A student measures the average mass of a marble (glass ball) and investigates the speed of a marble rolling down a slope.

1. (a)(i)The student: • places a small empty dish on a top pan balance. Fig. 3.1 shows the reading on the balance. • adds 5 marbles to the dish. Fig. 3.2 shows the new reading on the balance. Use the readings from Fig. 3.1 and Fig. 3.2 to calculate the mass of the 5 marbles. Show your working. mass of 5 marbles = g[1]
2. (a)(ii)Calculate the average mass of 1 marble. average mass of 1 marble = g[1]
3. (b)(i)The student uses the apparatus shown in Fig. 3.3. The distance between the bench and the bottom side of the rule at the 90 cm mark is h. The ramp is initially arranged with height h = 4.0cm above the bench. procedure The student: • places a marble on the gap between the rules so that its right-hand edge is on the 90.0 cm mark • releases the marble and records the time t₁ for the marble to roll down the ramp until it hits the stopper • repeats the experiment two more times. The second and third measurements of time are recorded as t₂ and t₃. Times t₁, t₂ and t₃ are shown. t₁ = 2.16s t₂ = 2.23 s t₃ = 2.25 s Calculate the average time tav for the marble to travel 90.0 cm down the ramp. tav = s[1]
4. (b)(ii)The procedure in (b)(i) is repeated for heights h = 6.0cm, 8.0cm, 10.0cm and 12.0 cm. All results are recorded in Table 3.1. Complete Table 3.1, finding the average time tav for each value of h. Include the results from (b)(i) in the table. Give all values to a suitable number of decimal places. Table 3.1 h/cm t₁/s t₂/s t₃/s tav/s 4.0 6.0 2.04 1.94 1.91 8.0 1.75 1.82 1.70 10.0 1.46 1.42 1.38 12.0 1.36 1.23 1.31 [2]
5. (b)(iii)On the grid provided in Fig. 3.4 on page 13, plot a graph of tav/s on the y-axis against h/cm on the x-axis. Draw a line of best fit through your points. You do not need to start your axes at (0, 0).[4]
6. (b)(iv)Describe the relationship between h and tav[1]
7. (c)(i)Use your graph to find tav when h = 7.0 cm. Show on the graph how you find tav for h = 7.0cm. tav = s[2]
8. (c)(ii)The average speed v of the marble is given by: v = 0.90 / tav Find the average speed v of the marble when h = 7.0 cm. Give the unit of your answer. average speed v = unit .........[2]

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