1. Why are the positions of the center of mass of the pendulum with the projecti

Question

1. Why are the positions of the center of mass of the pendulum with the projectile measured, rather than the empty pendulum?

2. Compute the % difference between the ballistic pendulum method and projectile motion method velocities. Is the velocity difference reasonable in view of the experimental limitations?

3.If the elevation change, h, in the Ballistic Pendulum Method were increased by 1%, then by what would be % change in the resulting velocity v? (Please use an approximation technique to answer this question.)

4. If the projectile’s velocity were doubled, then by what factor would its momentum be changed? By what factor would its kinetic energy be changed?

Momentum change factor:___ Kinetic energy change factor:____

Explanation / Answer

1)   positions of the center of mass of the pendulum with the projectile measured, rather than the empty pendulum because in imperfect collision the projectile get embedded into the pendulum .

2)    By ballistic pendulum method   velocity = 0.78 v

        By projectile motion method   velocity = 0.73 v

=>   % difference   =   (0.05/0.78) * 100   =   6 %

3)      Here, v = sqrt(2gh)

=>    If the elevation change, h, in the Ballistic Pendulum Method were increased by 1%

=>      % change in the resulting velocity v = 0.498 %

4)    If the projectile’s velocity were doubled

=>   Momentum change factor   = momentum is also doubled

=>    Kinetic energy change factor =   Kinetic energy is increased four times .

5)     Here, Kf = ((65)/(65 + 190)) * Ki

              =>   Kf = 0.2549 * Ki

% kinetic energy Loss = (0.7451/1) * 100

                                      =   74.51 %

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