Max Ball Height: No Mass Needed

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SUMMARY

The maximum height of a ball thrown directly upward with an initial velocity of 10.0 m/s, neglecting friction, is calculated to be 5.1 meters. The relationship between kinetic energy (Ek) and gravitational potential energy (Eg) is established through the equation Ek = Eg, leading to the conclusion that mass cancels out in the calculations. This demonstrates that the mass of the ball is irrelevant when determining the maximum height, as gravity accelerates all masses equally in a vacuum.

PREREQUISITES
  • Understanding of kinetic energy (Ek) and gravitational potential energy (Eg)
  • Familiarity with the equations Ek = 1/2mv^2 and Eg = mgh
  • Basic knowledge of gravitational acceleration (9.81 m/s²)
  • Concept of neglecting air resistance in physics problems
NEXT STEPS
  • Study the principles of energy conservation in physics
  • Explore the effects of air resistance on projectile motion
  • Learn about gravitational acceleration and its implications for different masses
  • Investigate real-world applications of projectile motion in sports and engineering
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the principles of motion and energy conservation.

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Homework Statement


you throw a ball directly upward, giving it an initial velocity of 10.0 m/s. neglecting friction, what would be the maximum height of the ball? (explain why you do not need to know the mass of the ball)



Homework Equations


now the problem itself i understand.

we need Eg=mgh, Ek=1/2mv^2



The Attempt at a Solution


Ek=Eg
1/2mv^2 = mgh
1/2v^2 = gh
1/2(10.0)^2 = 9.81h
50/9.81 = h
h = 5.1m

i understand that we do not have mass and so it must cancel out, but i am confused as to why we do not need to know the mass?
 
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What falls faster a feather or a cannon ball? (this problem assumes 0 resistance)
 
neglecting air friction, neither..
meaning mass doesn't matter
 
So you're saying that gravity accelerates all masses in an equal manner. This is correct. What is the one force acting upon the ball after you release it?
 
only gravity (in this instance because it says to neglect friction)
 
Yes, do you understand now why you don't need to know the mass of the ball?
 
i understand.
thank you
 

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