A bullet having a mass of 10g and moving with a speed of 1.5m/s penetrates a thick wooden plank of mass 90g. The plank was initially at rest. The bullet gets embedded in the plank and both moves together. Determine their velocity
momentum is conserved
10 * 1.5 = (90 + 10) * v
O.15m/s
I want the answer step wise...
Ans. Data: m, 10 g=10 x 10-3 kg, u, -1.5 m/s, m2=90 g = 90 × 10-3 kg. u, 0 m/s, v₁ = v₂ =v=?
=
By the law of conservation of momentum,
m,u,+m,u,m,v,+m₂v₂
As u₁ = 0 m/s and v₁ = v₁ =v, we have
m,u,(m, +m₂) v
..U = mu, m+m₂
10 x 10 kg x 1.5 m/s 10 x 10 kg +90 x 10 kg
110 x 1.5 100 m/s = 0.15 m/s
The speed with which the plank containing the bullet moves = 0.15 m/s
0.15m/s
0.15m/s
0.15m/s
To determine the final velocity of the bullet and plank system, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Momentum is defined as the product of mass and velocity, so we can calculate the initial momentum of the bullet and the final momentum of the bullet-plank system.
Initial momentum of the bullet = mass of the bullet × velocity of the bullet
= 0.01 kg × 1.5 m/s
= 0.015 kg⋅m/s
Since the plank was initially at rest, its initial momentum is zero.
Total initial momentum = initial momentum of the bullet + initial momentum of the plank
= 0.015 kg⋅m/s + 0
= 0.015 kg⋅m/s
After the collision, the bullet gets embedded in the plank, and they both move together. The mass of the bullet-plank system is the sum of the masses of the bullet and the plank.
Mass of the bullet-plank system = mass of the bullet + mass of the plank
= 0.01 kg + 0.09 kg
= 0.1 kg
Now, we can find the final velocity of the bullet-plank system using the equation:
Total final momentum = total initial momentum
(mass of the bullet-plank system) × (final velocity of the bullet-plank system) = (total initial momentum)
(0.1 kg) × (final velocity of the bullet-plank system) = (0.015 kg⋅m/s)
Solving for the final velocity:
(final velocity of the bullet-plank system) = (0.015 kg⋅m/s) / (0.1 kg)
= 0.15 m/s
Therefore, the final velocity of the bullet-plank system is 0.15 m/s.