# Motion of a ball rolling down a plank

##### Demonstration and Class practical

This is a version of an experiment devised and carried out by Galileo. He used it to discover and demonstrate that motion was subject to quite simple, and beautiful, mathematical description.

#### Apparatus and materials

Plank, long, with one grooved edge

Marbles, large, a supply of

Hanging pennants, metal or light plastic, up to 6

Clamps and stands for holding each pennant

String

Masses, 50 g, 5 or 6

#### Health & Safety and Technical notes

The long plank should be handled by two persons.

Do not stand on a stool or bench to drop an object on a string. It could be dropped down a stairwell as long as precautions are taken to prevent the object falling on anyone.

A length of 3 m of grooved plank is suitable. Alternatively, you could use a plain plank with grooved moulding fixed to it.

The 'pennants' can be small rectangles of metal sheet, just large enough to make a clear 'clink' as a marble hits one and rolls past. Christmas tree or similar decorations can add a touch of colour. They should make a clear sound without possibility of damage and without resisting the motion of the marble too much.

Horizontal rods held in clamps can be used to hang the pennants. Alternatively, you can fix wires from which to hang the pennants to curtain track fitted to the plank. Or you could make small wire 'goalposts' which could sit over the grooved track.

It must be possible to move the pennant holders to different positions on the track. And whichever system you use, the pennants should be hung before the lesson.

#### Procedure

**a** Set up the grooved plank inclined so that marbles can roll down the groove.

**b** Hang small tin pennants above the groove so that the marbles hit them and make' clinks'.

**c** Place the pennants at regular intervals: 25 cm, 50 cm, 75 cm, 100 cm from the beginning of the plank. Roll a marble down the track, and listen for the time intervals between each 'clink'.

**d** Try placing the pennants so that the 'clinks' happen at equal time intervals.

#### Teaching notes

**1** Galileo showed that the total distance travelled increases with the square of the time. The consequence here is that, for the desired regular clink of the pennants, they will be at distances from the start which have the ratio 1:4:9:16 and so on.

**2** As an extension activity, students could make graphs. They should first use values of time as 1, 2, 3, 4 units, plotted on the *x*-axis. They should plot the values of distance on the *y*-axis. They then make a second graph plotting the square of time on the *x*-axis, to obtain a straight line (unless friction plays a significant complicating role).

**3** The same ratio, 1:4:9:16, occurs for all accelerations and hence, provided that frictional effects are not too great, for all slopes of the runway. Students could try this. Where graphs of distance against the square of the time are plotted, lines obtained for different runway slopes will have different gradients.

**4** You can do a similar activity for a body in free fall, whose acceleration is 'the acceleration due to gravity'. Tie a length of string to a mass. Tie knots in the string. The first one should be 10 centimetres from where the string is tied to the mass. The next one should be 40 centimetres away, the third one should be 90 centimetres away, and the fourth one 160 centimetres away. Let the string fall through your fingers from 160 cm above the floor with the mass falling first.

**5** Feeling the knots is not as easy to discern as hearing masses hit the floor. Attach masses to the end of a string and at 10, 40, 90, 160, 250 cms from the original mass.

Hold the mass at the 250 cm position and lower the string out of a window or down a stairwell until the end mass reaches the floor. Leave go of the string, and the masses will hit the floor at equal time intervals.

*This experiment was safety-checked in January 2005*