Question

describe and find related formulas for ballistic pendulum? also find speed of bullet if mass of bullet if 40 gram and mass of block is 2.00kg and rise to 20cm height?

Answer 1

Consider the mass of bullet as m, its initial velocity as U. Consider the mass of the block as M, which was at rest initially. After collision, the bullet gets embedded in the block and the velocity of the bullet + block system is v.
Initial momentum, Pi = mU
Final momentum, Pf = (m + M) v
Using the conservation of momentum,
mU = (m + M) v
U = (1 + M/m) v           ...(1)

Using the conservation of energy for the bullet-block system,
1/2 (m+M) v² = (m + M) gh
Where h is the height to which the system rises.
v = SQRT[2gh]       ...(2)

Substituting (2) in (1),
Velocity of the bullet, U = (1 + M/m) x SQRT[2gh]
= (1 + 2/0.04) x SQRT[2 x 9.81 x 0.2]
= 51 x SQRT[3.924]
= 101.03 m/s