Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 7, Problem 7.27P
When different loads hang on a spring, the spring stretches to different lengths as shown in the following table. (a) Make a graph of the applied force versus the extension of the spring. (b) By least-squares fitting, determine the straight line that best fits the data. (c) To complete part (b), do you want to use all the data points, or should you ignore some of them? Explain. (d) From the slope of the best-fit line, find the spring constant k. (c) If the spring is extended to 105 mm, what force does it exert on the suspended object?
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We will now determine how the 1/3 rule comes about.
Consider a spring of mass ms which is attached to a wall and oscillates on a frictionless surface as shown below. The spring’s mass is uniformly distributed along the length of the spring.
We will start with the infinitesimal form of kinetic energy, i.e. dKE = ½ (dms )v2. This formula will apply to an infinitesimal segment of the spring of length dx and mass dms as indicated below.
For any point on the spring, the velocity of oscillation will be given by v = (ve/L)x where ve is the velocity of the spring at its end where the mass m is attached, and L is the stretched length of the spring at that instant. Thus, when x = 0 then v = 0, and when x = L/2 then v = ½ ve.
Hint: Figure out how to relate dms to dx and then integrate both sides of the infinitesimal kinetic energy equation to get an equation for the kinetic energy of the spring that includes ms/3.
Needs Complete typed solution with 100 % accuracy.
Jum
The mass of the block depicted in the image is 2.94 kg. The spring has a spring
constant of 77.2 N/m. The coefficient of static friction between the block and the
floor is 0.735. Assume that the spring makes no contact with the floor and
therefore friction only acts on the block.
How far must the block and spring assembly be compressed to just barely
overcome the force of static friction acting on the block?
Report your result in meters.
Chapter 7 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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