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.
ScanSolve AI Answer
Right I., let's go. a) What is the density of the alloy? Step 1: Identify the given information. • Mass percentage of aluminum (w_Al) = 60% = 0.60 • Mass percentage of tin (w_Sn) = 40% = 0.40 • Density of aluminum (_Al) = 2700 kg/m^3 • Density of tin (_Sn) = 7300 kg/m^3 Step 2: Use the formula for the density of an alloy based on mass fractions. The density of an alloy (_alloy) when given mass fractions (w_i) and individual densities (_i) is: _alloy = (1)/(w_Al)_Al + w_Sn_Sn Step 3: Substitute the values and calculate. _alloy = (1)/(0.60)2700 kg/m^3 + (0.40)/(7300 kg/m)^3 Calculate the terms in the denominator: (0.60)/(2700) ≈ 0.000222222 m^3/kg (0.40)/(7300) ≈ 0.000054795 m^3/kg Sum the terms: 0.000222222 + 0.000054795 = 0.000277017 m^3/kg Now, take the reciprocal: _alloy = (1)/(0.000277017 m)^3/kg _alloy ≈ 3609.89 kg/m^3 Rounding to three significant figures: The density of the alloy is 3610 kg/m^3. b) What is the mass of tin in 0.02 m^3 of the alloy? Step 1: Calculate the total mass of 0.02 m^3 of the alloy. Use the density calculated in part (a): m_alloy = _alloy × V_alloy m_alloy = (3609.89 kg/m^3) × (0.02 m^3) m_alloy = 72.1978 kg Step 2: Calculate the mass of tin in this total mass. The alloy consists of 40% tin by weight (mass). m_Sn = 0.40 × m_alloy m_Sn = 0.40 × 72.1978 kg m_Sn = 28.87912 kg Rounding to three significant figures: The mass of tin is 28.9 kg. Send me the next one 📸