# explian young's modulus by searle's method..

Searle’s method for finding the Young’s modulus of a wire

Searle’s method uses two wires of the same material, one of which will be loaded with various weights.

E = frac{F l}{A x}

E = To calculate Young’s modulus we need to know:

* The cross-section area of the wire (A). This is measured by using a micrometer to determine the radius of the wire, and then using the formula area of circle = ?r2. The radius must be measured in metres, and is typically 2 x 10-4 m. This gives an area of 1.26 x 10-7 m2.
* The length of the wire (l, measured in metres).
* The force and the extension.
* The weight of a 1 kg mass is 9.81 N.

We plot a graph of the extension (m, horizontal axis) against the weight (N, vertical axis).

The gradient of this graph (change in vertical measure / change in horizontal measure) is the ratio F/x. If we multiply this ratio by l and divide by A we have the Young modulus for the wire.

Measuring the extension:

The ‘business end’ of the apparatus is a device which holds the two wires parallel, and allows the extension of the loaded wire to be measured. Searle's apparatus for measuring Young modulus.

You need to label this diagram to show:

* Constant mass attached to stress the reference wire.
* Variable mass attached to stress the test wire.
* Flexible connectors.
* Level reference from one wire to the other.
* Thumbscrew with scale to level the reference.
* Clamps for wires.
* Reference wire.
* Test wire.

* Thermal expansion of the test wire is correct by thermal expansion of the reference wire.
* Long, thin wires allow maximum extension for minimum force.

Problems:

* Difficulty measuring the cross-section area.
* Extensions very small.
* Mass, not weight, is measured.
* Need high, secure mounting point unless apparatus adapted.

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mathematical calculation for calculating young's modulus using searle's method.

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searls apparatus with ful describe

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