Question

The three forces acting on a hot-air balloon that is moving vertically are its weight, the force due to air resistance and the upthrust force. The hot-air balloon descends vertically at constant speed. The force of air resistance on the balloon is F. Which weight of material must be released from the balloon so that it ascends vertically at the same constant speed? A F B 2F C 3F D 4F

Answer 1

Explanation :

The forces acting on hot- air balloon are:

Weight, (W)

Force due to air resistance, (F)

Upthrust force, (U)

Its weight W is acting in downward direction. The upthrust force U acts in upward direction. When the balloon is moving upward, the air resistance is in downward and vice versa.

In this case, the hot-air balloon descends vertically at constant speed.

so, $a=0$

and $F=ma=0$

so, $W = F + U$ ....................(1)

when it is ascending let the weight that it is releasing is R, so

$(W-R) + F = U$..........(2)

solving equation (1) and (2)

$(W-R)+F=W-F$

$R=2F$            

2F is the weight of material that must be released from the balloon so that it ascends vertically at the same constant speed.

Answer 2

Answer:  (B) .2 F

Explanation :

The weight is always downward and it is a constant.

The upthrust fore U acts  upward and it has always same value as it depend on the difference in height between the top and bottom surface of the air balloon.

The direction of the force due to air resistance depends on the motion and air resistance always opposite motion. air resistance downwards that means the air balloon will ascending and air balloon will descending then air resistance is upwards.

So, air resistance depends on speed .

When air balloon descending at constant speed

Air resistance = F

A constant speed means acceleration is zero that means the resultant force is zero.

W = F + U.....(I)

When air balloon ascending

air resistance = F downwards

Some weight of the material needs to be released for the resultant force to be zero.

Suppose, the weight to be released be R.

(W - R) + F = U......(II)

From equation (I)

U = W- F....(III)

The upthrust force has same value throughout the motion.

Now, put the value of U in equation (I)

W - R + F = W - F

-R = - F - F

R = 2 F

Hence, this is the required solution.