Depth / m Pressure / Pa 0.10 1000 0.20 2000 0.30 3000 0.40 4000 0.50 5000 A student fills a long vertical tube with water and measures the pressure at diffe...
Question 1 Report
| Depth / m | Pressure / Pa |
|---|---|
| 0.10 | 1000 |
| 0.20 | 2000 |
| 0.30 | 3000 |
| 0.40 | 4000 |
| 0.50 | 5000 |
A student fills a long vertical tube with water and measures the pressure at different depths using a pressure sensor. Table 4.1 shows the results.
(a) Plot pressure against depth. [2]
(b) Describe the relationship. [1]
(c) Calculate the gradient of the line. [1]
(d) State what the gradient equals in terms of physical quantities. [1]
(e) Using gradient = density x g, calculate the density of the liquid. Take g = 10 N/kg. [1]
Answer Details
(a) The five data points should be plotted on a graph of pressure (y-axis) against depth (x-axis) with suitable scales. All points lie on a straight line through the origin.
[1] for correctly plotted points, [1] for suitable scales and labelled axes.
(b) Pressure is directly proportional to depth. The graph is a straight line that passes through the origin, confirming that doubling the depth doubles the pressure. [1]
(c) The gradient is found by choosing two well-separated points on the line:
\[ \text{gradient} = \frac{\Delta P}{\Delta d} = \frac{5000 - 0}{0.50 - 0} = 10\,000 \text{ Pa/m} \][1]
(d) The gradient of the pressure-depth graph equals \( \rho g \), the product of the liquid's density and the gravitational field strength. [1]
(e) Rearrange \( \text{gradient} = \rho g \) to find the density:
\[ \rho = \frac{\text{gradient}}{g} = \frac{10\,000}{10} = 1000 \text{ kg/m}^3 \]This matches the known density of water, confirming the measurement is reliable. [1]
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