Why does velocity of object decrease when its height increases?
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Why does velocity of object decrease when its height increases
This problem is easiest solved, when you think in terms of potential and kinetic energy.
The potential energy of the ball is m*g*h (mass * height * gravity acceleration)
The kinetic energy is 1/2 * m * v squared. (mass * velocity squared)
What happens when you roll down, is that the potential energy is converted in to kinetic energy. The difference in potential energy is m*g* (h1-h2). So that's the amount of potential energy that’s going to be converted into kinetic energy.
When the ball reaches the end, m*g*(h1-h2) = 1/2 * m * v squared.
The mass is on both sides of the equation, and thus is cancelled out. g ( h1-h2) = 1/2 * v squared.
Thus the speed is only depending on the height difference.
NB: That’s assuming friction free motion. It doesn’t matter if the angle is large or small… the only things that builds up speed, is the conversion of potential energy. With a small angle, it will take longer to reach the final point, and final speed, but at h2, the same speed is reached, because the same amount of height was lost.
Increasing the mass will increase the potential energy… but it will also increase the energy needed to accelerate it to a certain speed by the same amount. Thus that cancels out in the end.
This problem is easiest solved, when you think in terms of potential and kinetic energy.
The potential energy of the ball is m*g*h (mass * height * gravity acceleration)
The kinetic energy is 1/2 * m * v squared. (mass * velocity squared)
What happens when you roll down, is that the potential energy is converted in to kinetic energy. The difference in potential energy is m*g* (h1-h2). So that's the amount of potential energy that’s going to be converted into kinetic energy.
When the ball reaches the end, m*g*(h1-h2) = 1/2 * m * v squared.
The mass is on both sides of the equation, and thus is cancelled out. g ( h1-h2) = 1/2 * v squared.
Thus the speed is only depending on the height difference.
NB: That’s assuming friction free motion. It doesn’t matter if the angle is large or small… the only things that builds up speed, is the conversion of potential energy. With a small angle, it will take longer to reach the final point, and final speed, but at h2, the same speed is reached, because the same amount of height was lost.
Increasing the mass will increase the potential energy… but it will also increase the energy needed to accelerate it to a certain speed by the same amount. Thus that cancels out in the end.
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