Fig. 3.1 gives a balance reading of 4.2 g for an empty dish. Fig. 3.2 gives a balance reading of 29.6 g for the dish plus 5 marbles. Use the readings from Fig. 3.1 and Fig. 3.2 to calculate the mass of the 5 marbles. Show your working.
Calculate the average mass of 1 marble.
Fig. 3.3 shows a ramp. The gap between the bench and the lower face of the rule at the 90 cm mark is h. The ramp starts with height $h=4.0\,\text{cm}$ above the bench. The times are $t_1=2.16\,\text{s}$, $t_2=2.23\,\text{s}$ and $t_3=2.25\,\text{s}$. Calculate the average time $t_{av}$ for the marble to travel 90.0 cm down the ramp.
The method in (b)(i) is carried out again for heights $h=6.0\,\text{cm}$, $8.0\,\text{cm}$, $10.0\,\text{cm}$ and $12.0\,\text{cm}$. All outcomes are entered in Table 3.1. Complete Table 3.1 by finding the average time $t_{av}$ for each value of h. Include the results from (b)(i) in the table. Give every value to a suitable number of decimal places.
On the grid provided in Fig. 3.4 on page 13, plot a graph of $t_{av}/\text{s}$ on the y-axis against $h/\text{cm}$ on the x-axis. Draw a line of best fit through your points. You do not need to begin your axes at (0,0).
Describe the relationship between h and $t_{av}$.
Use your graph to find $t_{av}$ when $h=7.0\,\text{cm}$. Show on the graph how you find $t_{av}$ for $h=7.0\,\text{cm}$.
The average speed v of the marble is given by $v=\frac{0.90}{t_{av}}$. Find the average speed v of the marble when $h=7.0\,\text{cm}$. Give the unit of your answer.