Need help with force of spring needed to launch mass from catapult

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SUMMARY

The discussion focuses on calculating the spring constant required to launch a 3 kg mass from a catapult at an angle of 30 degrees, achieving a launch velocity of 20 m/s. The gravitational acceleration is specified as 9.81 m/s², and the distance available for the mass in the catapult is 2 m. Key formulas mentioned include the conversion of spring potential energy to kinetic energy, taking into account the gravitational potential energy change due to the angle of launch.

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  • Understanding of Newton's laws of motion
  • Familiarity with the concepts of kinetic and potential energy
  • Knowledge of spring mechanics and Hooke's Law
  • Basic trigonometry for angle calculations
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  • Calculate the spring constant using the formula: K = (mv²)/(x²), where m is mass, v is velocity, and x is the compression distance.
  • Explore the relationship between gravitational potential energy and launch angle in projectile motion.
  • Study the principles of energy conservation in mechanical systems.
  • Review the effects of launch angle on projectile distance and trajectory.
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Mechanical engineering students, physics enthusiasts, and anyone involved in designing or analyzing catapult mechanisms and projectile motion.

DannyD
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Hi All

I need help with a physics calculation.

I have a mass of 3kg that has to be launched for Earth (9.81m/s^2 gravitational acceleration) at an angle of 30 degrees from horizontal from a catapult. The distance the mass can travel in the catapult is 2m.

What I need to know is what is the spring constant that the spring needs to have in order for the mass to leave the catapult at 20m/s?

Kind regards
Danny
 
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Are you familiar with the formulas of energy?
 
Yes I am. I'm currently studying mechanical engineering, my brain is just still in holiday mode, if I can be directed in the right direction that would also help a lot.

Regards
 
Spring potential initial = Kinetic final
 
Cool, thanks!
 
But don't forget that the mass is launched at an angle, not horizontally, so that in addition to the KE change, the gravitational PE of the mass also changes, during its motion along the catapult.
 

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