A 5.00-g bullet is fired into a 500-g block of wood suspended as a ballistic pendulum.
The combined mass swings up to a height of 10.00 cm. What was the magnitude of the
momentum of the combined mass immediately after the collision?
Ans: 0.707 Kg m/sec
To find the magnitude of the momentum of the combined mass immediately after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision in an isolated system.
The momentum of an object can be calculated using the formula:
Momentum = mass × velocity
Since the bullet is fired into the block of wood, it becomes embedded in the wood. Let's assume the velocity of the bullet before the collision is v1 and the velocity of the combined mass after the collision is v2.
The momentum of the bullet before the collision is given by:
Momentum of bullet before collision = mass of bullet × velocity of bullet before collision
Momentum of bullet before collision = 5.00 g × v1
The bullet becomes embedded in the block, so the total mass after the collision is the sum of the mass of the bullet and the mass of the block. Therefore, the total mass after the collision is:
Total mass after collision = mass of bullet + mass of block
Total mass after collision = 5.00 g + 500.00 g
Now, using the principle of conservation of momentum, we can equate the momentum before the collision to the momentum after the collision:
Momentum before collision = Momentum after collision
(5.00 g × v1) = (Total mass after collision × v2)
We are given that the combined mass swings up to a height of 10.00 cm. This means that there is a change in potential energy of the system. The change in potential energy is equal to the work done against gravity, which is given by:
Change in potential energy = mass × gravity × change in height
Change in potential energy = (Total mass after collision) × (9.8 m/s^2) × (0.10 m)
(0.10 m is equal to 10.00 cm in meters)
Now, since potential energy is converted from the initial kinetic energy of the system, we can equate the change in potential energy to the initial kinetic energy:
Change in potential energy = Initial kinetic energy
The initial kinetic energy of the system is equal to the sum of the kinetic energy of the bullet and the kinetic energy of the block immediately after the collision:
Initial kinetic energy = (1/2) × (mass of bullet) × (v1)^2 + (1/2) × (mass of block) × (v2)^2
By rearranging the formula, we can solve for (v2)^2:
(v2)^2 = (2 × Initial kinetic energy - (mass of bullet) × (v1)^2) / (mass of block)
Now that we have the value of (v2)^2, we can substitute it back into the equation for momentum after the collision:
Momentum after collision = Total mass after collision × v2
Substituting the values and solving this equation will give us the magnitude of the momentum of the combined mass immediately after the collision.
A 5.00-g bullet is fired into a 500-g block of wood suspended as a ballistic pendulum.
The combined mass swings up to a height of 10.00 cm. What was the magnitude of the
momentum of the combined mass immediately after the collision?
The Ans is 0.707 kg m/sec
I do not know how to go get this answer