Megan Rolls a Ball Down a Ramp

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Most recent answer: 10/22/2007

Q:

If a ball is running downward a ramp, why is it that when yous modify the height of the ramp, the brawl runs downwards the ramp faster?

– Bearding

A:

If you increment the steepness of the ramp, and so you will increment the acceleration of a ball which rolls down the ramp. This can be seen in two different ways:

1) Components of forces. Forces are vectors and have a direction and a magnitude. The force of gravity points straight downward, but a ball rolling downwards a ramp doesn’t become straight down, information technology follows the ramp. Therefore, only the component of the gravitational force which points forth the management of the brawl’s move tin accelerate the ball. The other component pushes the ball into the ramp, and the ramp pushes back, so there is no acceleration of the ball into the ramp. If the ramp is horizontal, and then the brawl does not accelerate, as gravity pushes the ball into the ramp and not forth the surface of the ramp. If the ramp is vertical, the ball merely drops with acceleration due to gravity. These arguments are inverse a bit past the fact that the ball is rolling and not sliding, simply that only affects the magnitude of the acceleration but non the fact that it increases with ramp steepness.

ii) Work and energy. The modify in potential energy of the ball is its mass times the alter in meridian (only the vertical component counts — horizontal displacements do not change gravitational potential energy) times the local gravitational acceleration grand. This loss of gravitational potential energy shows up as an increase in kinetic energy. If the brawl falls a farther distance vertically, information technology will have a greater kinetic free energy and be going faster. Again, the kinetic energy is shared betwixt the motion of the brawl going somewhere, and the rotation of the ball, and and so the details of the acceleration depend on the ball (is information technology hollow or solid?), but the dependence on the steepness of the ramp is the aforementioned.

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Tom

(published on 10/22/2007)

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Megan Rolls a Ball Down a Ramp

Source: https://van.physics.illinois.edu/QA/listing.php?id=183