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

In summary, the conversation is about proving that the distance of an object launched by a rubber band decreases as its mass increases, using algebraic methods. The rubber band is treated as a spring that follows Hooke's Law, allowing for a constant force to be applied. From Newton's 2nd Law, it is determined that acceleration is inversely proportional to mass. This leads to a kinematics problem. JohnnyA42 also explains that with an increase in mass, acceleration must decrease according to Newton's 2nd Law.
  • #1
Nastyusha
6
0
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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  • #2
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.
 
  • #3
Can you explain that further? I'm not quite getting it.
 
  • #4
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.
 

What is the relation between the mass of an object and the distance it travels when launched by a rubber band?

The distance traveled by an object launched by a rubber band decreases as its mass increases. This means that the heavier the object, the shorter the distance it will travel when launched by a rubber band.

Why does the distance of an object launched by a rubber band decrease as its mass increases?

This is because the rubber band has a limited amount of energy that it can transfer to the object. When the mass of the object increases, more energy is required to launch it and the rubber band is not able to provide enough force to make the object travel a long distance.

Does the type of rubber band used affect the relation between mass and distance traveled?

Yes, the type of rubber band used can affect the distance traveled by an object. Different types of rubber bands have different elasticity, which can impact the force they provide to launch an object. Therefore, the relation between mass and distance may vary depending on the type of rubber band used.

How does the length of the rubber band affect the distance traveled by an object?

The length of the rubber band also plays a role in the distance traveled by an object. A longer rubber band will have more potential energy, allowing it to launch heavier objects a greater distance. On the other hand, a shorter rubber band may not have enough energy to launch a heavier object a significant distance.

What other factors may affect the distance traveled by an object launched by a rubber band?

Aside from the mass and length of the rubber band, other factors such as the angle of launch, air resistance, and the surface the object is launched from can also impact the distance traveled. These factors can either increase or decrease the distance traveled by the object.

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