(a) State Hooke's law of elasticity (b) A spiral spring, loaded with a piece of metal, extends by 10.5cm hair. When the metal is fully submerged in water, t...
Question 1 Report
(a) State Hooke's law of elasticity
(b) A spiral spring, loaded with a piece of metal, extends by 10.5cm hair. When the metal is fully submerged in water, the spring extends by 6.8cm. Calculate the relative density of the metal. (Assume Hooke's law is obeyed).
Answer Details
(a) Hooke's law: provided the elastic limit is not exceeded, the extension of an elastic material (spring) is directly proportional to the stretching force (load) applied to it, i.e. \( F = ke \).
(b) Because the spring obeys Hooke's law, its extension is directly proportional to the force stretching it.
In air: the extension is caused by the full weight \(W\) of the metal, so \( W \propto 10.5 \).
In water: the metal experiences an upthrust, so the spring is stretched only by the apparent weight \(W'\), where \( W' \propto 6.8 \).
The upthrust equals the loss in weight (weight of water displaced):
\[ U = W - W' \propto (10.5 - 6.8) = 3.7 \]Relative density:
\[ \text{R.D.} = \frac{\text{weight of metal in air}}{\text{upthrust in water}} = \frac{W}{W - W'} = \frac{10.5}{3.7} \] \[ \text{R.D.} = 2.84 \]Answer: the relative density of the metal is \(2.84\).
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