another physics problemm?

Question

A hot air balloon, with a mass of 15 kg., hoovers at an altitude of 7 km. where the weight density of the air is 2.6 N/m^3. If a suitcase is dropped from the balloon, the balloon rises to an altitude where the weight density of the air is 2.1 N/m^3. What is the weight of the suitcase ? show work

only reply if u have an answer

Answer 1

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Answer 2

This is meant to be a simple exercise. As such, you do not nead (and cannot from the info given) account for the expansion of the balloon as it rises. Assuming constant balloon volume, proceed:

The balloon always displaces a volume of air equal to its mass. This volume is:

V = m/d where m is the mass and d is the air density.

Since we assume constant volume, for the two cases:

m1/d1 = V = m2/d2
m2 = m1 * (d2/d1)

We are intersted in the difference between m1 and m2 (the weight that was dropped)

m1 - m2 = m1 - m1*(d2/d1) = m1*(d1-d2)/d1 = 15 kg *(2.6 - 2.1)/2.6 = 2.88 kg

I dropped the units off the air density since they all cancel.

Answer 3

We have to assume that the temperature difference and loss is negligible. Oh and there is no change in balloons volume.

The volume however is the elusive element.

Before drop
(m1 + m2)g=V[p(hot air) -p(cold air 1)]
m1 - mass of the balloon
m2 - mass of the suitcase
g - acceleration due to gravity (9.81 m/s^2)
V - volume of the balloon
p - density

So the weight of the suitcase must be
m2=V[p(hot air) -p(cold air 1)]/g - m1

After drop
m1 g=V[p(hot air) -p(cold air 2)]

Finally
m2=V[p(hot air) -p(cold air 1)]/g - V[p(hot air) -p(cold air 2)]/g
a little algebra
m2=V[p(cold air 2) - p(cold air 1)]/g
where
p(cold air 1) - is air density at the release point
p(cold air 2) - is air density at 7 km up above

Answer 4

What a collection of complete BS for your answers...Ok look, this IS a basic physics problem disregarding air friction, rotational force, etc... First break down the 15.1 m/s into its J hat vector. Remember that I and J hat vectors are independent of each other so you need to solve using the Kinematic equations. Since we are talking about the time it takes for the force of the ball kicked acting against the force G. The point of the problem is to find how long it takes for the ball to reach a velocity of 0, the return to its original position. Remember the G force is gravitation constant (9.8 m/sec squared) Find the Vectors using trig: J^ = 15.1 m/s * sin(39.4)