Five Physics Problems

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1. (20 points) A grindstone in the shape of a solid disk with diameter 0.520 m and a mass of 50.0 kg is rotating at 850 rev/min. You press an ax against the rim with a normal force of 160 N, and the grindstone comes to rest in 7.50 s. Find the coefficient of kinetic friction between the ax and the grindstone. There is negligible friction in the bearings. m = 50.0 kg F = 160 N RON 1 2. (20 points) When a compact disc is playing, the angular speed of the turntable is adjusted so 500.0 rpm that the laser beam, which reads the digital information encoded in the surface of the disk, maintains a constant tangential speed. The laser begins tracking at the inside of the disc and spirals outward as the disc plays, while the angular speed of the disc varies between and 200.0 rpm. A certain CD plays for 74.0 minutes and has a playing area of outer diameter 12.1 cm (which is also essentially the outside diameter of the disc.) a) What is the tangential speed of the laser beam? b) What is the diameter of the inside of the playing area of this CD? c) What is the angular acceleration of the CD while it is playing, assuming it to be constant? 3. (20 points) On the ride “Spindletop” at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor on which the people were standing dropped about 0.5 m. The people remained pinned against the wall. a) Draw a free-body diagram for a person on this ride after the floor has dropped. b) What minimum coefficient of static friction is required if the person on the ride is not to slide downward to the new position of the floor? c) Does your answer in part (b) depend on the mass of the passenger? (Note: When the ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.) 4. (20 points) A uniform 8.0 m, 1500.0 kg beam is hinged to a wall and supported by a thin cable attached 2.0 m from the free end of the beam, as shown in the figure below. The beam is supported at an angle of 30.0° above the horizontal. a) Make a free-body diagram of the beam. b) Find the tension in the cable. c) How hard does the beam push inward on the wall? 40.0° K 2.0 m 30.0° tent Bonus Problem: (10 points) The Achilles tendon, which connects the calf muscles to the heel, is the thickest and strongest tendon in the body. In extreme activities, such as sprinting, it can be subjected to forces as high as 13 times a person's weight. According to one set of experiments, the average area of the Achilles tendon is 78.1 mm?, its average length is 25.0 cm, and its average Young's modulus is 1474 MPa. If a 75 kg sprinter exerts a force of 13 times his weight on his Achilles tendon, by how much will it stretch? 6
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