A hot-air balloon is accelerating upward under the influence of two forces, its

Question

A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon. In other words, ignore the balloon fabric and the basket.

The hot air inside the balloon has a density of 0.89 kg/m3, and the cool air outside the balloon has a density of 1.19 kg/m3.

What is the algebraic expression for the upward acceleration ay of the balloon? Express your answer in terms of the density ?C of the cool air outside the balloon, the density ?H of the hot air inside the balloon, and the magnitude g of the acceleration due to gravity. Upward is the positive direction.

Explanation / Answer

Let P = 1.19 density of cool air p = .89 density of hot air W = V P g weight of cool air w = V p g weight of hot air Fb = W - w buoyant force Fb = m a acceleration of balloon a = Fb / m = V g (P - p) / m substituting for W and w m = w / g = V p g / g = V p mass of air in balloon a = g (P - p) / p = (1.19 - .89) * 9.8 / .89 = 3.3 m/s^2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.