Can a Ball Climb Hill B? Potential & Kinetic Energy Explained

[indebluez]

jus one more qn on potenital n kinetic energy guys...

for instance a ball is at the top of hill A and now is let go...and after hill A there's one more hill/...hill B...and hill B is taller than hill A...


will the ball be able to climb hill B?

i noe its got to do with PE and KE...but i can't crack it...thawt abt it over the wkend...pleasezzzz help?

million thanxxxxxx:)

 

[arildno]

It may reach the top of hill B if its initial velocity at hill top A is larger than zero.
If "B" signifies the height of hill B, the minimum mechanical energy the ball has at the top of hill B is: mgB (i.e pure potential energy, no additional kinetic energy)

Since mechanical energy is conserved, the mechanical energy at A (MEA) must satisfy the following inequality to reach hilltop B:
MEA>=mgB

 

[indebluez]

thanx alot!

 

[BobG]

If the ball is at rest at the top of hill A, it'll never make it to the top of hill B.

The total mechanical energy stays constant and is equal to the sum of potential energy and kinetic energy. If the ball is at rest, it has no kinetic energy. When you let it go it loses potential energy, but gains kinetic energy (the total mechanical energy has to stay constant). On the way up, the kinetic energy will hit zero with all of the object's mechanical energy reflected as potential energy when the ball reaches the same height it started at (this assumes there's no energy lost due to friction, etc.)

Same idea as elliptical orbits, except the satellite is always starting with both potential and kinetic energy. When it's close to the Earth (least potential energy), the satellite's moving fast (most kinetic energy) - when it's at apogee (furthest point away from Earth with the most potential energy), the satellite moves slow (least kinetic energy). Total energy stays constant and the satellite follows the same orbit forever (theoretically, at least - if the funny shape of the Earth, the few molecules of atmosphere that exist in outer space, the gravitational tug from the moon, sun, and planets, photons from the sun, etc. are all ignored).