A 5.3-g bullet is fired horizontally into a 3.6-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 5.4 mm above its lowest position. The velocity of the bullet was:
To find the velocity of the bullet, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces act on the system.
In this case, the bullet is fired horizontally into the block of wood, causing it to swing in an arc. Since the bullet is embedded in the block, the final momentum of the system is zero (since the block comes to rest at its highest point).
Let's break down the steps to find the velocity of the bullet:
Step 1: Find the initial momentum of the bullet-block system.
The momentum of an object is given by the product of its mass and velocity (momentum = mass x velocity). In this case, the bullet has a mass of 5.3 grams (0.0053 kg), but we need to convert it to kilograms. The block has a mass of 3.6 kg.
Since the bullet is fired horizontally, its initial velocity is the same as the final velocity of the bullet-block system (which we need to find).
Initial Momentum = mass of bullet x velocity of bullet + mass of block x velocity of block
Step 2: Find the final momentum of the system.
At the highest point of the swing, the block comes to rest, so the velocity of the block is zero.
Final Momentum = mass of bullet x velocity of bullet + mass of block x 0
Step 3: Equate the initial and final momentum.
Since momentum is conserved, we can set the initial momentum equal to the final momentum.
mass of bullet x velocity of bullet + mass of block x velocity of block = 0
Step 4: Solve for the velocity of the bullet.
Rearrange the equation to solve for the velocity of the bullet:
velocity of bullet = (-mass of block x velocity of block) / mass of bullet
Step 5: Substitute the values into the equation.
- Substitute the known values into the equation.
- Mass of bullet = 0.0053 kg
- Mass of block = 3.6 kg
- Velocity of block = 0 (at highest point)
velocity of bullet = (-3.6 kg x 0) / 0.0053 kg
Step 6: Calculate the velocity.
The velocity of the bullet is given by the equation:
velocity of bullet = 0 m/s
Therefore, the velocity of the bullet is 0 m/s.