This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Okay, Santika, let's break down Question 2 again, focusing on how to plot and read the graph step-by-step. First, we need the calculated dry unit weights for each moisture content. Given: Volume of Proctor Mold (V) = 944 \, cm^3 = 944 × 10^-6 \, m^3 Acceleration due to gravity (g) = 9.81 \, m/s^2 The formulas are: Wet unit weight: _wet = M_wet × gV Dry unit weight: _dry = _wet1 + w (where w is in decimal form) Step 1: Calculate the dry unit weight for each data point. Here are the calculated values, which will be our plotting points: | w (%) | w (decimal) | M_wet (kg) | _wet (kN/m^3) | _dry (kN/m^3) | | :-----: | :-----------: | :------------: | :-----------------------: | :-----------------------: | | 9.9 | 0.099 | 1.68 | 17.46 | 15.89 | | 10.5 | 0.105 | 1.71 | 17.77 | 16.08 | | 12.1 | 0.121 | 1.77 | 18.39 | 16.41 | | 13.8 | 0.138 | 1.83 | 19.01 | 16.70 | | 15.1 | 0.151 | 1.86 | 19.32 | 16.79 | | 17.4 | 0.174 | 1.88 | 19.53 | 16.64 | | 19.4 | 0.194 | 1.87 | 19.43 | 16.27 | | 21.2 | 0.212 | 1.85 | 19.22 | 15.86 | Step 2: Set up the graph axes and plot the points. • Draw a horizontal axis (x-axis) and label it "Moisture Content (w %)". Choose a scale that covers the range from approximately 8% to 22%. For example, each major grid line could represent 1% moisture content. • Draw a vertical axis (y-axis) and label it "Dry Unit Weight (_dry kN/m^3)". Choose a scale that covers the range from approximately 15.5 \, kN/m^3 to 17.0 \, kN/m^3. For example, each major grid line could represent 0.1 \, kN/m^3. • Now, plot each data point from the table on your graph: Point 1: (w=9.9\%, _dry=15.89 \, kN/m^3) Point 2: (w=10.5\%, _dry=16.08 \, kN/m^3) Point 3: (w=12.1\%, _dry=16.41 \, kN/m^3) Point 4: (w=13.8\%, _dry=16.70 \, kN/m^3) Point 5: (w=15.1\%, _dry=16.79 \, kN/m^3) Point 6: (w=17.4\%, _dry=16.64 \, kN/m^3) Point 7: (w=19.4\%, _dry=16.27 \, kN/m^3) Point 8: (w=21.2\%, _dry=15.86 \, kN/m^3) Step 3: Draw the compaction curve. • Once all points are plotted, draw a smooth curve that connects these points. This curve should rise to a peak and then fall, forming a bell-like shape. Step 4: Determine the maximum dry unit weight and optimum moisture content from the graph. a) • Locate the highest point on the smooth curve you just drew. This is the peak of the compaction curve. • From this peak, draw a horizontal line to the y-axis. The value where it intersects the y-axis is the maximum dry unit weight (_d,max). You should read approximately 16.79 \, kN/m^3. • From the same peak, draw a vertical line down to the x-axis. The value where it intersects the x-axis is the optimum moisture content (OMC). You should read approximately 15.1\%. The maximum dry unit weight is 16.79 kN/m^3 and the optimum moisture content is 15.1%. Step 5: Determine the moisture content required to achieve 95% of _d,max from the graph. b) • Calculate 95% of the maximum dry unit weight: 0.95 × _d,max = 0.95 × 16.79 \, kN/m^3 = 15.95 \, kN/m^3 • Locate 15.95 \, kN/m^3 on the y-axis. • Draw a horizontal line from 15.95 \, kN/m^3 across to the left side of your compaction curve. • Where this horizontal line intersects the curve (on the "dry" side, before the peak), draw a vertical line straight down to the x-axis. • Read the value on the x-axis where this vertical line lands. This is the moisture content required. You should read approximately 10.09\%. The moisture content required to achieve 95% of _d,max is approximately 10.09%. That's 2 down. 3 left today — send the next one.