A pendulum bob of mass 2 kg is hanging by a steing of length 1m . A bullet of maa 0.5 kg moves with 10 m/s strikes the bob and gets embrdded into it.

Question

Find the maximum angle of deflection from verticle to which the string will be deflected by conservation of energy principle. 

Answer 1

I will set this up for you and you work the math.

 

L = length of pendulum
M = mass of pendulum bob
m = mass of bullet

v = speed of bullet

θ = maximum angle from vertical

 

The bob rises by

 

h = L(1 - cosθ)

 

mv²/2 = (m + M)gh 

 

mv²/2 = (m + M)gL(1 - cosθ)

 

Solve for cosθ, then evaluate the arc cosine of θ, with 

 

0 < θ < 90°

 

You should be able to finish from here.