If a 5.40g bullet is fired horizontally into a suspended(hanging)10kg block of wood and causes the block, with bullet embedded, to move off with horizontal velocity of 0.30m/s,
What is the impact velocity of the bullet?
momentum before = momentum after
.0054 v = 10.0054 ( .3)
To find the impact velocity of the bullet, we need to apply the principle of conservation of momentum. The momentum before the impact is equal to the momentum after the impact.
1. Calculate the momentum before the impact:
The momentum of an object is given by the formula momentum = mass × velocity.
The mass of the bullet is given as 5.40g. To convert it to kilograms, divide by 1000: 5.40g ÷ 1000 = 0.0054 kg.
The velocity of the bullet before impact is not provided, but since it is fired horizontally into the suspended block, we can assume it is zero since there is no mention of any external force acting on the bullet.
Therefore, the momentum before the impact is 0 kg⋅m/s.
2. Calculate the momentum after the impact:
The momentum of the bullet embedded in the block can be calculated using the formula momentum = mass × velocity.
The mass of the bullet embedded in the block remains the same, 0.0054 kg.
The velocity of the block is given as 0.30 m/s.
Therefore, the momentum after the impact is 0.0054 kg × 0.30 m/s = 0.00162 kg⋅m/s.
3. Apply the principle of conservation of momentum:
The principle of conservation of momentum states that the total momentum before the impact is equal to the total momentum after the impact. Therefore, we can set up the equation:
Momentum before impact = Momentum after impact
0 kg⋅m/s = 0.00162 kg⋅m/s
Since the bullet is embedded in the block, the total mass after the impact is the sum of the bullet's mass (0.0054 kg) and the block's mass (10 kg).
Let V be the impact velocity of the bullet. The momentum after impact can be written as (0.0054 kg + 10 kg) × V.
Therefore, we have the equation:
0.00162 kg⋅m/s = (0.0054 kg + 10 kg) × V
4. Solve for the impact velocity:
First, simplify the equation by adding the masses:
0.00162 kg⋅m/s = 10.0054 kg × V
Divide both sides of the equation by 10.0054 kg:
0.00162 kg⋅m/s ÷ 10.0054 kg = V
Therefore, the impact velocity of the bullet is approximately 0.000162 m/s.
Keep in mind that this calculation assumes ideal conditions with no energy lost to friction, air resistance, or other factors.