Work done by a balloon that is rising

[shirozack]

Homework Statement

a 0.01kg balloon rises 20m with an upward constant force of 1N. what is the work done by this upward force?

Relevant Equations

wd = f x d

the answer just takes wd = 1N x 20m = 20J.

My question is why does it not account for the weight?

In physics, when we say work done by the upward force, do we just take that force or must we calculate what the net force is?

the next part of the qn then asks,
"gpe + ke = work done by this upward force. "
"why is the balloon's KE lesser in reality ?"

the answer states it is due to some energy being used to counter air resistance.
i would like to know if the answer can also be " some energy is used to counter the weight"?

thanks.

 

[BvU]

My question is why does it not account for the weight?

Who says it doesn't ?

In physics, when we say work done by the upward force, do we just take that force or must we calculate what the net force is?

The former.

the next part of the qn then asks,
"gpe + ke = work done by this upward force. "
"why is the balloon's KE lesser in reality ?"

the answer states it is due to some energy being used to counter air resistance.
i would like to know if the answer can also be " some energy is used to counter the weight"?

The energy 'to counter the weight' is the change in gpe, so already accounted for.

$\$

 

[Steve4Physics]

I'd already written this before I saw @BvU had replied. So I'll post it anyway in case it helps..

@shirozack, you could try this exercise...

An object weighs 30N.
You apply an upwards force, F, which make the object rise.
F and the object’s weight (30N) are the only forces on the object (you are in a vacuum chamber!).

When the object has risen 5m:

Q1 What is the object’s change in GPE?
Q2 How much work was done by the weight (remember weight acts downwards)?

You are now told that force F is 40N upwards.

Q3 How much work was done by the 40N force?
Q4 What was the object's change in KE?
Q5 What was the total force on the object?
Q6 How much work was done by the total force?

If you've answered correctly you should have found:

i) The answer to Q2 is the negative of the answer to Q1.
ii) The answers to Q4 and Q6 are the same.

If you do then analysis with symbols rather than values, you can prove i) and ii)) are always true.

Then you can consider how any air resistance would have changed your answers!

 

[shirozack]

so 30N of the 40N upwards force is used to counter the 30N of the weight, some work done by the upwards force is used to counter the work done by the weight.
and the other 10N is used to give the object KE?
so the net force gives the KE?
since some net force is used to counter air resistance, the available force left will have lesser KE.

 

[kuruman]

so the net force gives the KE?

No, no and no. The net force is mass times acceleration. It changes the kinetic energy if it has a component along the direction of motion. If the net force is zero the object will rise at constant velocity and the kinetic energy will not change. The change in kinetic energy is equal to the work done on the object by the net force.

since some net force is used to counter air resistance, the available force left will have lesser KE.

The net force is the vector sum of all the forces. Here you have gravity (down), buoyant force (up) and air resistance (down). The net force is the sum of all three. You are not told anything about the air resistance so you cannot say anything about the kinetic energy of the balloon unless you assume that air resistance is not there. That assumption is necessary to answer Q4, Q5 and Q6.

 

[Steve4Physics]

In addition to what @kuruman said...

so 30N of the 40N upwards force is used to counter the 30N of the weight

That's one intuitive way to think about it. Another way is this: the vector-sum of the 2 forces is 10N upwards, so the object behaves the same as if there were a single force of 10N upwards.

some work done by the upwards force is used to counter the work done by the weight.

Not keen on use of the word 'counter'. To get the total work done on an object, we just add together the work done by each individual force, remembering values can be positive or negative.

and the other 10N is used to give the object KE

You have to use words more carefully. You mean:
'The work done by the net (10N) force equals the change in the object's kinetic energy.'

so the net force gives the KE?

The work done by the net force on an object equals the change in the object's kinetic energy.
(This idea is important and is called the 'work-energy theorem'.)

since some net force is used to counter air resistance, the available force left will have lesser KE.

Air resistance will reduce the magnitude of the net force. Therefore less work will be done by the net force. Therefore the change in KE will be smaller.

Suppose work done by air resistance = -30J:
Change in KE = (work done by weight) + (work done by F) + (work done by air resistance)
= (-150)+ 200+(-30) = 20J.

Don't forget your original question about GPE. The work done by weight is (-change in GPE). For example, if work done by weight = +1234J, the change in GPE = -1234J.

Change in KE = (work done by weight) + (work done by F) + (work done by air resistance)
is equivalent to
Change in KE = (-change in GPE) + (work done by F) + (work done by air resistance)

 

[DrBanana]

Also, the change in potential energy is the negative of the work done by the gravitational force because potential energy is defined that way (and it can be defined that way because the gravitational force is a conservative force).

 

[jbriggs444]

None of the other forces acting on the balloon are relevant.
The change in kinetic energy (if any) of the balloon is irrelevant.
The change in gravitational potential energy of the balloon is irrelevant.

We are asked for the work done by a particular force. We are given the value of the force and the distance over which it acts. That is all we need to calculate the work done by that force.

 

[kuruman]

None of the other forces acting on the balloon are relevant.
The change in kinetic energy (if any) of the balloon is irrelevant.
The change in gravitational potential energy of the balloon is irrelevant.

We are asked for the work done by a particular force. We are given the value of the force and the distance over which it acts. That is all we need to calculate the work done by that force.

I am not sure that we have the complete statement of the problem as given to OP. See OP's statement below.

the next part of the qn then asks,
"gpe + ke = work done by this upward force. "
"why is the balloon's KE lesser in reality ?"