# Multiflash photographs of motion down a slope

##### Demonstration

A steel ball rolls down a slope, starting from rest.

#### Apparatus and materials

Steel ball, 15-25 mm in diameter, polished

Runway that will allow the ball to roll all the way down

Camera and multiflash system

Grid

Bright lamp, 500 W

Matt black background

#### Health & Safety and Technical notes

Provide a catcher (person or box) to prevent the ball falling on the floor.

Read the Multiflash Photography guidance page for general hints and detail of specific methods.

A high frequency of exposure is required. This reduces any error in identifying the time of the start of the motion, relative to later images.

There should be a good contrast between the bright ball and its surroundings.

#### Procedure

** Making the image
a **Set up the runway with a slope. Place a grid behind it so that you are able to measure positions on the photographs. Darken the room. See guidance note Classroom mangement in semi-darkness.

**b** Start the multiflash system and then release the ball. Stop it when the ball passes out of the field of view.

**Analyzing the image**

**c** Measure the distances between the positions of the ball. Use the known multiflash frequency to find the time interval between each position (*time = 1/frequency*).

**d** Plot two graphs: distance against time, and distance against time^{2}.

**e** Compare the shapes of the graphs.

**f** The gradient of the distance - time graph is equal to velocity. Describe how the velocity changes.

**g** The gradient of the distance - time^{2} graph provides an average value for the acceleration of the ball. Work out the average acceleration.

####

Teaching notes

**1** Acceleration can be studied carefully using this variation on a freely falling object. Galileo is credited with the idea and performed the experiment with a rolling ball in 1604, publishing it in his*Discourses Concerning Two New Sciences*. He wanted to study the motion of a falling object, which moved too fast for his crude timing devices (his pulse or, in this case, a water clock). He came up with the idea of diluting the effect of gravity by only using a component of the full gravitation along the track.

The beauty of this experiment lies in the dramatic and convincing way in which a relatively simple piece of equipment reveals the nature of acceleration due to gravity.

**2** Measure the positions of the ball and look for a pattern. Most students will find Galileo's answer: the successive distances grow by jumps (3, 5, 7, 9 etc). However, the total distances themselves run as squares of the integers (1, 4, 9, 16 etc). (Measure the length of the first distance and see how many times longer the second distance is.)

The start of the motion may not be clear on the image. The flash of light into the camera may not occur as the ball starts to move. Start the analysis where positions are distinct. The kind of results you might expect are shown here.

**3** Some students might like to try to calculate the acceleration of the ball down the plank algebraically using the formula given below. You can calculate the average velocity between two consecutive positions of the ball near to the beginning of the run from:

- the distance between the positions
- the time taken to travel that distance.

Do the same for two positions of the ball near to the end of its run.

The acceleration is the change in velocity divided by the time taken for the change.

The formula to use is:

*a = v - u / t*

where *a* is the acceleration

*v* is the second average velocity

*u* is the first average velocity

*t* is the time between the two average velocities.

Time *t* is the time between the midpoints of the two pairs of images used to find the average velocities (if the time represented by each image pair is not great). This is one less time interval than the number of 'intervals' between the first and last ball images you have used.

*This experiment was safety-checked in March 2005*