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 is the solution to Question 1d) from the exam paper: Question 1d) Given data for an agricultural product material: Length (L) = 10.5 mm Width (W) = 7.2 mm Thickness (T) = 5.8 mm Mass (M) = 0.5 g Volume (V) = 0.4 cm^3 Assumptions: The given dimensions (L, W, T) define the overall envelope volume* of the single agricultural product material (i.e., the volume of the smallest rectangular prism enclosing it). The given Volume (V = 0.4 cm^3) represents the true solid volume* of the material, excluding any internal voids or air spaces within its envelope. The given Mass (M = 0.5 g) is the mass of this single material. Step 1: Convert dimensions to centimeters (cm) for consistency. L = 10.5 mm = 1.05 cm W = 7.2 mm = 0.72 cm T = 5.8 mm = 0.58 cm Step 2: Calculate the envelope volume (V_envelope) of the particle. This is the volume of the smallest rectangular prism enclosing the particle. V_envelope = L × W × T V_envelope = 1.05 cm × 0.72 cm × 0.58 cm V_envelope = 0.43848 cm^3 i. Bulk density (_b) Step 1: State the formula for bulk density, using the envelope volume for a single particle. _b = MassEnvelope Volume = (M)/(V_envelope) Step 2: Substitute the values. _b = 0.5 g0.43848 cm^3 Step 3: Calculate the bulk density. _b ≈ 1.140 g/cm^3 The bulk density is: 1.140 g/cm^3 ii. True density (_t) Step 1: State the formula for true density. _t = MassTrue Volume = (M)/(V) Step 2: Substitute the values. _t = 0.5 g0.4 cm^3 Step 3: Calculate the true density. _t = 1.25 g/cm^3 The true density is: 1.25 g/cm^3 iii. Porosity () Step 1: State the formula for porosity for a single particle. = Envelope Volume - True VolumeEnvelope Volume = V_envelope - VV_envelope Step 2: Substitute the values. = 0.43848 cm^3 - 0.4 cm^30.43848 cm^3 = 0.03848 cm^30.43848 cm^3 Step 3: Calculate the porosity. ≈ 0.0877 Expressed as a percentage: ≈ 8.77\% The porosity is: 0.0877 or 8.77\% 3 done, 2 left today. You're making progress.