1. The bead of mass m and radius r, released from a height of 4R at the top of the frictionless ramp, rolls without slipping. At the end of the ramp, the bead moves on a frictionless path that is curved in a circle in a vertical plane. When the bead reaches the top point of the circle, obtain the magnitude of the normal force between the circular path and the bead in terms of the ball's weight, mg. (Moment of inertia of the bead is given by -mr?)

1. The bead of mass m and radius r, released from a height of 4R at the top of the frictionless ramp, rolls without slipping. At the end of the ramp, the bead moves on a frictionless path that is curved in a circle in a vertical plane. When the bead reaches the top point of the circle, obtain the magnitude of the normal force between the circular path and the bead in terms of the ball's weight, mg. (Moment of inertia of the bead is given by -mr?)

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter7: Rotational Motion And The Law Of Gravity

Section: Chapter Questions

Problem 8P: A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel...

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One method of pitching a softball is called the wind-mill delivery method, in which the pitchers arm rotates through approximately 360 in a vertical plane before the 198-gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 98.0 mi/h. Assume the angular acceleration is uniform throughout the pitching motion and take the distance between the softball and the shoulder joint to be 74.2 cm. (a) Determine the angular speed of the arm in rev/s at the instant of release, (b) Find the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released, (c) Determine the force exerted on the ball by the pitchers hand (both radial and tangential components) just before it is released.
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One method of pitching a softball is called the wind-mill delivery method, in which the pitchers arm rotates through approximately 360 in a vertical plane before the 198-gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 98.0 mi/h. Assume the angular acceleration is uniform throughout the pitching motion and take the distance between the softball and the shoulder joint to be 74.2 cm. (a) Determine the angular speed of the arm in rev/s at the instant of release, (b) Find the value of the angular acceleration in rev/s2 and the radial and tangential acceleration of the ball just before it is released, (c) Determine the force exerted on the ball by the pitchers hand (both radial and tangential components) just before it is released.
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A bicycle is turned upside down while its owner repairs a flat tire. A friend spins the other wheel and observes that drops of water fly off tangentially. She measures the heights reached by drops moving vertically (Fig. P7.8). A drop that breaks loose from the tire on one turn rises vertically 54.0 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The radius of the wheel is 0.381 m. (a) Why does the first drop rise higher than the second drop? (b) Neglecting air friction and using only the observed heights and the radius of the wheel, find the wheels angular acceleration (assuming it to be constant). Figure P7.8 Problems 8 and 69.
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