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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Here's how to solve the problem: Given: Alloy composition: 60% aluminum (Al) by mass, 40% tin (Sn) by mass. Density of aluminum (_Al) = 2700 kgm^-3 Density of tin (_Sn) = 7300 kgm^-3 a) What is the density of the alloy? Step 1: Use the formula for the density of a mixture when mass fractions are known. The density of an alloy (_alloy) composed of components with mass fractions f_i and densities _i is given by: (1)/(_alloy) = _i (f_i)/(_i) In this case, for aluminum and tin: (1)/(_alloy) = f_Al_Al + f_Sn_Sn Where f_Al = 0.60 (60%) and f_Sn = 0.40 (40%). Step 2: Substitute the given values into the formula. (1)/(_alloy) = (0.60)/(2700 kgm)^-3 + (0.40)/(7300 kgm)^-3 Step 3: Calculate the individual terms. (0.60)/(2700) = (6)/(27000) = (1)/(4500) m^3kg^-1 (0.40)/(7300) = (4)/(73000) = (1)/(18250) m^3kg^-1 Step 4: Add the terms. (1)/(_alloy) = (1)/(4500) + (1)/(18250) To add these fractions, find a common denominator or convert to decimals. (1)/(_alloy) = (18250)/(4500 × 18250) + (4500)/(4500 × 18250) (1)/(_alloy) = (18250 + 4500)/(82125000) = (22750)/(82125000) m^3kg^-1 Step 5: Calculate the density of the alloy. _alloy = (82125000)/(22750) kgm^-3 _alloy = 3610 kgm^-3 The density of the alloy is 3610 kgm^-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. We use the formula M = × V. M_alloy, total = _alloy × V_alloy, total M_alloy, total = 3610 kgm^-3 × 0.02 m^3 M_alloy, total = 72.2 kg Step 2: Calculate the mass of tin in this total mass. The alloy is 40% tin by mass. M_Sn = 0.40 × M_alloy, total M_Sn = 0.40 × 72.2 kg M_Sn = 28.88 kg The mass of tin in 0.02 m^3 of the alloy is 28.88 kg. That's 2 down. 3 left today — send the next one.