1.1. A student investigates the balancing of a metre rule.

Fig. 1.1 shows the arrangement.

The student places the metre rule on the pivot at the 50.0 cm mark. He places an object Q on the metre rule with its centre at the 90.0 cm mark. He places a load of weight P = 2.0 N on the metre rule and adjusts the position of the load so that the metre rule is as near as possible to being balanced.

He measures the distance x from the centre of the load to the pivot.

He repeats the procedure using loads of weight P = 3.0 N, 4.0 N, 5.0 N and 6.0 N. All the values of P and x are recorded in Table 1.1.

Calculate, and record in Table 1.1, the values of $\frac{1}{x}$

1.2. Plot a graph of P / N (y-axis) against $\frac{1}{x}/\frac{1}{cm}$ (x-axis). Start both axes at the origin (0,0).      

1.3. In this experiment, x_max , the maximum possible value for x is 50.0cm. Calculate $\frac{1}{{x}_{max}}$.                             

$\frac{1}{{x}_{max}}$ = .................................................. $\frac{1}{cm}$

Use the graph to determine the minimum value of P required to balance the metre rule in this experiment. Show clearly on the graph how you determined this value.

minimum value of P = ..................................................... 

1.4. In this experiment, the width of object Q is slightly greater than the width of the metre rule. Explain briefly how you would place the object Q as accurately as possible on the 90.0 cm mark of the metre rule. You may draw a diagram.

1.5. Extended tier only

In this experiment, it is difficult to determine the exact position of the load that will make the metre rule balance.

(i) Explain briefly why this is difficult.

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(ii) Explain briefly how you would find the best position of the load that will make the metre rule balance.

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