A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position.(a) Find the position x of the mass at the times t = 1/12, x/8, n/6, n/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.)x(1/12) = 0.666X ftX(x/8) = 0.666X ftx(x/6) = 0.665X ftx (π/4)0.663X ft=x(9л/32)0.662X ft(b) What is the velocity of the mass when t = 3x/16 s?16ft/s3In which direction is the mass heading at this instant?upwarddownward(c) At what times does the mass pass through the equilibrium position?164X , n = 0, 1, 2, . A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position.(a) Find the position x of the mass at the times t = n/12, n/8, n/6, a/4, and 97/32 s. (Use g = 32 ft/s? for the acceleration due to gravity.)X(1/12) =-0.33X ftx(x/8) =-0.66X ftx(л/6) %3-0.33X ftx(T/4) =0.66X ftx(9x/32) =0.47X ft(b) What is the velocity of the mass when t = 37/16 s?16ft/s3In which direction is the mass heading at this instant?upwarddownward(c) At what times does the mass pass through the equilibrium position?164X , n = 0, 1, 2,+

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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = r/12, n/8, 1/6, x/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(7/12) = 0.666 X ft x(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x(x/4) = 0.663 X ft x(9x/32) = 0.662 X ft (b) What is the velocity of the mass whent = 37/16 s? 16 3 ft/s In which direction is the mass heading at this instant? upward o downward (c) At what times does the mass pass through the equilibrium position? + 16 X , n = 0, 1, 2, ...

A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position. (a) Find the position x of the mass at the times t = r/12, n/8, 1/6, x/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(7/12) = 0.666 X ft x(x/8) = 0.666 X ft x(x/6) = 0.665 X ft x(x/4) = 0.663 X ft x(9x/32) = 0.662 X ft (b) What is the velocity of the mass whent = 37/16 s? 16 3 ft/s In which direction is the mass heading at this instant? upward o downward (c) At what times does the mass pass through the equilibrium position? + 16 X , n = 0, 1, 2, ...

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest. 

Question

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A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 8 inches below the equilibrium position.
(a) Find the position x of the mass at the times t = 1/12, x/8, n/6, n/4, and 97/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.)
x(1/12) = 0.666
X ft
X(x/8) = 0.666
X ft
x(x/6) = 0.665
X ft
x (π/4)
0.663
X ft
=
x(9л/32)
0.662
X ft
(b) What is the velocity of the mass when t = 3x/16 s?
16
ft/s
3
In which direction is the mass heading at this instant?
upward
downward
(c) At what times does the mass pass through the equilibrium position?
16
4
X , n = 0, 1, 2, .

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