Calculating the Spring Constant and Work Done by an Archer's Bow

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SUMMARY

The discussion focuses on calculating the spring constant and work done by an archer's bow when pulling the bowstring back 0.400 m with a maximum force of 230 N. The spring constant (k) is derived from Hooke's Law, where k equals the maximum force divided by the displacement. The work done by the archer is calculated using the formula for spring potential energy, PE = 1/2 kx², where x is the displacement of the bowstring. The participants clarify the relationship between force, displacement, and the spring constant, leading to a better understanding of the concepts involved.

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  • Understanding of Hooke's Law and its application in mechanics
  • Familiarity with the concept of spring potential energy
  • Basic knowledge of work and energy principles in physics
  • Ability to perform calculations involving force and displacement
NEXT STEPS
  • Study the derivation and applications of Hooke's Law in various contexts
  • Learn how to calculate work done using different force-displacement scenarios
  • Explore the concept of potential energy in elastic systems
  • Investigate real-world applications of spring constants in archery and other sports
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Physics students, archery enthusiasts, and anyone interested in understanding the mechanics of elastic forces and energy calculations.

Trista
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An archer pulls her bowstring back .400 m by exerting a force that increases uniformly from zero to 230 N. (a) what is the equivalent spring constant of the bow?
(b) How much work does the archer do in puling the bow?

The spring potential energy is defined by PE = 1/2kx^2. So, what does the k stand for? Force? That doesn't work. x must be the displacement of the string, which is .40, so 1/2k times (.40)^2? Friction isn't an issue, so its non conservative force. I know the theorem, but am having difficulty using it. :cry:

I know work is defined by Force times the displacement(x) and that equals Force cos theta times displacement(x). But I haven't been able to figure out theta.

Thank you, ahead of time, for your help!
Trista
 
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Look at "Hooke's Law." F = kx . k is the spring constant. F (in this equation) is maximum force.
 
Thanks! That was what I was missing, thank you!
 

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