A balloon of volume 2000m 3 is filled with hydrogen of density 0.09Kg/m 3 as shown in the figure below. If the mass of the fabric is 100kg and that of the pilot is 75kg, determine the greatest mass of equipment that can be carried by the balloon when operating in air of density 1.25kg/m 3 (4 marks

Tunatumia fomula ya masi, $m = \rho \times V$, ambapo $\rho$ ni msongamano na $V$ ni ujazo.

$$m_{\text{hidrojeni}} = \rho_{\text{hidrojeni}} \times V$$ $$m_{\text{hidrojeni}} = 0.09 \text{ kg/m}^3 \times 2000 \text{ m}^3$$ $$m_{\text{hidrojeni}} = 180 \text{ kg}$$

Hii ndiyo masi ya juu kabisa ambayo puto inaweza kuinua.

$$m_{\text{hewa iliyoondolewa}} = \rho_{\text{hewa}} \times V$$ $$m_{\text{hewa iliyoondolewa}} = 1.25 \text{ kg/m}^3 \times 2000 \text{ m}^3$$ $$m_{\text{hewa iliyoondolewa}} = 2500 \text{ kg}$$

Hii inajumuisha masi ya hidrojeni, kitambaa, na rubani.

$$M_{\text{jumla ya vipengele}} = m_{\text{hidrojeni}} + m_{\text{kitambaa}} + m_{\text{rubani}}$$ $$M_{\text{jumla ya vipengele}} = 180 \text{ kg} + 100 \text{ kg} + 75 \text{ kg}$$ $$M_{\text{jumla ya vipengele}} = 355 \text{ kg}$$

Ili puto iweze kuelea, masi ya hewa iliyoondolewa lazima iwe sawa na jumla ya masi ya puto na mizigo yake yote.

$$m_{\text{vifaa}} = m_{\text{hewa iliyoondolewa}} - M_{\text{jumla ya vipengele}}$$ $$m_{\text{vifaa}} = 2500 \text{ kg} - 355 \text{ kg}$$ $$m_{\text{vifaa}} = \boxed{\text{2145 kg}}$$