[jsmith6131]

if a body falls at terminal velocity x m/s at time ta and then reaches a new terminal velocity after opening a parachute at time tb why do both have the same air-resistance acting on them?

[jsmith6131]

i thought drag = air resistance = weight of displace fluid

[chaz1992]

Terminal velocity means the person travels at the same speed downwards. This means there is no acceleration and so the force upward (air resistance) = the force downwards (weight) and so at any point where terminal velocity is reached, the force caused by air resistance equals the sky diver's weight.

The reason why the second terminal velocity is less than the initial terminal velocity is because opening a parachute has more drag (greater surface area exposed to the air) than free falling and so the resistive force equals the weight at a much lower velocity.

[The Mr Z]

at both times the body is moving at terminal velocity, so is in equilibrium (not accelerating)

hence by Newton's first Law (or second, your choice) there is no net force acting on it at both times.

in both situations it has two forces acting on it in opposite directions;its weight, and air resistance. it has the same mass so assuming gravity to be constant it has the same weight at both times.

weight + air resistance = 0 in both cases, if weight is the same in both cases air resistance must be the same (and equal to the weight)



the weight of displaced fluid doesn't come into it at all, that's to do with buoyancy.

[jsmith6131]

so air resistance is the same as drag? which always acts in the opposite direction to motion?

[jsmith6131]

but not upthrust which is weight of displace fluid

[chaz1992]

(Original post by jsmith6131)
so air resistance is the same as drag? which always acts in the opposite direction to motion?

Essentially yes. Air resistance is the drag an object experiences as it is moving through air.

Ask yourself:

Is there any acceleration?

In this case there isn't as the body is travelling at constant speed.

Newton's Second Law tells us resultant force = mass x acceleration. As there is no acceleration, there is no resultant force and so the body is in equilibrium.

If something is in equilibrium it means all forces in all planes are balanced.

The forces in the vertical plane are air resistance and weight.

As the system is in equilibrium air resistance = weight in both scenarios.

[jsmith6131]

so it should be for a falling body
weight = upthrust + drag
BUT as drag is so small due to the exremely small density of air we ignore drag so
weight = upthrust

[The Mr Z]

(Original post by jsmith6131)
so it should be for a falling body
weight = upthrust + drag
BUT as drag is so small due to the exremely small density of air we ignore drag so
weight = upthrust

no, we ignore upthrust, as upthrust from air is negligible.

upthrust comes from the difference in pressure between the top and bottom of a body. For air and small bodies, this is very very small, due to the small density of air.

However, as drag is related to both density and velocity squared (and factors involving shape), the fast speed of descent means that drag is actually a substantial force and needs to be considered.

(Original post by jsmith6131)
so air resistance is the same as drag? which always acts in the opposite direction to motion?

but not upthrust which is weight of displace fluid

yes, air resistance is a drag force, and will act against motion. If you fly horizontally air resistance is horizontally against you.

up-thrust is always in the direction of decreasing pressure (upwards)

[chaz1992]

(Original post by jsmith6131)
so it should be for a falling body
weight = upthrust + drag
BUT as drag is so small due to the exremely small density of air we ignore drag so
weight = upthrust

You're getting confused here. A few years back I too didn't get the difference between upthrust and air resistance but I do now and so can explain it.

If you think about friction you'll discover it is a resistive force. It cannot create movement only hinder it (If you put something on a table no matter how long you wait, friction won't move it but if you give it a push, it'll move for a bit and stop as friction slows it down and stops it). Air resistance and drag is like this. Air resistance or drag won't move an object, it'll only hinder its motion. Air resistance or drag won't ever cause an object to move upwards, it'll only slow its downward movement. It will always act in the direction that opposes motion.

Upthrust is a FORCE that CAN move an object and CAN hinder its movement. When you apply a force acting upwards this is upthrust. A hot air balloon is a good example of this. When it sets off, the fire causes air to rush upwards as hot air rises. This is a force acting upward and so it starts to move upwards. The forces downwards are the weight and the air around it which slows it down. So when it sets off upwards, the upthrust from the fire acts upwards and the weight and air resistance acts downwards. When the hot air balloon wants to got back on the ground, upthrust is reduced (flames are turned down) and weight acts downwards so it starts to move downwards. As it does this air resistance acts upwards (in the opposite direction of motion) to hinder movement.

Your example with the sky diver, there is no upthrust. There is NO physically applied force upward that if increased can cause motion upwards. There is just the weight and air resistance.

Air resistance/drag is NOT upthrust.

Hope that makes sense. The Mr Z has explained it better than I have.

[Euclid]

(Original post by The Mr Z)
no, we ignore upthrust, as upthrust from air is negligible.

upthrust comes from the difference in pressure between the top and bottom of a body. For air and small bodies, this is very very small, due to the small density of air.

However, as drag is related to both density and velocity squared (and factors involving shape), the fast speed of descent means that drag is actually a substantial force and needs to be considered.



yes, air resistance is a drag force, and will act against motion. If you fly horizontally air resistance is horizontally against you.

up-thrust is always in the direction of decreasing pressure (upwards)

You also find, since the force of air resistance is proportional to the square of the velocity, the v^2 term in the equation of motion, leads you to find (when you solve the differential equation) that v(t) ~ tanh (...t), in other words the terminal velocity is an asymptote and is therefore never attained.

[The Mr Z]

(Original post by Euclid)
You also find, since the force of air resistance is proportional to the square of the velocity, the v^2 term in the equation of motion, leads you to find (when you solve the differential equation) that v(t) ~ tanh (...t), in other words the terminal velocity is an asymptote and is therefore never attained.

True, although far beyond the scope of the question and OP's course.

[jsmith6131]

thanks guys