Question: What is the firing speed of the ballistic pendulum?

 

Data: Effective mass of the catching mechanism: 116 g.

68.7g is the mass of the ball

7.7 Initial height

11.4 Final height

3.7 is the change in height

Angle: 55 degrees

 

Data Analysis:

                Conservation of energy

                Mgh m(ball+catcher)        

                Mgh=1/2mg^2

                Conservation of momentum

                M(ball)v(ball)=(m(ball)+m(catcher)*1/2mv^2

Conversions:

(68.7 g) * [(0.001 kg)/(1 g)] = 0.0687 g

(116 g) * [(0.001 kg)/(1 g)] = 0.116 g

(3.7 cm) * [(0.01 m)/(1 cm)] = 0.037 m

Conservation of Energy:

(0.0687 kg + 0.116 g) * (9.8) * (0.037 m) = 0.0669

0.0669 = (1/2) * (0.068 + 0.116) v^2

v = 0.8511 m/s

Conservation of Momentum:

(0.0687 * vball) = (0.0687 * 0.116) * (0.8511)

vball = 2.288 m/s


Conclusion:

The firing speed of the ballistic pendulum shown in the video below is about 2.288 m/s.



Describe an experiment that you could conduct to test your calculation.

A possible test to make sure that the result was accurate is to use a motion detector and graph the motion of the pendulum.