Velocity of spring being made to go in a circle

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SUMMARY

The discussion centers on calculating the speed of a 5 kg block attached to a spring with a spring constant of 250 N/m, which is stretched while moving in a circular path of radius 0.75 m. The correct approach involves using the centripetal force formula, F = (mv²)/r, rather than linear motion equations. The final speed of the block is determined to be 3.1 m/s, confirming the solution provided in the practice exam. Key calculations include determining the net force exerted by the spring as it stretches from its relaxed length of 0.5 m.

PREREQUISITES
  • Understanding of Hooke's Law (Fspring = k|s|)
  • Knowledge of centripetal force in circular motion (F = (mv²)/r)
  • Basic principles of Newton's second law (F = ma)
  • Ability to perform algebraic manipulations to solve for variables
NEXT STEPS
  • Study the derivation and application of centripetal force equations in circular motion.
  • Explore advanced topics in oscillatory motion and spring dynamics.
  • Learn about energy conservation in systems involving springs and circular motion.
  • Practice solving similar problems involving forces and motion in different contexts.
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of spring dynamics and circular motion applications.

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Homework Statement


A 5 kg block is attached to the end of a spring with relaxed length 0.5 m and spring constant 250 N/m. The free end of the spring is held stationary and the block is made to go in a circle of radius 0.75 m, thus stretching the spring. What is the speed of the block (neglecting gravity and air resistance)?


Homework Equations


Fspring=k|s|
F*\Deltat= m*v
p=Fnet*\Deltat


The Attempt at a Solution


F=k|s|
F=250 (.5-.75)
F=-1000
F=mv?

I don't know what to do from here... this is on a practice exam, so I have the answer: 3.1 m/s, but I have no idea how to get to it. I tried F=mv, but got v to be 2.0, which isn't even an option. Please help!
 
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From
F=k|s|
You should get 62.5N with this, check your calculation.

Note that This is not linear motion.
You should be using the Centripetal force of Circular motion to find the answer,
in which F=(mv^2)/r.
 
Oops! I did a hasty calculation in my head... thanks for catching that! It makes perfect sense, too- thank you very much.
 

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