Calculating Stopping Distance with Spring Forces and Friction

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SUMMARY

The discussion focuses on calculating the stopping distance of a block with a mass of 1.5 kg sliding at an initial velocity of 1.15 m/s, which encounters a spring with a spring constant of 170 N/m and a kinetic friction coefficient of 0.1. The stopping distance is determined by the balance of forces acting on the block, including the spring force and the frictional force. The key equation involves equating the work done by the spring to the work done against friction to find the stopping distance, which is equal to the spring compression.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of kinetic friction and its coefficient
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the work done by the spring using the formula W = (1/2)kx²
  • Determine the frictional force using fk = μk * N, where N is the normal force
  • Set up the equation for energy conservation to find the stopping distance
  • Explore the effects of varying the mass and spring constant on stopping distance
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding dynamics involving springs and friction.

wxscientist
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So I've been working on this for hours and trying to understand it but I just don't. It doesn't make sense to me. Here is my problem:

A block (M = 1.5 kg) is sliding along a frictionless surface with initial velocity Vo = 1.15 m/s. It comes in contact with the spring (k = 170 N/m) in the diagram, and when it does, it also experiences a friction force fk that opposed the motion. The coefficient of kinetic friction, (μk = 0.1).What is the stopping distance of the block?

The main thing is that I have no distance given or spring compression. Just Vo, k, M, and the coefficient of kinetic friction.
 
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The amount of spring compression is equal to the stopping distance.
 

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