27-APR-2015 Ballistic Pendulum Activity

Ballistic Pendulum Activity

(Using Concepts of Momentum and Energy to Determine Initial Velocity of Projectile)

Purpose:  This activity demonstrates how the combined use of the concepts of energy and conservation of momentum can be utilized to determine the initial velocity of a projectile ball launched out of the apparatus shown below.

(Ballistic Pendulum Device)

Procedure:  A small metal ball is set into the launcher.  It is then shot out into the white block shown above (an inelastic collision).  These combined masses are then lifted together to some height h at an angle theta from the vertical (measured on the device itself as shown).  All relevant data is given below:

m1 = mball =          7.63 g  +/- 0.1 g 

m2 = mholder =      80.9 g +/- 0.1 g

theta =    21.0 degrees +/- 0.5 degrees --> 0.00873 radians

L =  length of string = 19.8 cm +/- 0.1 cm

After collecting this data, we derived an equation for the initial velocity of the projectile utilizing equations for momentum and energy as shown below:

(Derivation of Initial Velocity of Projectile)

Using our values from above, we have:

Vo = 5.89 m/s

However, it's necessary to take into account the propagated uncertainty in our calculation of initial velocity.  The determination of dVo is shown below:

(Determination of propagated uncertainty in Vo calculation)

So, for our final calculation for Vo, we have:

Vo = 5.89 m/s +/- .0898 m/s