Why does increasing mass also increase kinetic energy and velocity?

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Homework Help Overview

The discussion revolves around the relationship between mass, potential energy, kinetic energy, and velocity in the context of falling objects. The original poster seeks clarification on why increasing mass seems to lead to increased kinetic energy and velocity, despite the principle that all objects fall at the same rate in the absence of air resistance.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the apparent contradiction between mass, potential energy, and kinetic energy, seeking to understand the underlying principles. Some participants clarify that kinetic energy is dependent on both mass and velocity, while others discuss the conservation of total energy in free fall.

Discussion Status

Participants are exploring different interpretations of the relationship between mass and energy. Some have provided insights into the conservation of energy and the independence of velocity from mass in free fall, indicating a productive direction in the discussion.

Contextual Notes

The original poster's inquiry is framed within the context of a homework assignment, with specific equations related to gravitational potential energy and kinetic energy mentioned. There is an emphasis on understanding the concepts rather than solving a specific problem.

aatari
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Homework Statement


Hi Guys, I don't have a particular problem that I need to solve but I need help with understanding a concept. So we agree that irrespective of mass of an object they will both fall at a same rate if there is no air resistance. However, why is it then when we increase the mass of an object, the potential energy increases, which as a result increases the kinetic energy and which would also increase the velocity of that object.

Isn't this contradictory? Or am I misunderstanding something? Please help!

Homework Equations


Eg = mgh
Ek = 1/2mv^2

The Attempt at a Solution

 
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aatari said:
why is it then when we increase the mass of an object, the potential energy increases, which as a result increases the kinetic energy and which would also increase the velocity of that object.
That is false. Kinetic energy is not velocity. It depends on both mass and velocity. Different mass, different KE for the same velocity.
 
For an object dropped from rest from a specific height, y = h, the total energy at h, is TE = PE + KE. At y = h, PE = mgh and KE = 0 (rest). So TE = mgh.

The value of TE calculated does not change as the object falls. At any y value along the path, the total energy is the same, this includes the point at y=0. So, at y = 0, TE = PE + KE --> mg0 + 1/2 mv2 = TE = mgh. The mass cancels out which makes the velocity independent of the mass.
 
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in a simple way...try imagining a bowling ball falling from 1m on your hand vs a tennis ball falling they're pulled at the same speed 9.8m/s just the mass differs the impact on your hand) that velocity is the same just if maybe your friend pushes it down while dropping it it increases the speed..
 
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