# Making sense of data - finding a value for the young modulus of a flexxible strip of material.

MAKING SENSE OF DATA

FINDING A VALUE FOR THE YOUNG MODULUS OF A FLEXIBLE STRIP OF MATERIAL

I have picked the first method out of the three options of experiments to conduct based on the flexion of a cantilever. I now have to decide on a method of collecting and processing the data for the first method, taking care to reach a value for Young modulus with some estimate of accuracy attached to it.

Method 1: Wood (metre rule)

Diagram

Apparatus

. 2 Measuring rulers (1m each)

2. Drawing Pin

3. 9 Weights (50g each, totalling 450g)

4. Approximately 50cm of string

5. G-Clamp

6. Clamp Stand with clamp

7. Screw gauge with a sensitivity of 0.1mm (Micrometer)

8. Vernier Calipers with a sensitivity of 0.2mm

The Micrometer

Vernier Calipers - read the sliding scale along the top and bottom

Variables

The variables that will be kept constant are the length of the overhang of the ruler, the position where the ruler is clamped and the position on the ruler where the weights are hung. The only variable that will change during the experiment is the amount of weight that is hung on one end of the ruler to measure the different deflection of the ruler at different heights. The weights that are hung on one end of the ruler will vary each time by adding 50g to the previous weight and each time the deflection of the ruler is read until 450g of weights have been added.

Method

Arrange the apparatus as shown in the diagram. As the apparatus is fixed appropriately we can then start the experiment. As the apparatus is fixed we might see the ruler has a slight bend without any weights on it this is due to its own weight, this can be counted as a systematic error. Now I am going to start adding 50g weights to the ruler. The weights will be added from 50g till it becomes 450g, and every time we add 50g we must measure the depression at the end (deflection) of the ruler. This can be done by measuring the initial position of the ruler and measure the deflection from the initial position to the bend position of the ruler with a ruler, to give the bend or deflected height of the ruler.

As the weights are added to the ruler the side of the ruler where the weights are hung is under tension and the other side is in compression. Now we have to measure the depth of the ruler using a screw gauge (micrometer). We also have to measure the breadth of the ruler using the vernier calipers. Since we have the measure of the deflection of the ruler, width, height, length of the overhang of the ruler we can now work out the Young modulus of the ruler.

The relationship for calculating Young modulus in this experiment is:-

E = 4gL3 * M

BD3 Y

Where

E = young's modulus

L = length of the overhang of the ruler (cantilever)

M = mass

Y = depression at the end (deflection of the ruler)

B = width of the ruler (strip)

D = thickness of the ruler (strip)

g = 9.80 Nkg-1

We repeat the above experiment two more times by measuring again the deflection of the ruler with the same weights and from the same ...