How far does the block travel after being released?

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SUMMARY

A block with a mass of 0.08 kg is compressed against a spring with a spring constant of 31 N/m and released from a compression of 0.15 meters. The block slides on a surface with a coefficient of friction of 0.45. The discussion revolves around calculating the distance the block travels after being released, emphasizing the need to account for both the work done by the spring and the work done against friction. The equation presented by the user requires refinement to accurately represent the forces involved.

PREREQUISITES
  • Understanding of Hooke's Law and spring mechanics
  • Knowledge of kinetic friction and its calculation
  • Familiarity with the work-energy principle
  • Basic algebra for solving equations involving forces
NEXT STEPS
  • Calculate the potential energy stored in the spring using the formula PE = 0.5 * k * x^2
  • Determine the frictional force using the formula F_friction = μ * m * g
  • Apply the work-energy principle to find the distance traveled by the block
  • Explore the effects of varying the coefficient of friction on the distance traveled
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the dynamics of spring systems and frictional forces in motion.

Aggie
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A block of mass 0.08 kg is pushed against a spring with spring constant k=31 N/m. The srping is compressed 0.15 meters from its natural length. The block is released and it slides along a surface with coefficient of frition 0.45. How far does the block travel from the point at which is is released?


I am having a problem developing an equation for this. It seems i am always short on something.

this is what i have so far

Work due to friction - work due to spring = work due to spring - work due to friction.

I know i am missing something but i don't know what it is.
 
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Assume it is all horizontal. You have an initial set of numbers to calculate the force along the x-axis and the frictional forces, Soecifty these, and we can help more.
 
is my equation right or wrong
 
Your equation says

1 = -1

Forget the spring and think about what happens if you just push the block with force f for 1 cm. Then return to the spring ...
 

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