Experiment to measure the acceleration due to gravity

Introduction

To measure this acceleration we will drop a magnet and measure the time taken for the magnet to travel between two points. This information used with the distance formula below will allow us to calculate the acceleration of the magnet due to gravity.

s = ut + ½ at²

Equipment required

• Thin enameled wire (magnet wire) for the coils.
• Cardboard
• A plastic tube, at least 80 cm in length.
• Clamp and stand.
• A magnet.
• ADC-40, running PicoScope.

Experiment setup

• Wrap two pieces of cardboard around the plastic tube about 60 to 70 cm apart.
• Wind two coils (150 turns each) around the cardboard tubes, using the enameled wire. The two coils should then be connected in series, as shown in Figure 1.
• Once the coils are wound and attached securely the plastic tube can be mounted vertically using a clamp and stand.
• A foam pad should then be placed between the plastic tube and the bench to protect the falling magnet and the bench.
• A few prelimary runs need to be done to make sure PicoScope is setup correctly and capturing all the required information. These settings depend on the distance between the two coils on the plastic tube, but an example of the settings can be seen on the screen shots for this experiment in Figures 2 and 3.

Figure 1: diagram showing the arrangement of the two coils

Carrying out the experiment

1. Measure and note the distance between the two coils.
2. Start PicoScope to capture the data (using the single trigger event).
3. Drop the magnet into the tube.
4. Save the waveform.
5. Repeat steps 2 to 4, until you have 4 to 5 sets of results.

Analyzing the results

To use the distance formula the times taken (t) to travel distances (s) to each coil have to be found.

s = ut + ½ at²

The two distances of the coils are taken from the start point to the top of each coil. The start point is taken from the front face of the magnet, as is illustrated in Figure 2.

Figure 2: diagram showing measurements for the coils

To find the time taken for the magnet to travel between the two coils:

1. Place the cursor on the first peak of the waveform from the experiment.
2. PicoScope will display the time (t₁) of the first peak (shown as 13.39 ms in the screenshot below).
3. Place the cursor on the second peak of the waveform from the experiment.
4. PicoScope will display the time (t₂) of the second peak.
5. Subtract t2 from t1 to find the time taken to travel from the first coil to the second.

Figure 3: Measurement taken using PicoScope

now using

s = ut + ½ at²

For the magnet falling to the first coil, where t is the time taken to reach the first coil.

s₁ = 0 + ½ at²

For the magnet falling from the start position to the second coil, (where dt = t2–t1).

s₂ = 0 + ½ a(dt + t)²

Solving the two equations for a will arrive at a value for the acceleration due to gravity (g).

Questions

1. Was the value for g the value you expected. If not, can you think why the value for g is less or greater than what you expected?

Further study

• Faraday’s Law states that the induced e.m.f. is proportional to the rate of cutting of field lines. Since the same magnet is passing through two identical coils it would be possible to investigate if the induced e.m.f. — measured directly from the trace — is indeed proportional to the speed of the magnet calculated using the data already obtained.