Review. A light spring has unstressed length 15.5 cm. It is described by Hooke’s law with spring constant 4.30 N/m. One end of the horizontal spring is held on a fixed vertical axle, and the other end is attached to a puck of mass m that can mow without friction over a horizontal surface. The puck is set into motion in a circle with a period of 1.30 s. (a) Find the extension of the spring x as it depends on m. Evaluate x for (b) m = 0.070 0 kg. (c) m = 0.140 kg, (d) m = 0.180 kg, and (e) m = 0.190 kg. (f) Describe the pattern of variation of x as it depends on m.
(a)
The extension of the spring as it depends on
Answer to Problem 7.67CP
The extension of the spring is
Explanation of Solution
Given info: The unscratched length of spring is
The extension of spring is
Here,
From Newton’s law, the force of an object is,
Here,
From the Hooke’s law, the spring force of spring is,
Here,
Substitute
The expression for the acceleration of the object is,
Here,
The formula for the speed of the object is,
Rearrange the above equation.
Substitute
The speed of an object in term of oscillation is,
Here,
Substitute
Here,
Substitute
Substitute
Substitute
Substitute
Conclusion:
Therefore, the extension of the spring is
(b)
The extension in spring for
Answer to Problem 7.67CP
The extension in spring is
Explanation of Solution
Given info: The mass of puck is
From part (a), the extension in spring is,
Substitute
Conclusion:
Therefore, the extension in spring is
(c)
The extension in spring for
Answer to Problem 7.67CP
The extension in spring is
Explanation of Solution
Given info: The mass of puck is
From part (a), the extension in spring is,
Substitute
Conclusion:
Therefore, the extension in spring is
(d)
The extension in spring for
Answer to Problem 7.67CP
The extension in spring is
Explanation of Solution
Given info: The mass of puck is
From part (a), the extension in spring is,
Substitute
Conclusion:
Therefore, the extension in spring is
(e)
The extension in spring for
Answer to Problem 7.67CP
The situation for extension in spring for
Explanation of Solution
Given info: The mass of puck is
From part (a), the extension in spring is,
Substitute
The extension in spring is the distance of spring after extension and distance cannot measure in left side
Conclusion:
Therefore, the situation for extension in spring for
(f)
The variation of
Answer to Problem 7.67CP
The value of
Explanation of Solution
From part (a), the extension in spring is,
From the above expression, it is shown that the extension in spring is directly proportional to the mass of puck so the extension in spring increases as
After a certain point the extension of spring diverge to infinity.
The mass of puck when the extension of spring diverges to infinity,
Conclusion:
Therefore, the value of
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Chapter 7 Solutions
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