Difference in Height = h
h = 6.9cm X 1.67 – 4.5 X 1.67 (We multiply 1.67 here to get the value that are shown on the picture)
h = 11.523 – 7.515
h = 4.008cm = 0.04008m (scale on the picture)
h = 0.04008m (scale on the picture)
Acceleration due to Gravity = g = 9.81 m/s2
Mass of bullet = 0.128g = 0.000128kg
Mass of Target = 6.94g = 0.00694kg
Mass of Both Bullet and Target = 0.000128+ 0.00694 = 0.007068kg
Gravitational Potential Energy = Kinetic Energy
GPE = KE
=
=
=
=
=
= 0.887 m/s (Velocity of Both Bullet and Target)
Bullet = Bullet + Target (Conservation of Momentum)
=
0.000128 X = 0.007068 X 0.887
= 48.98 m/s (m/s)
Hence, the Velocity of Bullet is, 48.98 m/s
Data Analysis: error analysis
It was reported to my attention that an error occurred while measuring the top height reached by the pendulum. As I was on a field trip to Singapore, I was unfortunately out of town during the experiment. Only a single measurement of the experiment was transmitted to me afterwards. Having more data would be useful to confirm the results obtained.
A slow motion detector/camera was used to measure the exact height of the pendulum. A photograph of the pendulum before the experiment and a photograph of the pendulum at maximum height are included in annex to this report.
Conclusion and Evaluation
The Laws of conservation of momentum energy is respected. The Kinetic Energy of measured on the bullet is exactly equipotent to the Gravitational Potential Energy measured on the pendulum. Linear momentum and mechanical energy are conserved.
The BB speed we have obtained from this experiment (48.98m/s) is sensibly lower than the speed measured on commercial guns. For instance, the Daisy Model 499, one of the most widely used BB gun and a standard model for competition, has a velocity of 80m/s. In general, the velocity of normal BB guns is between 80 and 90m/s.
As the kinetic energy is transferred to the pendulum, some energy can be lost to heat, lateral deviation of the pendulum or friction. But we estimate to be negligible in the present experiment.
The pendulum must be perfectly static at the beginning of the experiment. The measurement equipment, including the pendulum should be decoupled from the table with a layer of foam. This would prevent vibrations from the floor or from the equipment to affect the results of the experiment.