Question

A hot-air balloon and its basket are accelerating upward at 0.265 m/s2, propelled by a net upward force of 688 N. A rope of negligible mass connects the balloon and basket. The rope tension exceeds the basket's weight by 79.8 N.

Answer 1

Question: Find, separately, them mass of the balloon and the basket (incidentally, most of the balloon's mass is air)

Answer:

The mass of the balloon is 2295 kg, and the mass of the basket is 301 kg.

Step-by-step explanation:

Let us call the mass of the balloon
`m_1` and the mass of the basket
`m_2`, then according to newton's second law:

`(1). \:F = (m_1+m_2)a`,

where
`a =0.265m/s^2` is the upward acceleration, and
`F = 688N` is the net propelling force (counts the gravitational force).

Also, the tension
`T` in the rope is 79.8 N more than the basket's weight; therefore,

`(2). \:T = m_2g+79.8`

and this tension must equal

`T -m_2g =m_2a`

`(3). \:T = m_2g +m_2a`

Combining equations (2) and (3) we get:

`m_2a = 79.8`

since
`a =0.265m/s^2`, we have

`\boxed{m_2 = 301.13kg}`

Putting this into equation (1) and substituting the numerical values of
`F` and
`a`, we get:

`688N = (m_1+301.13kg)(0.265m/s^2)`

`\boxed{m_1 = 2295 kg}`

Thus, the mass of the balloon and the basket is 2295 kg and 301 kg respectively.