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
Here's the solution to 9(a): 9. (a) To calculate the density of the sand, we need its mass and its volume. Step 1: Determine the mass of the water that fills the bottle. Mass of water = (Mass of bottle + water) - (Mass of empty bottle) Mass of water = 98 g - 35 g = 63 g Step 2: Determine the volume of the bottle. Assuming the density of water is 1 g/cm^3. Volume of bottle = Volume of water that fills the bottle V_bottle = Mass of waterDensity of water = 63 g1 g/cm^3 = 63 cm^3 Step 3: Determine the mass of the sand. Mass of sand = (Mass of bottle + some sand) - (Mass of empty bottle) Mass of sand = 65 g - 35 g = 30 g Step 4: Determine the volume of the sand. The line "Mass of bottle + sand + water on top of the sand = 80g" tells us the total mass when the bottle is filled with sand and then water is added to fill the remaining space. Mass of (sand + water) in the bottle = (Mass of bottle + sand + water) - (Mass of empty bottle) Mass of (sand + water) = 80 g - 35 g = 45 g Now, subtract the mass of the sand (from Step 3) to find the mass of the water added on top of the sand. Mass of water added = Mass of (sand + water) - Mass of sand Mass of water added = 45 g - 30 g = 15 g Using the density of water (1 g/cm^3), find the volume of the water added. Volume of water added = Mass of water addedDensity of water = 15 g1 g/cm^3 = 15 cm^3 The volume of the sand is the total volume of the bottle minus the volume of the water added. Volume of sand = Volume of bottle - Volume of water added Volume of sand = 63 cm^3 - 15 cm^3 = 48 cm^3 Step 5: Calculate the density of the sand. Density of sand = Mass of sandVolume of sand Density of sand = 30 g48 cm^3 Density of sand = (5)/(8) g/cm^3 Density of sand = 0.625 g/cm^3 The density of the sand is 0.625 g/cm^3.