Materials:
- Measuring tape (± 1 cm; estimated)
- Scale 2000 ± 1g
- Stopwatch ( ± 0.10 second; estimated)
- Muffin forms
Method:
- A height of 2 meters was measured and marked on the wall.
- The mass of five muffin forms was measured collectively; they were then released from two meters and the time taken for it to fall was measured. This was repeated 10 times.
- Five more muffin forms were added to the previous five forms and step two was repeated.
- In this manner, readings were taken for 15, 20, 25 and 30 muffin forms.
- The average velocity for different masses falling was calculated.
- The data was processed and a diagram was drawn.
Table 1: Time taken for the fall of muffin forms of various masses from a height of 2 meters
Calculating uncertainty:
Mass: The uncertainty of the scale is 2000 ± 1 g;
Mass 1: 1/2 ×100 = 50.0%
Mass 2: 1/4 ×100 = 25.0%
Mass 3: 1/6 ×100 = 16.7%
Mass 4: 1/8 ×100 = 12.5%
Mass 5: 1/10 ×100 = 10.0%
Mass 6: 1/12 ×100 = 8.33%
Time: The uncertainty of the stopwatch is estimated as ± 0.10 second; as ten readings were taken for every mass, the uncertainty becomes:
0.10/10 = 0.01 ×100 = 1%
Velocity: velocity = displacement / time;
Displacement: the estimated uncertainty of the measuring tape: ± 1 cm; Displacement: 2 meters = 200 cm; so: 1/200 ×100 = 0.5%
Time: the calculated uncertainty in time is 1%
The uncertainty in velocity then becomes: 0.5% + 1% = 1.5%
Table 2: Average velocity (displacement/time) calculated and shown with corresponding masses of the muffin forms
Fig.1: Depicting the rise in velocity with increase in the mass of the falling muffin forms
Conclusion and Evaluation:
Observing the pattern in table 2 and Fig. 1, it could be seen that the increase in velocity is somewhat linearly proportional to the increase in mass; hence supporting the hypothesis.
The fact that heavier objects fall faster than lighter objects could be connected to the topic of terminal velocity. When an object falls from a particular height, there are two forces acting on the object in opposite directions namely the force of gravity (drawing it downwards) and the air resistance (drawing it upwards). Initially the force of gravity is greater than the air resistance; therefore, the object tends to gain more and more speed as it falls; when it reaches a point where the force of gravity becomes equal to the air resistance, the object stops accelerating (gaining further speed) and attains a velocity known as terminal velocity. For lighter objects, the forces of gravity and air resistance take a much shorter time to equalize each other compared to heavier objects; therefore, it takes a longer time for lighter objects to reach the earth since they attain their terminal velocity much earlier due to their weight and stop accelerating. Whereas, the force of gravity tends to be greater for heavier objects due to their weight and makes them accelerate; as a result they reach their terminal velocity much later. This explanation could be the reason why 30 muffin forms took a shorter time (higher velocity) to reach the ground compared to 5 muffin forms.
A limitation in the experiment was that the scale could not show any values beyond 1 g; it would be a good improvement to use a more sensitive scale for objects as light as muffin forms. The sensitivity of the measuring tape and stopwatch were quite reasonable.