A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are u. The block is displaced a distance xo to the right of the unstretched position for the spring and released from rest. If the value for xo is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = ug - k/m x, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 10 kg, k = 210 N/m, = 0.34, and xo = 370 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop. The distance xf will be positive if to the right (spring stretched) and negative if to the left (spring compressed).

A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are u. The block is displaced a distance xo to the right of the unstretched position for the spring and released from rest. If the value for xo is large enough, the spring force will overcome the maximum available static friction force and the block will slide toward the unstretched position of the spring with an acceleration a = ug - k/m x, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 10 kg, k = 210 N/m, = 0.34, and xo = 370 mm and determine the final spring stretch (or compression) xf when the block comes to a complete stop. The distance xf will be positive if to the right (spring stretched) and negative if to the left (spring compressed).

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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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Laws of Equilibrium

A body is said to be in equilibrium if the system of forces acting on the body tends to keep the body at rest, in other words, there is no translation motion or net torque on the body. Under such conditions, the equilibrium conditions are to be applied to analyze the condition. The branch of mechanics that deals with this condition is known as 'statics'. Under equilibrium, there are no net forces on the body.

Question

Unless the value for xo is large enough, no motion will occur. Verify that motion does occur in this case by calculating the minimum
value that xo must exceed in order for motion to occur?. Use the values m = 10 kg, k = 210 N/m, p=0.34, and xo = 370 mm.
Unstretched spring
position
Liw
Answer: Xomin
Hint
xo
m
mm
The acceleration due to the spring must have a larger magnitude than the acceleration due to friction.
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A block of mass m rests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and
kinetic friction are u. The block is displaced a distance xo to the right of the unstretched position for the spring and released from rest.
If the value for xo is large enough, the spring force will overcome the maximum available static friction force and the block will slide
toward the unstretched position of the spring with an acceleration a = μg - k/m x, where x represents the amount of stretch (or
compression) in the spring at any given location in the motion. Use the values m = 10 kg, k = 210 N/m, u = 0.34, and xo = 370 mm and
determine the final spring stretch (or compression) xf when the block comes to a complete stop. The distance xf will be positive if to
the right (spring stretched) and negative if to the left (spring compressed).
Unstretched spring
position
x
xo
m

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