Find g by free fall using an electronic timer.

Experiment to accurately determine the acceleration due to gravity (g) using the free-fall method with a precise electronic timer and timing apparatus.

Apparatus

• Electronic free-fall apparatus (solenoid, gate switch, stand, electronic timer, metallic bob, leads)

• Meter rod

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Introduction

Galileo first demonstrated that all objects, regardless of their mass or material, fall with the same acceleration in a vacuum. Everyone observes gravity as it pulls objects downward. In the absence of air resistance, all objects fall vertically at the same acceleration near the Earth’s surface.

If the fall distance is small compared to Earth’s radius, this acceleration remains essentially constant. This idealized motion, where air resistance is neglected, is called free-fall.

The acceleration due to gravity, denoted as $g$, points downward toward the center of the Earth. Near the surface:

$$g\approx 9.80\text{m/s²}\text{or}g\approx 32.2\text{ft/s²}$$

This experiment measures $g$ using an electronic timer. The timer records the exact time a ball takes to fall through a known height. Using this time and the distance fallen, we calculate $g$ with equations of motion.

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Principle

For small distances, air resistance is negligible. The electronic timer starts automatically when the electromagnet releases the bob. It stops when the bob hits the gate switch.

At the start of the fall:

vi=0,a=g,s=h,t=timev_i = 0, \quad a = g, \quad s = h, \quad t = \text{time}vi​=0,a=g,s=h,t=time

Using the second equation of motion:

s=vit+12at2  ⟹  h=12gt2s = v_i t + \frac{1}{2} a t^2 \implies h = \frac{1}{2} g t^2s=vi​t+21​at2⟹h=21​gt2

Thus, the acceleration due to gravity is:

g=2ht2g = \frac{2h}{t^2}g=t22h​

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Procedure

1. Turn on the electromagnet and attach the bob to its lower end.

2. Reset the electronic timer to zero.

3. Press the start switch. The timer starts as the electromagnet releases the bob.

4. The timer stops when the bob hits the gate switch. Record the time in centiseconds, then convert to seconds.

5. Measure the distance $S$ from the bob to the gate switch using a meter rod.

6. Repeat for six different distances.

7. Calculate $g$ using g=2h/t2g = 2h / t^2g=2h/t2.

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Observations and Calculations

• Distance between bob and gate switch: $S=\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ cm

• Time readings: t1,t2,…t6t_1, t_2, \dots t_6t1​,t2​,…t6​ seconds

• Calculated values of $g$: __________ m/s²

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Precautions

1. Measure the distance accurately from the lower side of the bob to the gate switch.

2. Ensure the timer is reset to zero before each run.

3. Handle the bob carefully to avoid swinging or bouncing.

4. Record measurements immediately to reduce errors.