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.

From the diagram, when the load is 0 N, the length of the spring is 3.0 cm.

Using the first loaded spring:
Load ($F_1$) = 2.0 N
Stretched length ($L_1$) = 6.0 cm
Extension ($e_1$) = $L_1 - L_0 = 6.0 \text{ cm} - 3.0 \text{ cm} = 3.0 \text{ cm}$

Using the second loaded spring:
Load ($F_2$) = 4.0 N
Stretched length ($L_2$) = 9.0 cm
Extension ($e_2$) = $L_2 - L_0 = 9.0 \text{ cm} - 3.0 \text{ cm} = 6.0 \text{ cm}$

Convert extensions to meters:
$e_1 = 3.0 \text{ cm} = 0.030 \text{ m}$
$e_2 = 6.0 \text{ cm} = 0.060 \text{ m}$

Using $F_1$ and $e_1$:

Using $F_2$ and $e_2$:

Rounding to three significant figures:

The final answer is $\boxed{66.7 \text{ N/m}}$.

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.

From Table 1, when the load L = 0.00 N, the length $l = 2.1 \text{ cm}$.
So, $l_0 = 2.1 \text{ cm}$.

From Table 1, when the load L = 1.00 N, the length $l = 6.0 \text{ cm}$.

The final answer is $\boxed{3.9 \text{ cm}}$.

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.

From Table 1, when L = 0.00 N, $l = 2.1 \text{ cm}$. So, $l_0 = 2.1 \text{ cm}$.

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)