An 8.0 g bullet is fired horizontally into a 9 kg block of wood and sticks in it.The block,which is free to move,has a velocity of 40cm/s after impact.Find the initial velocity of a bullet.
You know the momentum (total mass) of the bullet/block combo after the collision, and you know the momentum of the block before the collision(zero).
Momentumbullet+momentumblock=totalmomentumafter
Very bad
The momentum of an object can be calculated by multiplying its mass by its velocity. So the momentum of the bullet before the collision is given by:
momentum_bullet = mass_bullet × velocity_bullet
Let's assume the initial velocity of the bullet is v_bullet, and the mass of the bullet is m_bullet (8.0 g = 0.008 kg).
momentum_bullet = m_bullet × v_bullet
After the collision, the bullet is embedded in the block, so the momentum of the bullet is transferred to the block. The total momentum of the bullet and the block after the collision is given by:
momentum_total = (mass_bullet + mass_block) × velocity_total
Given that the mass of the block is m_block (9 kg) and the velocity of the block after the collision is v_total (40 cm/s = 0.4 m/s), we can write:
momentum_total = (m_bullet + m_block) × v_total
Since momentum is conserved in a collision, we can equate the two equations:
m_bullet × v_bullet = (m_bullet + m_block) × v_total
Now we can solve for the initial velocity of the bullet, v_bullet:
v_bullet = [(m_bullet + m_block) × v_total] / m_bullet
Substituting the given values:
v_bullet = [(0.008 kg + 9 kg) × 0.4 m/s] / 0.008 kg
v_bullet = [9.008 kg × 0.4 m/s] / 0.008 kg
v_bullet = 36.032 m/s
Therefore, the initial velocity of the bullet is 36.032 m/s.
To solve this problem, we can use the principle of conservation of momentum.
Before the collision, the block is at rest, so its momentum is zero. The momentum of the bullet is given by its mass (8.0 g or 0.008 kg) multiplied by its initial velocity, which we need to find.
Let's denote the initial velocity of the bullet as v.
The total momentum after the collision is the sum of the momentum of the block and the momentum of the bullet. The momentum of the block is given by its mass (9 kg) multiplied by its final velocity (40 cm/s converted to m/s, which is 0.4 m/s).
So, we have:
0.008 kg * v + 9 kg * 0.4 m/s = 0
This equation represents the conservation of momentum. Since the block and bullet are sticking together after the collision, their momentum together is zero.
Now, we can solve for v:
0.008 kg * v = -9 kg * 0.4 m/s
Dividing both sides by 0.008 kg:
v = (-9 kg * 0.4 m/s) / 0.008 kg
v = -45 m/s
Therefore, the initial velocity of the bullet is -45 m/s (negative because it's moving horizontally in the opposite direction).
So, the initial velocity of the bullet is -45 m/s.