how will the weight of a body be affected when it falls with its terminal velocity?

Question

My book says that it will be 0 as net force on body is 0. But I reason that it will be mg b'cos the reaction offered by liquid is mg.
Which ans is correct?
I would be grateful if you clear my conceptual doubt.
Thank you

Answer 1

When an object falls through the Earth's atmosphere, it is subject to the force of gravity pulling it down, and the resistance force of air friction acting up. The total force down acting on the object is then simply:

Total Force=Gravity-Friction

the force of gravity acting on an object of mass m is mg, and the magnitude of this force will not change unless the mass changes or you travel sufficiently far from the surface of the Earth that g decreases; but if you are near the surface of the earth then the force of gravity on an object is mg

When an object reaches terminal velocity, the amount of friction acting up equals the amount of gravity acting down, so there is NO NET FORCE acting on an object falling at terminal velocity. If there is no net force, there is no acceleration on the object (this is the meaning of Newton's Second Law), and the object continues to move in a straight path down at a constant speed.

Your book is correct to say that there is no net force on the object. If you placed your object on a scale and could monitor the scale reading as the object fell; the scale would register the "normal" weight of the object once it reached terminal velocity. Before reaching terminal velocity, the object would still be accelerating down, and the scale would register a value LESS than the "normal" weight of the object. In fact, if the object were falling with no friction on it, the object would not record a weight on the scale at all.

Your simple question leads us into some interesting nuances, but your book is quite correct in stating that an object falling at terminal velocity has no NET forces acting on it, since gravity and friction balance out.

Answer 2

Book. Very. Wrong.

Your weight is defined as the force between you and the Earth.

Even though your net force is zero, your weight is NOT. You weigh the same whether you are moving or not.

The problem with the bathroom scale is the method by which it measures weight. It relies on a normal force exerted on it by the floor. If you place it under your feet as you fall, the bathroom scale simply cannot measure your weight.

People often refer to the "feeling of weightlessness" as the net force you talk about when you reach terminal velocity. You feel no net force, so it's *like* floating. Yet, your weight still has not changed - it's the fact that there is another force canceling the gravitational pull of the Earth.

Answer 3

The book is correct. At the terminal velocity, the body starts falling with a constant velocity. This constant velocity is under all the external forces (including its weight). And as the velocity is not changing, the accn. is zero. Now accordong to N's law of motion, there should be no force acting on it. ( P = m.accn). Hence it must fall in "Free fall condition"

Answer 4

The only factors that affect gravity's acceleration, which is always -9.8 m/s otherwise, is air resistance (or air friction). Mass, weight, and velocity do not alter gravity's acceleration. EDIT: I don't know who the idiot was who thumbs downed my answer was, but this is true. Weight in fact does not affect Terminal Velocity, which is when an object is in free fall under the earth's atmosphere, hence the reason why it's called terminal.

Answer 5

The answer depends on your definition of weight.
If you define weight as the magnitude of attraction between the Earth and another body, then the weight remains the same. When I stand on a bathroom scale my weight is displayed as 200 pounds, but the net force on my body is zero, my weight down, the scale is pushing up. The same is true of the body falling at terminal velocity, the air resistance is pushing up and is equal to the weight pushing down.

When a body is floating in water, the weight down is equal to the buoyant force up, but it's weight doesn't change.

Now if you define weight as what a bathroom scale would read, and I don't like that definition, a scale with a rock resting on it, all submerged in water would read less than the same setup in air therefore it would weigh less.

To keep things simple lets just define weight as "mg".

Answer 6

the book is correct, the net force should be zero so that the object will not experience any accelaration. Terminal velocity is a constant velocity which results to the balance of forces. Newton's law states that an object experiencing a force F = ma will continue to accelarate unless a force act upon it. It is a wrong perception that any object that moves is accelarating or experiencing a force. When the object's velocity is changing over time, then we can say that that object is experiencing a force. Consider this: an object with constant velocity = 0 m/s and and another object with constant velocity = 2 m/s. Both are not experiencing any force or that summation of forces = 0. I hope I did help you.

Answer 7

An object's weight, or the "actual weight", is the downward force exerted upon it by a gravitational field.

Weight is a measurement of the gravitational force acting on an object.

By contrast, an object's apparent weight is the (upward) force (the normal force, or reaction force), that opposes the (downward) acceleration of a supported object, preventing it from accelerating.

By these defenitions, an objects weight can never be equal to zero unless g = 0.

When objects attain terminal velocity, its apparent weight = the actual weight.

The net force which is neither actual weight nor apparent weight is zero.

Your book is wrong and
if you mean by 'weight' the upward force then that is also wrong.

The upward force is called apparent weight.

Answer 8

The book is wrong.

The weight depends on which frame you measure it in. In the Earth rest frame it never changes - it is always mg.

In the objects rest frame the weight is give by m multiplied by the net acceleration - g minus the accleration of the reference frame. If the body is in freefall, the net acceleration is g - g = 0, and its weight is zero. But at terminal velocity the objects rest frame is not accelerating, and so the net acceleration is once again g and the weight is mg.

Whichever way you look at this one the weight is mg and the book is wrong.

Answer 9

I feel that the book is right, because the body has acquired a terminal velocity, and the velocity does not increase after that.. This shows that, as such, no force is acting on the body..

Answer 10

You are correct, your book is wrong.

At terminal velocity, acceleration is zero, weight is mg


Reply to Cruz J

Don't confuse net force with weight. If I am standing on the bathroom scales, my acceleration and net force are zero but my weight is about 75 Kg.

As far as this question is concerned acceleration is zero, so the answer is clear.

But how should we define weight under acceleration. We could define it as mg, so weight would not change unless the gravitational field changed. Or should we define weight as the vector sum of mg and aceleration (with opposite sign). By this definition weight would be zero if falling freely in a vacuum or if in an orbiting satelite. If in an aeroplane flying a horizontal circle with the wings banked at 60 deg, weight would be twice normal.

Epidavros has the best answer to this, it depends on the reference frame.