Physics question?

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/m3. 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/m3. What is the weight of the suitcase ? show work

whats w in eq 1

Answer 1

At the first location, the buoyant force equals the weight of the displaced air. This is the balloon's volume V, times the air's weight density (2.6 N/m^3)

Buoyant force (posn 1) = V*(2.6 N/m^3)

And since the balloon is "hoovering," the buoyant force on the balloon exactly balances the two weights; which are the weight W of the suitcase, plus the weight mg of the balloon.

total weight = buoyant force

W + mg = V*(2.6 N/m^3) [eq. 1]

At Position 2, the new weight of the balloon (no suitcase), balances the new buoyant force. Using reasoning similar to above, that gives you this equation:

mg = V*(2.1 N/m^3) [eq. 2]

We don't know the value of V, so we would like to eliminate that from the equations. We can do that as follows:

Rearrange eq. 2:

V = mg/(2.1 N/m^3)

Substitute that into eq. 1:

W + mg = (mg/(2.1 N/m^3))*(2.6 N/m^3)

Now just solve for W. The value of "m" is given in the question (15 kg); and "g" is of course 9.8 m/sec²