a) A 1.5kg rock is tied to the end of a 1.25m string and is swung in a vertical circle at a constant speed of 4.5 m·s−1. i) What are the magnitude and direction of the rock’s acceleration when it is at the bottom of the circle? ii) What is the tension in the string when the rock is at the bottom of the circle? iii) What is the tension in the string when the rock is at the top of the circle?

a) A 1.5kg rock is tied to the end of a 1.25m string and is swung in a vertical circle at a constant speed of 4.5 m·s−1. i) What are the magnitude and direction of the rock’s acceleration when it is at the bottom of the circle? ii) What is the tension in the string when the rock is at the bottom of the circle? iii) What is the tension in the string when the rock is at the top of the circle?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 25P: As their booster rockets separate, Space Shuttle astronauts typically feel accelerations up to 3g,...

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In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?
A single bead can slide with negligible friction on a stiff wire that has been bent into a circular loop of radius 15.0 cm as shown in Figure P5.59. The circle is always in a vertical plane and rotates steadily about its vertical diameter with a period of 0.450 s. The position of the bead is described by the angle θ that the radial line, from the center of the loop to the bead, makes with the vertical. (a) At what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (b) What If ? Repeat the problem, this time taking the period of the circle’s rotation as 0.850 s. (c) Describe how the solution to part (b) is different from the solution to part (a). (d) For any period or loop size, is there always an angle at which the bead can stand still relative to the loop? (e) Are there ever more than two angles? Arnold Arons suggested the idea for this problem. Figure P5.59
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