Distance of an object launched by a rubber band decreases as its mass increases

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Homework Help Overview

The discussion revolves around understanding the relationship between the mass of an object and the distance it travels when launched by a rubber band, framed within the context of physics principles such as Hooke's Law and Newton's Second Law.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the application of Hooke's Law and Newton's Second Law to analyze the effect of mass on distance traveled. Questions arise regarding the interpretation of these laws and their implications in the context of the problem.

Discussion Status

Some participants have provided insights into the physics principles involved, suggesting that the force applied by the rubber band remains constant while the mass increases, leading to a decrease in acceleration. However, there is a request for further clarification on these concepts, indicating that not all participants fully grasp the reasoning presented.

Contextual Notes

The original poster seeks algebraic proof, which may influence the direction of the discussion and the types of explanations provided. There is an emphasis on understanding the underlying physics rather than deriving a final solution.

Nastyusha
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I need to prove that the distance of an object launched by a rubber band decreases as its mass increases, algebratically. Can anyone help me? Thanks.
 
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Treat the rubber band as a spring that obeys Hooke's Law (F=-kx). If you displace the rubber band from equilibrium by the same amount for each mass, then the force you apply will be constant. From Newton's 2nd Law, if your force is constant, acceleration is inversely proportional to mass. Then it becomes a kinematics problem.
 
Can you explain that further? I'm not quite getting it.
 
Nastyusha said:
Can you explain that further? I'm not quite getting it.

JohnnyA42 wanted to point this out: from Newton's 2nd law you have F / a = m. Since F is constant, if you increase m, a must decrease.
 

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