What is the equation for a spring launcher?

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Homework Help Overview

The discussion revolves around deriving the equation for the initial launch speed of a spring launcher, incorporating the potential energy of the spring, mass, and launch angle. Participants express confusion regarding the correct formulation and integration of these elements.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants attempt to formulate the relationship between potential energy, kinetic energy, and gravitational work, while questioning how to include the angle of launch in their equations. There are multiple attempts to express the energy balance involved in the spring launcher setup.

Discussion Status

Several participants have shared their attempts at formulating the equation, indicating a collaborative exploration of the problem. While some guidance has been offered, there is no explicit consensus on the correctness of the approaches presented, and confusion remains regarding the integration of the angle.

Contextual Notes

Participants express frustration over their understanding and the need for clarity on how to incorporate the launch angle into their equations. There is an emphasis on the requirement for a generalized equation, which may be contributing to the complexity of the discussion.

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Homework Statement
What is the generalized equation of the initial launch speed for a spring launcher at different angles? Use PE of the spring, mass, and angle in the equation.
Relevant Equations
Ei = Ef
PEspring = 1/2 kx^2
KE = 1/2 mv^2
I am really stuck and confused. I just need the equation. Thanks!

Here is my attempt at solving:

PEspring = 1/2m(Vx^2 +Vy^2)
 
Last edited:
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Riman643 said:
Problem Statement: What is the generalized equation of the initial launch speed for a spring launcher at different angles? Use PE of the spring, mass, and angle in the equation.
Relevant Equations: Ei = Ef
PEspring = 1/2 kx^2
KE = 1/2 mv^2

I am really stuck and confused. I just need the equation. Thanks!
What have is your assessment so far?
 
This is my attempt

PEspring = 1/2m(Vx^2 +Vy^2). I know this is not right. I am confused and have been trying to figure this out for two days now. I do not know how to incorporate the angle of the launcher.
 
So here is my next attempt

PEspring = Wgrav + KE
(1/2)kx^2 = mgsin(theta)x + (1/2)mv^2

Is this correct?
 
Last edited:
Riman643 said:
So here is my next attempt

PEspring = Wgrav + KE
(1/2)kx^2 = mgsin(theta)x + (1/2)mv^2

Is this correct?
Looks right.
 

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