A student hangs different loads on a spring as shown. a) Determine the spring constant of the spring. b) The student suspends a load L = 1.00 N from the spring.

Here are the solutions to the questions: Question 10: A student hangs different loads on a spring as shown. a) Determine the spring constant of the spring. Step 1: Determine the unstretched length of the spring. From the diagram, when the load is 0 N, the length of the spring is 3.0 cm. L_0 = 3.0 cm Step 2: Calculate the extension for a given load. Using the first loaded spring: Load (F_1) = 2.0 N Stretched length (L_1) = 6.0 cm Extension (e_1) = L_1 - L_0 = 6.0 cm - 3.0 cm = 3.0 cm Using the second loaded spring: Load (F_2) = 4.0 N Stretched length (L_2) = 9.0 cm Extension (e_2) = L_2 - L_0 = 9.0 cm - 3.0 cm = 6.0 cm Step 3: Calculate the spring constant (k) using Hooke's Law (F = ke). Convert extensions to meters: e_1 = 3.0 cm = 0.030 m e_2 = 6.0 cm = 0.060 m Using F_1 and e_1: k = (F_1)/(e_1) = 2.0 N0.030 m k = 66.66... N/m Using F_2 and e_2: k = (F_2)/(e_2) = 4.0 N0.060 m k = 66.66... N/m Rounding to three significant figures: k ≈ 66.7 N/m The final answer is 66.7 N/m. b) The student suspends a load L = 1.00 N from the spring. He calculates the extension e of the spring using the values of e in Table 1. Step 1: Identify the unstretched length (l_0) from Table 1. From Table 1, when the load L = 0.00 N, the length l = 2.1 cm. So, l_0 = 2.1 cm. Step 2: Identify the stretched length (l) for L = 1.00 N from Table 1. From Table 1, when the load L = 1.00 N, the length l = 6.0 cm. Step 3: Calculate the extension (e). e = l - l_0 e = 6.0 cm - 2.1 cm e = 3.9 cm The final answer is 3.9 cm. --- Question 11: A student investigates the stretching of a spring. a) Describe one technique you would use to obtain an accurate value for l_0. Draw a diagram to illustrate your answer. To obtain an accurate value for l_0 (the unstretched length of the spring), follow these steps: 1. Hang the spring vertically from a clamp stand. 2. Position a metre ruler vertically alongside the spring, ensuring it is parallel to the spring. 3. Adjust the ruler so that its zero mark is aligned with the top of the coiled part of the spring (not including the loop). 4. Read the position of the bottom of the coiled part of the spring. This reading is l_0. 5. Ensure your eye is at the same horizontal level as the reading point to avoid parallax error. Diagram Description: Imagine a vertical clamp stand holding a spring. A metre ruler is placed vertically next to the spring. The top of the spring's coils is aligned with a specific mark on the ruler (e.g., 0 cm or a convenient higher mark). An arrow points from the bottom of the spring's coils to the ruler, indicating the reading for l_0. A horizontal line from the eye to the reading point on the ruler would show how to avoid parallax error. b) The student repeats the procedure using different loads. The readings and results are recorded in Table 1. He calculates the extension e of the spring using this value of e in Table 1. Step 1: Identify the unstretched length (l_0). From Table 1, when L = 0.00 N, l = 2.1 cm. So, l_0 = 2.1 cm. Step 2: Calculate the extension (e = l - l_0) for each load. | L/N | l/cm | e/cm (l - 2.1 cm) | | :-- | :--- | :-------------------------- | | 0.00 | 2.1 | 0.0 | | 1.00 | 6.0 | 3.9 | | 2.00 | 10.8 | 8.7 | | 3.00 | 14.7 | 12.6 | | 4.00 | 18.6 | 16.5 | | 5.00 | 22.5 | 20.4 | c) Plot a graph of L (N) (y-axis) against e (cm) (x-axis). Draw the best-fit line. To plot the graph: 1. Draw a set of axes. Label the y-axis "Load L (N)" and the x-axis "Extension e (cm)". 2. Choose appropriate scales for both axes to accommodate the range of values. For L, from 0.00 N to 5.00 N. For e, from 0.0 cm to 20.4 cm. 3. Plot the data points from the table in part (b): (0.0, 0.00) (3.9, 1.00) (8.7, 2.00) (12.6, 3.00) (16.5, 4.00)