Hooke's law and kinetic energy?

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SUMMARY

The discussion focuses on a physics problem involving a 0.75 kg block released from a spring with a spring constant of 735 N/m, initially compressed by 27.0 cm. The key calculations involve determining the kinetic energy of the block when the spring is compressed to 13.5 cm using the formula for elastic potential energy and the conservation of energy principle. The force exerted by the spring at full compression is calculated as 198.45 N, but the primary goal is to find the kinetic energy at the reduced compression and the radius of the loop necessary for the block to complete its motion.

PREREQUISITES
  • Understanding of Hooke's Law (F = kx)
  • Knowledge of kinetic energy formula (Ek = (1/2)mv^2)
  • Familiarity with conservation of energy principles
  • Basic concepts of potential energy in springs
NEXT STEPS
  • Calculate the kinetic energy of the block at 13.5 cm compression using energy conservation.
  • Determine the velocity of the block at various points along its path.
  • Explore the relationship between the radius of the loop and the minimum velocity required to maintain motion at the top.
  • Review examples of similar spring and loop problems to reinforce understanding.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for practical examples of Hooke's law and energy conservation in action.

jevillan
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Homework Statement


A 0.75 kg block is held at rest against a spring compressing it 27.0 cm. The spring constant is 735 N/m. The block is released and it begins to move toward a loop across a frictionless surface. How much kinetic energy does the block have when the spring is compressed 13.5 cm? What is the radius of the loop if it just makes it around the top of the loop?


Homework Equations


F = kx
Ek = (1/2)mv^2


The Attempt at a Solution


F = kx
F = 735*0.27 = 198.45

So far I've found the force when the spring is compressed 27 cm...not too sure how that value of Force is even relevant to finding the answer :S
 
Physics news on Phys.org
Investigate the energy stored in the spring and the use of conservation of energy to determine the velocity of the block at various points along its journey.
 

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