A student carries out an investigation into balancing a metre rule.
She uses a metre rule with a small hole drilled through it at the 5.0 cm mark.
• She places the pivot at the 5.0 cm mark.
• She supports the far end of the rule with a newton meter attached to a loop of string at the 95.0 cm mark.
• She hangs a 200 g mass from the rule by means of a loop of thread.
• The student shifts the loop of thread holding the 200 g mass until it is positioned at the 25.0 cm mark on the metre rule.
Fig. 1.1 shows the apparatus arranged by the student.
• She works out the distance $d$ of the mass from the pivot and enters her value in the first row of Table 1.1.
• She changes the height of the clamp supporting the newton meter until the rule is horizontal.
• She notes the reading $F$ on the newton meter in the first row of Table 1.1.
• The student then repeats the procedure with the loop of thread supporting the mass placed at the 40.0 cm, 55.0 cm, 65.0 cm and 80.0 cm marks on the metre rule.
(a(i))[1]
Enter the distance $d$ of the mass from the pivot in Table 1.1.
(a(ii))[1]
Enter the reading $F$ shown on the newton meter in Table 1.1.
(b)[4]
On Fig. 1.3, draw a graph of $F$ on the y-axis against $d$ on the x-axis. Let both axes start from the origin. Draw the straight line of best fit.
(c(i))[2]
Calculate the gradient $m$ of your line. Show all of your working and mark on the graph the values you choose.
(c(ii))[1]
Extend your line until it meets the y-axis. Record the intercept $c$ made with the y-axis.
(c(iii))[1]
Calculate $w$, where $w = \frac{c}{m}$.
(c(iv))[2]
The weight $W$ of the metre rule is found using the equation shown:
$W = \frac{w}{k}$
where $k = 22.5\,\text{cm N}^{-1}$. Calculate $W$. Give your answer to a suitable number of significant figures.
(d(i))[1]
During the investigation, the student places a spirit level on the rule to check that the rule is horizontal before taking each newton meter reading. Suggest why using a spirit level in this way is not suitable for making the check in this case.
(d(ii))[1]
Describe a method, other than using a spirit level, of checking that the rule is horizontal.