Gravity

[sexycani]

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some quick questions on gravitational potential energy and acceleration when accounting for air resistance:

1) as an object gets farther and farther from earth, does its gravitational energy increase or decrease?

2) would a heavier object (greater inertia) reach the ground faster when launched up into the air, versus a lighter object? (What is the formula for this again?)

 

[shinbeats]

some quick questions on gravitational potential energy and acceleration when accounting for air resistance:

1) as an object gets farther and farther from earth, does its gravitational energy increase or decrease?

2) would a heavier object (greater inertia) reach the ground faster when launched up into the air, versus a lighter object? (What is the formula for this again?)

1) Gravitational potential energy has two formulas one is U= mgh which clearly indicates that as the distance increases the P.E increases. The other formula is P.E = -GMm/r which a lot of people mistake with as + and end up getting the whole concept incorrect. Thus according to formula 2 since it's negative increasing the radius will actually increase P.E UNLESS you reach the point of infinity where P.E is of course 0.

2) if you are talking about a vacuum than NO both will reach the ground at the same time. However if you're accounting for air resistance than the heavier object . When air resistance plays a role, the shape of the object becomes important.
Formula is v= vo+at to determine the the time to the top of the peak with projectile motion where you set up v final = 0 and v initial to it's vertical component and plug in 9.8 m/s^2 for the g. You determine the time till reaching the top and multiply it by 2.

 

[ModusProbandi]

2) would a heavier object (greater inertia) reach the ground faster when launched up into the air, versus a lighter object? (What is the formula for this again?)

Yes. A heavier object would have a greater force due to gravity. Terminal Velocity is reached when the F(g) = F(air resistance). As you can imagine it takes a certain amount of time for the F(air resistance) to "catch up" to the force of gravity. Which one has the greater F(g)?

I assume both objects have the same shape.

 

[Rabolisk]

Yes. A heavier object would have a greater force due to gravity. Terminal Velocity is reached when the F(g) = F(air resistance). As you can imagine it takes a certain amount of time for the F(air resistance) to "catch up" to the force of gravity. Which one has the greater F(g)?

I assume both objects have the same shape.

I suppose, if you can assume that the distance is long enough that a terminal velocity will be reached.

 

[ilovemcat]

Q1: From a conceptual stand point, by increase height, you're increasing the capacity to do useful work - or more specifically, you're increasing the POTENTIAL (gravitational potential energy) to do work. For example, raising a ball from say, ground level to a platform 20 meters in the air; The ball being 20 meters higher has the capacity to do useful work. Once dropped, the gravitational "potential" is converted to kinetic energy. As a result, the ball speeds up, faster and faster until it slams into the ground. This is no different from pulling a slingshot. The further you pull the rubber band of a slingshot, the further the object will travel. However, instead of considering gravitational potential energy, the rubber band stores elastic potential energy instead. Just like gravitational energy was transformed into kinetic energy, this energy too is transformed into useful work (once you let go).