Using Hooke's law to find the pull back distance?

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SUMMARY

This discussion focuses on applying Hooke's Law, represented by the equation F = -kx, to determine the pull back distance of a slingshot when launching an object. The participant correctly identifies that as the pull back distance (x) increases, the force (F) also increases, leading to greater acceleration (a) of the object due to the net force equation F_net = ma. Consequently, a larger pull back distance results in a higher exit speed and increased travel distance for the object. The relationship between force, pull back distance, and acceleration is crucial for accurate calculations in this context.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Knowledge of Newton's Second Law (F_net = ma)
  • Basic principles of kinematics
  • Familiarity with the concept of acceleration due to gravity
NEXT STEPS
  • Explore the relationship between force and displacement in elastic systems
  • Study the effects of varying pull back distances on projectile motion
  • Investigate energy conservation in slingshot mechanics
  • Learn about the dynamics of elastic potential energy and its conversion to kinetic energy
USEFUL FOR

Physics students, educators, and anyone interested in understanding the mechanics of slingshots and projectile motion.

grover1213
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Homework Statement


I'm given the mass of the object and acceleration (gravity), and I'm given the pull back distance of one test of the slingshot. I've found the k constant by finding force with f=ma, but I need to find the pull back distance using the same slingshot in order to propel the object a certain distance. My question is that because the distance seems to have no effect on the force, (because it is only mass times acceleration), if I solved for the pull back distance with the force, wouldn't I get the same pull back distance that i used with the first equation?


Homework Equations


F=-kx


The Attempt at a Solution

 
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You will have to be more specific about the problem statement. Since F = kx, as you pull back the slingshot more, x increases, so therefore, F increases. And since F_net = ma, since F is now larger when you pull the slingshot back, then the object in the sling will accelerate more during its period of contact with the sling, until it leaves it. And since it accelerates more, then it's speed will be higher when it leaves the sling, and will travel a greater distance. hcceleration of the object in the slingshot is not the acceleration of gravity in either case.
 

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