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2012_hw3 - 1 In a test of vertical leaping ability a...

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Unformatted text preview: 1. In a test of vertical leaping ability, a basketball player (a) crouches just before jumping, (b) has given his mass center G a vertical velocity v0 at the instant his feet leave the surface, and (c) reaches the maximum height. If the player can raise his mass center 3 feet as shown, estimate the initial velocity v0 of his mass center in position (b). ME 577/BME 595D Human Motion Kinetics HW 3 2. Write out the kinematic equations (position, velocity, acceleration) in polar coordinates 17 times. 3. Consider a pilot in a human centrifuge. How fast does the arm of the centrifuge have to rotate in order to generate a 5G, 6G, and 7G acceleration (assume that it is moving at constant angular velocity)? A human centrifuge. You may assume the distance from the axis of rotation to the center of the gondola holding the pilot is 25 ft. Reference: Balldin, U.I. Acceleration Effects on Fighter Pilots. Chapter 33, Medical Aspects of Harsh Environments. 4. Spider-Man (height 5' 10", 165 lbs.) spends a lot of time swinging around New York City. Below is an image as he just starts his swing. The webline attaches to a building approximately 200 ft. away and makes an initial angle of 25o with the horizontal. If he starts with zero velocity, how fast will he be moving at the bottom of his swing? What is the maximum force in the webline? 5. The Gravitron is an interesting ride. You start by leaning against the outside wall facing the inside (the ride is a giant cylinder). The operator then starts it spinning, eventually reaching a constant angular velocity. If the coefficient of friction between the rider and the wall is 0.60 and the radius of the cylinder is 7.5 m, determine the minimum constant angular velocity required to keep a person from sliding down when the floor drops out beneath them. 6. Beginning from rest when = 10o, a 30 kg child slides without kinetic friction down the slide which is in the shape of a 2.5 meter circular arc. Determine the child's speed when they reach the bottom. Write out the governing equations when there is a friction coefficient of 0.1. Determine the speed of the child at the bottom of the slide using numerical methods. r h ...
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