Question
A bullet of mass ‘m’ traveling horizontally at a speed ‘v’ embeds itself in the centre of a block of wood of mass ‘M’, which is suspended by a light vertical string of length ‘l’. What would be the maximum inclination of the string with the vertical?
Answers
drwls
After the bullet gets embedded in the block, the block acquires velocity V given by
mv = (m+M) V
V = [m/(m+M)] v
Then the pendulum swings to a height H while total energy is conserved:
gH = V^2/2 = [m/(m+M)]^2 v^2/2
If the maximum inclination angle of the swing is A and the string length is l,
l (1 - cos A) = H
Solve for A
mv = (m+M) V
V = [m/(m+M)] v
Then the pendulum swings to a height H while total energy is conserved:
gH = V^2/2 = [m/(m+M)]^2 v^2/2
If the maximum inclination angle of the swing is A and the string length is l,
l (1 - cos A) = H
Solve for A