This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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You're on a roll — ii) I cannot determine the average relative density of the spirit as the necessary information (such as its density, mass, or volume) is not provided in the visible part of the question. This question likely refers to data from a preceding section. c) Given: Volume of balloon, V = 1.2 m^3 Mass of fabric, m_fabric = 0.3 kg Density of air, _air = 1.25 kg/m^3 Density of helium, _helium = 0.018 kg/m^3 Acceleration due to gravity, g = 9.8 m/s^2 (assumed standard value) The maximum tension on the string occurs when the balloon is fully inflated and the net upward force (buoyant force) is balanced by the total downward forces (weight of helium, weight of fabric, and tension in the string). Step 1: Calculate the buoyant force (F_B) acting on the balloon. The buoyant force is equal to the weight of the air displaced by the balloon. F_B = _air × V × g F_B = (1.25 kg/m^3) × (1.2 m^3) × (9.8 m/s^2) F_B = 14.7 N Step 2: Calculate the weight of the helium gas (W_helium) inside the balloon. First, find the mass of the helium: m_helium = _helium × V. m_helium = (0.018 kg/m^3) × (1.2 m^3) m_helium = 0.0216 kg Now, calculate its weight: W_helium = m_helium × g W_helium = (0.0216 kg) × (9.8 m/s^2) W_helium = 0.21168 N Step 3: Calculate the weight of the balloon fabric (W_fabric). W_fabric = m_fabric × g W_fabric = (0.3 kg) × (9.8 m/s^2) W_fabric = 2.94 N Step 4: Determine the maximum tension (T) on the string. The forces are in equilibrium, so the upward force equals the sum of downward forces: F_B = W_helium + W_fabric + T Rearrange to solve for T: T = F_B - W_helium - W_fabric T = 14.7 N - 0.21168 N - 2.94 N T = 11.54832 N Rounding to three significant figures: T ≈ 11.5 N The maximum tension on the string is 11.5 N. What's next?