Solve the following examples.

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 90 g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

0.15 m/s

Given:

Mass of bullet, m₁ = 10g = 0.01 kg

Speed of bullet, v₁ = 1.5 m/sec

Mass of wooden plank, m₂ = 90 g = 0.09 kg

Velocity of plank + bullet system = ?

Here, we will apply the law of conservation of momentum,

i.e. Final momentum = initial momentum

If we take bullet and thick wooden plank as a system then, initially only bullet is moving with speed of 1.5 m/s and plank is in rest.

∴ initial Momentum (p_i) = mass of bullet × velocity

= 0.01 kg ×1.5 m/sec

= 0.015 kgms^-1

⇒ p_i = 0.015 kgms^-1 ….(1)

Now, when the bullet hits the plank, then both the objects are attached.

So, new mass(M) = mass of bullet + mass of plank

= 0.01 kg + 0.09 kg

= 0.1kg

Then,

Final momentum, p_f = New mass (M) × (velocity of plank & bullet system)

⇒ p_f = 0.1kg × v….(2)

Now, from equation (1) & (2), we get,

P_i = p_f

⇒ 0.015 kgms^-1 = 0.1kg × v

⇒

⇒ v = 0.15 m/s