Work done by air resistance compared to gravity

[Jengreef]

Assuming these two forces are opposing each other, is the work done by air resistance always less than the work done by gravity?

To be more general, does this apply to work done by any non-conservative force (friction, heat, etc.) compared to conservative forces? Are they always lesser in comparison?

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[shaboobly]

Assuming these two forces are opposing each other, is the work done by air resistance always less than the work done by gravity?

To be more general, does this apply to work done by any non-conservative force (friction, heat, etc.) compared to conservative forces? Are they always lesser in comparison?

air resistance is friction within the air so it is a nonconservative force. nonconservative forces like friction are negative because they oppose the movement (in the opposite direction) which makes them lesser in comparison. heat is not a force.

 

[Jengreef]

What about comparing the absolute value of work done by each? Would the non-conservative force still be lesser in magnitude?

 

[shaboobly]

What about comparing the absolute value of work done by each? Would the non-conservative force still be lesser in magnitude?

are you referring to the question in aamc 11 because i took it on tuesday and remember it pretty well. i got it right.

the air resistance is proportional to the square of the velocity, so that means the work done by the air resistance starts out small and increases until it reaches terminal velocity, in which case the force of gravity and air resistance are equal but opposite.

the result causes the work done by air resistance to be less than or equal to the work done by gravity.

in the cases of friction it is different. you can have material that has high static or kinetic coefficients and the work would be large, or something with small coefficients and the magnitude would be small.

 

[Jengreef]

If the forces are equal, how is the magnitude of one lesser than the other?

 

[shaboobly]

If the forces are equal, how is the magnitude of one lesser than the other?

you didnt read my post above.

 

[Jengreef]

work done by the air resistance starts out small and increases until it reaches terminal velocity,

I'm guessing this is the key to the answer? So while work done by gravity is constant and equal to the work done by air resistance at its maximal value, the total work done by gravity is greater than the work done by air resistance because air resistance has to build up to terminal velocity while gravity does not.

Does that imply that the magnitude of work done by air resistance will always be lesser than the magnitude of work done by gravity?

 

[shaboobly]

I'm guessing this is the key to the answer? So while work done by gravity is constant and equal to the work done by air resistance at its maximal value, the total work done by gravity is greater than the work done by air resistance because air resistance has to build up to terminal velocity while gravity does not.

Does that imply that the magnitude of work done by air resistance will always be lesser than the magnitude of work done by gravity?

yea i think i kind of worded it wrong. the FORCE of the air resistance is small (work is Fd) in the beginning because it is proportional to the square of the velocity, and as the object accelerates from gravity, the velocity will increase until the terminal velocity is reached in which case the force of gravity is equal to the force of air resistance and the object is now moving in translational equilibrium (minus effects of wind etc).

since work depends on the magnitude of the force, the constant, larger force of gravity cause the work done by gravity to always be greater than the work done by air resistance, because like i said (and it seems you understand this now) the air resistance depends on the velocity.

or you can think of it in real life. if the work done by air resistance was larger than the work done by gravity, the object would be falling up, not down.

 

[Jengreef]

or you can think of it in real life. if the work done by air resistance was larger than the work done by gravity, the object would be falling up, not down.

Perhaps, but wouldn't this imply that once work done by air resistance and gravity are equal to each other, that the person would neither fall up or down?

During translational equilibrium, what determines what direction an object is moving? Is it the direction of whatever initial velocity that object began from? That is to say, since gravity was initially greater, thereby directing the direction of the initial velocity, once work done by gravity and air resistance are equal in magnitude, is the person falling down only because that's the original direction of his initial velocity?

 

[shaboobly]

Perhaps, but wouldn't this imply that once work done by air resistance and gravity are equal to each other, that the person would neither fall up or down?

During translational equilibrium, what determines what direction an object is moving? Is it the direction of whatever initial velocity that object began from? That is to say, since gravity was initially greater, thereby directing the direction of the initial velocity, once work done by gravity and air resistance are equal in magnitude, is the person falling down only because that's the original direction of his initial velocity?

no because the person is already moving, it just so happens when the force of gravity, not work, and air resistance are equal then there are no net forces acting and the person is moving with constant velocity in translational equilibrium. one of the definitions of translational equilibrium is that the object is moving at constant velocity or zero velocity (not accelerating because F=ma and F is zero because air resis and gravity are equal).

if the work done by air resistance (and it never is) greater than the work done by gravity, more energy would be going to move the object against the gravitational force and it would then be moving away from the earth, not towards it. however, since the work by gravity is always greater than the work done by air resistance, the object eventually ends up on the ground and is now in static equilibrium (where the gravitation force is equal to the normal force and no other forces are acting).

edit: actually misread your question. yes when the work of gravity is equal to the work of air resis the object wont move (static equil, but that is never the case)

 

[Jengreef]

Ah thanks