In a \"ballistic pendulum,\", the bullet is fired at a massive pendulum bob that
ID: 1265205 • Letter: I
Question
In a "ballistic pendulum,", the bullet is fired at a massive pendulum bob that is hanging straight downward at rest. The bullet embeds itself in the bob, and the bob+bullet together swing up to some maximum height before pausing to swing back downward.
a. If the bullet has a mass of 30.g, the bob's mass is 5.0 kg, and the bob+bullet reaches a final height of 50.cm after impact, what is the speed of bullet just before impact? show work
b. If the length of the pendulum arm is 1.2m, what maximum angle of displacement does the pendulum arm reach? show work. Include a diagram of the triangle, clearly showing the angle in question.
Explanation / Answer
a) conservation of energy
KE = PE
0.5*mv^2 = (m+M)*g*h
0.5*30x10^-3*v^2 = (5 + 30x10^-3)*9.8*0.5
v = 40.5355 m/s
b) H = L*[1 - cos(theta) ]
0.5 = 1.2 [ 1 - cos(theta]
cos(theta) = 0.5833
theta = 54.314 degrees