Spring constant, find height of projectile

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Homework Help Overview

The discussion revolves around a physics problem involving a dart shot vertically from a catapult, focusing on the relationship between spring constant, mass, and height achieved by the projectile. The subject area includes concepts of energy conservation, kinetic energy, and potential energy.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the dart's velocity as it leaves the catapult and question whether gravitational potential energy was adequately considered. There is also a suggestion to use conservation of energy as a more effective approach to the problem.

Discussion Status

The discussion is active, with participants providing feedback on calculations and suggesting alternative methods to approach the problem. There is an exploration of the implications of energy conservation in the context of the problem.

Contextual Notes

Participants are navigating the assumptions regarding energy types involved in the problem, including kinetic, gravitational potential, and elastic potential energy. There is an indication of a need to clarify the specific question asked in the original problem statement.

subopolois
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Homework Statement


A 48 gram dart is shot vertically upwards from a catapult with a spring constant of 350 N/m. The catapult is initially stretched from the equilibrium point by 21 cm. What is the height above the starting point reached by the dart?

Homework Equations


KE=PE, rearranging to find h gets h= v^2/2g

find the velocity as it leaves the catapult as v= d(sqrt(k/m))

The Attempt at a Solution


v= 0.21m (sqrt(350Nm/0.048kg))
= 17.93 m/s

h= (17.93m/s)^2 / 2(9.81m/s^2)
= 16.38 m

does this seem right?
 
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Your work looks good. But did you answer the specific question that was asked?
 
Sorry, subopolois. I read your post too quickly.

When you calculated the speed at which the dart leaves the catapult, did you take into account the increase in gravitational potential energy of the dart? How did you get the formula v = d√(k/m)?
 
I did not, how would i do that?
I did take gravity into account when i found the height...
 
You could find the speed at which the dart leaves the catapult by using conservation of energy. You will need to include kinetic energy, gravitational potential energy, and elastic potential energy.

There is a better approach to the problem. You don't need to find the speed at which the dart leaves the catapult. Is energy conserved overall between the point of release and the point where the dart reaches the highest point?
 

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