A 10.0g bul let traveling horizontally at 365 m/s strikes and becomes embedded in a 2.25kg block of wood placed on a large table. What will be the speed of the bullet block combination immediately after impact ?
Assuming this is an inelastic collision, you use this equation:
m1v1 + m2v2 = (m1 + m2)vf
In this equation let
m1 = mass of bullet
v1 = initial velocity of bullet
m2 = mass of block
v2 = initial velocity of block
vf = final velocity of the bullet-block combination
Okay, let's plug in what we know.
(0.01 kg)(365 m/s) + (2.25 kg)(0 m/s) = (0.01 + 2.25 kg)vf
Notice how v2 is 0 m/s because the block was initially at rest. Then, solve for the final velocity.
3.65 kg-m/s = (2.26 kg)vf
Thus,
vf = 1.62 m/s
To find the speed of the bullet-block combination immediately after impact, we can use the law of conservation of momentum. According to this law, the total momentum before the impact should be equal to the total momentum after the impact.
1. First, let's calculate the momentum of the bullet before the impact:
momentum = mass x velocity
Given:
mass of the bullet (m1) = 10.0 g = 0.01 kg
velocity of the bullet (v1) = 365 m/s
momentum of the bullet = m1 * v1 = 0.01 kg * 365 m/s
2. Next, let's calculate the momentum of the block of wood before the impact:
momentum = mass x velocity
Given:
mass of the block of wood (m2) = 2.25 kg
velocity of the block of wood (v2) = 0 (since the block is at rest)
momentum of the block of wood = m2 * v2 = 2.25 kg * 0
3. The total momentum before the impact is the sum of the momentums of the bullet and the block of wood:
total momentum before = momentum of bullet + momentum of block of wood
4. According to the conservation of momentum, this total momentum should be equal to the total momentum after the impact.
5. Let's assume the speed of the bullet-block combination immediately after the impact is v3.
total momentum after = (m1 + m2) * v3
6. Equating the total momentum before and after the impact, we have:
total momentum before = total momentum after
(momentum of bullet + momentum of block of wood) = (m1 + m2) * v3
7. Now, we can solve this equation to find v3:
v3 = (momentum of bullet + momentum of block of wood) / (m1 + m2)
Plug in the values of the quantities we found earlier and calculate the result.