Question

c) A bullet having a mass of 10 g and
moving with a speed of 1.5 m/s,
penetrates a thick wooden plank of
mass 900 g. The plank was initially
at rest. The bullet gets embedded in
the plank and both move together.
Determine their velocity.​

Answer 1

0.0165 m/s is the required answer.

GIVEN :

• Mass of bullet , m = 10 g

• Mass of wooden planck , M = 900 g

• Initial velocity of bullet, u = 1.5 m/s

• Initial velocity of wooden planck, v = 0

TO FIND:

The final velocity , V

Since the bullet gets embedded in the Planck and move together , the final velocity of both the bullet and the planck is same.

FORMULA:

According to law of conservation of momentum, in the absence of external force acting on the system , total momentum before collision will be equal to total momentum after collision.

Momentum = m v

mu + Mv = mV + MV

SOLUTION:

STEP 1:

CONVERTING MASS IN STANDARD UNITS:

• Standard unit of mass is kilogram.

• 1 gram = 10^-3 kg

• m = 10 g = 10 × 10^-3 kg

• Mass of bullet, m = 10^-2 kg

• M = 900 g = 900 × 10^-3 kg

• Mass of the wooden planck , M = 90 × 10^-2 kg

STEP 2:

FINDING VELOCITY :

mu + Mv = mV + MV

(10^-2 × 1.5) + (9 × 10^-2 × 0) = (10^-2 × V) + (90 × 10^-2 × V)

(1.5 × 10^-2 ) + 0 = V × 10^-2 × ( 1 + 90 )

1.5 × 10^-2 = V × 91 × 10^-2

1.5 = 91 V

V = 1.5 / 91

V = 0.0165 m/s

ANSWER:

The velocity of both bullet and Planck is 0.0165 m/s.

TYPES OF COLLISION:

• Collision is of three types namely perfectly elastic collision, inelastic collision and perfectly inelastic collision.

• In perfectly elastic collision , there is no loss of energy.

• Since the bullet gets embedded in the planck , the move with same velocity. This is an example of perfectly in elastic collision.