You will measure the average mass of a marble (glass ball) and investigate the speed of a marble rolling down a slope. You are provided with: • a small dish • 5 identical marbles (glass balls) • access to a top pan balance. • a clamp, stand and boss • 2 metre rules or wooden strips, arranged as shown in the diagram with a small gap between them to act as a track (ramp) for a marble • a small block of wood to act as a stopper at the end of the track • a stopwatch • an additional metre or half-metre rule, or a 30 cm ruler. The apparatus has been set up for you as shown in [Figure 3.1].

1. (a)(i)Empty the dish and place it on the top pan balance. Press the zero (tare) button. Add the 5 marbles back to the dish. Write down the mass of the 5 marbles. 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 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 = 4.0 cm above the bench. Place one marble on the gap between the rules so that its right-hand edge is on the 90.0 cm mark as shown. Release the marble, and record the time t₁ for it to roll down the ramp until it hits the stopper. Repeat the experiment two more times, recording the results as times t₂ and t₃. Calculate the average time t_av for the marble to travel 90.0 cm down the ramp. t₁ = ................................................................. s t₂ = ................................................................. s t₃ = ................................................................. s t_av = ................................................................. s[1]
4. (b)(ii)Repeat the experiment in (b)(i) for heights h = 6.0cm, 8.0cm, 10.0cm and 12.0cm. The ramp height is adjusted using the clamp, boss and stand. Record all your results in [Table 3.1], including your results from (b)(i).[2]
5. (b)(iii)On the grid provided in Fig. 3.2 on page 13, plot a graph of t_av/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 t_av.[1]
7. (c)(i)Use your graph to find t_av when h = 7.0 cm. Show on the graph how you find t_av for h = 7.0 cm. t_av = ................................................................. s[2]
8. (c)(ii)The average speed v of the marble is given by v = d / t_av where d is the distance the ball travels along the track. Find the average speed of the marble when h = 7.0 cm. Give the unit of your answer. average speed = ..................................................... unit ....................[2]

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