Find launch speed given spring constant and compressed distance

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SUMMARY

The launch speed of a .00321 kg piece of potato from a potato gun with a spring constant of 41 N/m and a compression distance of 0.073 m is calculated using energy principles. The energy stored in the spring is equated to the kinetic energy of the potato. The formula for the energy in the spring is E = 0.5 * k * x^2, where k is the spring constant and x is the compression distance. The final calculated launch speed is 8.3 m/s, as confirmed by the lecturer.

PREREQUISITES
  • Understanding of Hooke's Law and spring potential energy
  • Basic knowledge of kinetic energy and its formula
  • Familiarity with projectile motion equations
  • Ability to perform unit conversions (e.g., cm to m)
NEXT STEPS
  • Study the derivation of spring potential energy using the formula E = 0.5 * k * x^2
  • Learn about the conservation of energy principles in mechanical systems
  • Explore projectile motion equations in detail, focusing on their applications
  • Practice problems involving energy transformations in spring-loaded mechanisms
USEFUL FOR

Students in physics courses, particularly those studying mechanics, as well as educators looking for practical examples of energy conversion in spring systems.

Chica1975
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Homework Statement


A potato gun contains a spring which is compressed a distance of 7.30cm (0.073m) when it is loaded. If the spring's constant is 41N/m, what is the launch speed of a .00321kg piece of potato when the gun is fired? Give the answer in m/s.


Homework Equations


Power = W/T
V^2=Vi^@+2a(y-y0) (projectile motion)
I have no idea what else I need - am stuck.


The Attempt at a Solution


I drew what it might look like and tried to work out mg (0.00321*9.8 = .31458) as the height but am really stuck.

the lecturer has given the answer as 8.3m/s

Help!
 
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Equate the energy stored in the spring to the kinetic energy of the potato piece.
You should know a formula for the energy in the spring in terms of the spring constant and the compression.
 

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