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

AI Thread Summary
The discussion focuses on proving that the distance an object launched by a rubber band decreases as its mass increases, using algebraic principles. It applies Hooke's Law, stating that the rubber band acts like a spring with a constant force when displaced equally for different masses. According to Newton's Second Law, a constant force results in inversely proportional acceleration to mass, meaning as mass increases, acceleration decreases. This relationship leads to a kinematics problem where the distance traveled is affected by the object's mass. The key takeaway is that increased mass results in decreased acceleration, ultimately reducing the launch distance.
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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