Question

Place a 50g load on the hanger and measure the extension. Add 50g load on the hanger in about 5 steps and measure the extension each time. Plot a graph between load and extension . repeat this activity with springs made of iron,copper and brass. Plot load extension graph in each case compare these graphs. Which of the above material obey hooks law?

Answer 1

Answer on Question #44651, Physics, Mechanics | Kinematics | Dynamics

For all three strings:

$\mathrm{L} = 0,1\mathrm{m}$ (length)

$\mathrm{A} = 1 \mathrm{~mm}^{2}$ (cross section area)

$g = 9,8m / sec^2$

Hoock's Law:

$F = -K\cdot X$ , K - extension coefficient, X - extension of the string. $\Delta \mathbf{X}$ - error for X value. M - mass of the block that was put on the string.

Cooper

Brass

As we can see from the graphs all three strings obey Hoock's law.

To compare our results with the table data with the table data, we need to find Young's modulus.

$$K = \frac {E \cdot A}{L} \Rightarrow E = \frac {K \cdot L}{A}$$

We can find K from the plot. Linear law was used to fit the data:

$$F = K \cdot X = M \cdot g \quad \Rightarrow \quad X = M \cdot \frac {g}{K}$$

For Iron: $X = a * M + b = 4,89 \cdot 10^{-6} \cdot M + 2 \cdot 10^{-22}$ , So $\frac{g}{K} = 4,89 \cdot 10^{-6} \Rightarrow K = 2 \cdot 10^{6} \mathrm{~m/N}$

$$E = \frac {2 \cdot 10^{6} \cdot 0,1}{1 \cdot 10^{-6}} = 200 \, \text{GPa} \quad \text{(the same as table data)}$$

For cooper we make the same calculations:

$$E = 110 \, \text{GPa} \quad \text{(the same value as table data)}$$

For Brass:

$$E = 115 \, \text{Gpa} \quad \text{(the same value as table data)}$$

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