Question

A bullet of mass A and velocity B is fired into a wooden block of mass C. If the bullet gets embedded in the wooden block, then the magnitude of velocity of the system just after the collision will be *

Answer 1

Answer:

The bullet strikes the block and after collision they become a system and

(Mass)

bullet

=A

(Velocity)

bullet

=B

(Mass)

block

=C

(Velocity)

block

=0

Momentum before impact = Momentum after impact

AB+0=(A+C)(v)

system

(v)

system

=

A+C

AB

The velocity of the system (v)

system

=

A+C

AB

Answer 2

When a bullet of mass A is fired with velocity B, it gets embedded in the block of mass C. The magnitude of velocity after the collision is

$v = \frac{AB}{A + C}$

Explanation -

LAW OF CONSERVATION OF MOMENTUM -

• According to the law, the total momentum of the collision objects is equal to the total momentum after the collision.
• Momentum is the product of mass and the velocity of an object.
• The total momentum of a system is a conserved and constant value.
• The law of conservation of momentum is based on Newton's third law of motion that is on collision, the objects apply equal and opposite on each other.
• In the given example,

Mass of bullet = A

Initial velocity of bullet = B

Mass of wooden block = C

Initial velocity of block = 0 m/s

Final velocity of the block and bullet,

By the law of conservation of momentum,

         Total momentum before collision = Total momentum after collision

         Momentum of bullet + Momentum of block = Total momentum

                AB + C(0) = (Mass of bullet + Mass of block) final velocity

                      AB  =  (A + C)v

                        $v = \frac{AB}{A + C}$