to be a part of the American Ninja Warior �tnesschallenge is a giant rotating �repole that swivels about a horizontal axle attachedat one end. Contestants must shinny up when the pole when it is in a verticalposition. After reaching the top, they push a button that releases the pole sothat it is free to rotate about the axle. Then they hang on using only theirarms as they rotate around in a vertical circle. What is their apparent weight(in multiples of their own weight) as they rotate across the bottom (an angle of180 degrees from the vertical)? Assume that the pole�s mass is inconsequential,and that a contestant can be modeled as a point-mass attached to the end ofthe rotating pole. The length of the pole is not known.

7. A small bead slides on a rigid wire, as shown in the �gure. The beadstarts from a height h0 = 2:000 m, and slides over an in�nite periodic array ofbarriers having height h1 = 0:600 m, as shown. There is no friction between thebead and the wire except along short locally-�at segments of length d = 1:000cm, where the coe¢ cient of kinetic friction is 0:1500:Where will the bead cometo a stop? (i.e. does it stop between the 1st and 2nd humps? Between the 10thand 11th hump? Between the 98th and 99th hump? etc.)

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