Item 3 You have a bucket containing an unknown liquid. You also have a cube-shaped wooden block that you measure to be 8.0 cm on a side, but you don't know the mass or density of the block. To find the density of the liquid, you perform an experiment. First you place the wooden block in the liquid and measure the height of the top of stack various numbers of U.S. quarter-dollar coins onto the block and measure the new value of h. The straight line that gives the best fit to the data you have collected is shown in (Figure 1). The mass of one quarter is 5.67 g. Use this information and the slope and intercept of the straight-line fit to your data. The lowest point on the graph corresponds to 1.2 cm. Part A the floating block above the liquid surface. Then you Calculate the density of the liquid. Express your answer in kilograms per cubic meter. Vα ΑΣφ kg/m³ Submit Request Answer Part B Figure 1 of 1 Calculate the mass of the block. Express your answer in kilograms. h (cm) 3.5 E ? 3.0 kg m = 2.5 2.0 1.5 Submit Request Answer 1.0 0. 10 15 20 25 30 Provide Feedback Number of quarters

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Chapter1: Units, Trigonometry. And Vectors
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**Item 3**

You have a bucket containing an unknown liquid. You also have a cube-shaped wooden block that you measure to be 8.0 cm on a side, but you don’t know the mass or density of the block. To find the density of the liquid, you perform an experiment. First, you place the wooden block in the liquid and measure the height of the top of the floating block above the liquid surface. Then you stack various numbers of U.S. quarter-dollar coins onto the block and measure the new value of \( h \). The straight line that gives the best fit to the data you have collected is shown in (Figure 1). The mass of one quarter is 5.67 g. Use this information and the slope and intercept of the straight-line fit to your data. The lowest point on the graph corresponds to 1.2 cm.

**Part A**

Calculate the density of the liquid.

**Express your answer in kilograms per cubic meter.**

\[ \rho = \, \, \, \, \, \, \, \, \, \,\, \, \,\,\, kg/m^3 \]

**Part B**

Calculate the mass of the block.

**Express your answer in kilograms.**

\[ m = \, \, \, \, \, \, \, \, \, \,\, \, \,\,\, kg \]

**Figure 1:**

The graph in Figure 1 plots \( h \) (cm) on the y-axis versus the number of quarters on the x-axis. The graph shows a decreasing linear relationship, indicating that as more quarters are added, the height \( h \) decreases. The data points form a straight line that begins at approximately 3.5 cm when no quarters are added and decreases to 1.2 cm at the highest number of quarters. Here's a detailed description:

- The vertical axis is labeled \( h \) (cm) and ranges from 0 to 3.5 cm.
- The horizontal axis represents the number of quarters added, ranging from 0 to 30.
- The line of best fit indicates a negative slope, showing a downward trend as the number of quarters increases. 

This graph is essential to understanding the relationship between the height of the block above the liquid surface and the number of quarters stacked on the block.
Transcribed Image Text:**Item 3** You have a bucket containing an unknown liquid. You also have a cube-shaped wooden block that you measure to be 8.0 cm on a side, but you don’t know the mass or density of the block. To find the density of the liquid, you perform an experiment. First, you place the wooden block in the liquid and measure the height of the top of the floating block above the liquid surface. Then you stack various numbers of U.S. quarter-dollar coins onto the block and measure the new value of \( h \). The straight line that gives the best fit to the data you have collected is shown in (Figure 1). The mass of one quarter is 5.67 g. Use this information and the slope and intercept of the straight-line fit to your data. The lowest point on the graph corresponds to 1.2 cm. **Part A** Calculate the density of the liquid. **Express your answer in kilograms per cubic meter.** \[ \rho = \, \, \, \, \, \, \, \, \, \,\, \, \,\,\, kg/m^3 \] **Part B** Calculate the mass of the block. **Express your answer in kilograms.** \[ m = \, \, \, \, \, \, \, \, \, \,\, \, \,\,\, kg \] **Figure 1:** The graph in Figure 1 plots \( h \) (cm) on the y-axis versus the number of quarters on the x-axis. The graph shows a decreasing linear relationship, indicating that as more quarters are added, the height \( h \) decreases. The data points form a straight line that begins at approximately 3.5 cm when no quarters are added and decreases to 1.2 cm at the highest number of quarters. Here's a detailed description: - The vertical axis is labeled \( h \) (cm) and ranges from 0 to 3.5 cm. - The horizontal axis represents the number of quarters added, ranging from 0 to 30. - The line of best fit indicates a negative slope, showing a downward trend as the number of quarters increases. This graph is essential to understanding the relationship between the height of the block above the liquid surface and the number of quarters stacked on the block.
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