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 p. 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/mx, where x represents the amount of stretch (or compression) in the spring at any given location in the motion. Use the values m = 9 kg. k = 105 N/m, p = 0.50, and xo = 1110 mm and determine the final spring stretch (or compression) x, when the block comes to a complete stop. The distance x, will be positive if to the right (spring stretched) and negative if to the left (spring compressed).

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Topic: Dynamic Of Rigid Bodies

A block of mass mrests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and
kinetic friction are p. 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 = 9 kg. k= 105 N/m, p = 0.50, and xo = 1110 mm and
determine the final spring stretch (or compression) x, when the block comes to a complete stop. The distance x, will be positive if to
the right (spring stretched) and negative if to the left (spring compressed).
Unstretched spring
position
Part 1
wwwww
xo
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 = 9 kg, k = 105 N/m, p = 0.50, and xo = 1110 mm.
Unstretched spring
position
Answer: Xomin=
m
xo
m
mm
Transcribed Image Text:A block of mass mrests on a rough horizontal surface and is attached to a spring of stiffness k. The coefficients of both static and kinetic friction are p. 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 = 9 kg. k= 105 N/m, p = 0.50, and xo = 1110 mm and determine the final spring stretch (or compression) x, when the block comes to a complete stop. The distance x, will be positive if to the right (spring stretched) and negative if to the left (spring compressed). Unstretched spring position Part 1 wwwww xo 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 = 9 kg, k = 105 N/m, p = 0.50, and xo = 1110 mm. Unstretched spring position Answer: Xomin= m xo m mm
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