In a ballostic pendulum an object of mass m is fired with an initial speed at a
ID: 2296227 • Letter: I
Question
In a ballostic pendulum an object of mass m is fired with an initial speed at a pendulum bob. the bob has a mass M which is suspended by a rod of length L and negligible mass. After the collision the pendulum and object stick together and swing to a maximum angular displacement angle as shown find an expression for initial speed of the fired object. Express your answer in terms of some or all of the variable m,M,L and theta and the acceleration due to gravity g 2. Determine the numerical value of speed initial if m=10g,M=1200G,L150cm and an angle 40 degree
Explanation / Answer
The height the bob rises is related to ? as
h=L*(1-cos(?))
the energy required to raise the bob is
(M+m)*g*h
this is related to the speed of the bob after collision as
.5*(M+m)*vc^2=(M+m)*g*h
and it is related to v0 using conservatin of momentum
m*v0=(M+m)*vc
combine it all together now
v0=(M+m)*vc/m
vc=sqrt(2*g*h)
v0=(M+m)*sqrt(2*g*L*(1-cos(?)))/m
v0 =(1200+10)*sqrt(2*981*150(1-cos40)) /10 = 317.5 m/s