I posted something concerning this question earlier.. and thank you for checking and letting me know of my mistake.
I said that for a given velocity, the height does not depend on the mass of the ball. How could I explain this, besides the fact that when calculuting it, I don't need the mass?
Thanks again.
The balls initial momentum and gravity determine how long it is in the air. But the force of gravity is proportional to mass...Weight=mg
intialmomenum-mg*deltaTime=0
deltatime in the air= initialmomentum/mg
= mVi/mg= Vi/g
So because the force of gravity is proportional to gravity, as is momentum, mass is not revelent to the time in air. The time it is in the air determines its height as it goes up to its stopping point.
THanks for the explanation.
You're welcome! I'm glad I could help clarify the misconception.
To explain why the height reached by a ball does not depend on its mass, we can consider the principles of projectile motion.
When a ball is thrown into the air, its motion can be analyzed as two separate components: horizontal motion and vertical motion. The mass of the ball only affects its horizontal motion, but it has no impact on its vertical motion.
The vertical motion of the ball is determined by the force of gravity acting on it. According to the law of conservation of energy, the total mechanical energy of the ball (the sum of its kinetic energy and potential energy) remains constant throughout its flight, neglecting air resistance.
When the ball is thrown upwards, its kinetic energy decreases, and this energy is converted into potential energy as it gains height. Likewise, when the ball falls back down, its potential energy is converted back into kinetic energy.
The key point here is that the amount of potential energy gained by the ball depends on its height above the ground, not on its mass. The potential energy is given by the equation PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height.
However, since the mass of the ball is multiplied by the acceleration due to gravity and the height, these factors cancel each other out. This means that for a given vertical displacement (height), the mass of the ball does not affect the amount of potential energy gained or the final height reached.
In conclusion, mass does not play a role in determining the height reached by a ball because the potential energy gained only depends on the height itself, not on the mass of the ball.