(a)
The extension of the spring for a mass of
(a)
Answer to Problem 65P
The extension of the spring for a mass of
Explanation of Solution
Write the expression for
Here,
Write the expression for velocity in terms of time period.
Here,
Write the expression for force from hooks law.
Here,
Use equation (II) and (III) in equation (I) and rearrange.
Write the expression for radius of the pluck’s motion.
Use equation (V) in equation (IV), to find
Conclusion:
Therefore, the extension of the spring for a mass of
(b)
The extension of the spring for the mass
(b)
Answer to Problem 65P
The extension of the spring for the mass
Explanation of Solution
Substitute
Conclusion:
Substitute
Therefore, the extension of the spring for the mass
(c)
The extension of the spring for the mass
(c)
Answer to Problem 65P
The extension of the spring for the mass
Explanation of Solution
From equation (VII).
Conclusion:
Substitute
Therefore, the extension of the spring for the mass
(d)
The extension of the spring for the mass
(d)
Answer to Problem 65P
The extension of the spring for the mass
Explanation of Solution
From equation (VII).
Conclusion:
Substitute
Therefore, the extension of the spring for the mass
(e)
The extension of the spring for the mass
(e)
Answer to Problem 65P
For the mass
Explanation of Solution
From equation (VII) the spring extension is given by
Conclusion:
Substitute
Therefore, For the mass
(f)
To explain the pattern of variation of
(f)
Answer to Problem 65P
The extension of the spring is directly proportional to the mass
Explanation of Solution
The extension of the spring is directly proportional to the mass
Conclusion:
Therefore, the extension of the spring is directly proportional to the mass
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Chapter 6 Solutions
Principles of Physics: A Calculus-Based Text
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- Review. A light spring has unstressed length 15.5 cm. It is described by Hookes 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.arrow_forwardIn a laboratory experiment, 1 a block of mass M is placed on a frictionless table at the end of a relaxed spring of spring constant k. 2 The spring is compressed a distance x0 and 3 a small ball of mass m is launched into the block as shown in Figure P11.22. The ball and block stick together and are projected off the table of height h. Find an expression for the horizontal displacement of the ballblock system from the end of the table until it hits the floor in terms of the parameters given. FIGURE P11.22arrow_forwardA small particle of mass m is pulled to the top of a friction less half-cylinder (of radius R) by a light cord that passes over the top of the cylinder as illustrated in Figure P7.15. (a) Assuming the particle moves at a constant speed, show that F = mg cos . Note: If the particle moves at constant speed, the component of its acceleration tangent to the cylinder must be zero at all times. (b) By directly integrating W=Fdr, find the work done in moving the particle at constant speed from the bottom to the top of the hall-cylinder. Figure P7.15arrow_forward
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