a bullet of mass 30g is fired in 180mls into a block of wood of mass 2g hanging freely a, find the speed of block just after impact
conserve momentum:
30 * 180 + 2*0 = (30+2)v
velocity is m/s, not mls.
I find a block of wood weighing 2g a bit unrealistic...
To find the speed of the block just after impact, we can use the principle of conservation of momentum.
1. Calculate the initial momentum of the bullet:
Momentum = Mass * Velocity
Mass of the bullet = 30g = 0.03kg
Velocity of the bullet = unknown, let's call it v1
Initial momentum of the bullet = 0.03kg * v1 = 0.03v1
2. During the impact, the bullet gets embedded in the block. So the combined mass of the bullet and the block becomes:
Total mass = Mass of bullet + Mass of block
Total mass = 0.03kg + 0.002kg = 0.032kg
3. After the impact, the combined mass moves together:
Let the final velocity of the bullet and the block be v2.
Using conservation of momentum:
Initial momentum of the bullet = Final momentum of the bullet + Final momentum of the block
0.03v1 = (0.032) * v2
4. Rearrange the equation to solve for v2:
v2 = (0.03v1) / 0.032
5. Finally, substitute the given value of v1 to find v2.
To find the speed of the block just after impact, we can use the principle of conservation of momentum. According to this principle, the total momentum before the impact is equal to the total momentum after the impact.
Step 1: Calculate the momentum of the bullet before the impact.
Momentum (p) is given by the formula:
p = mass × velocity
The mass of the bullet is 30g, which is 0.03 kg.
The bullet is given a velocity (speed) but we don't know the exact value.
Step 2: Calculate the momentum of the wooden block before the impact.
The wooden block is hanging freely, so its initial velocity is zero.
The mass of the wooden block is 2g, which is 0.002 kg.
Since the initial velocity of the wooden block is zero, its momentum before the impact is also zero.
Step 3: Calculate the total momentum before the impact.
Since momentum is a vector quantity, we can express the total momentum before the impact as:
Total momentum before = Momentum of bullet before + Momentum of wooden block before
Total momentum before = p(bullet) + p(wooden block before)
Total momentum before = p(bullet) + 0 (since p(wooden block before) = 0)
Step 4: Calculate the total momentum after the impact.
The bullet hits the wooden block and becomes embedded in it.
As a result, the bullet and the wooden block move as one system after the impact.
Let's assume that the combined mass of the bullet and the wooden block is M.
The final speed of the block just after impact is denoted by V.
The total momentum after the impact is given by:
Total momentum after = (M × V)
According to the principle of conservation of momentum,
Total momentum before = Total momentum after
Therefore, we can write:
p(bullet) = (M × V)
Step 5: Solve for V (speed of the block just after impact).
We know that p(bullet) = mass × velocity (from Step 1)
So, (mass × velocity) = (M × V)
Rearranging the formula, we find:
V = (mass × velocity) / M
In this case, the mass of the bullet is 0.03 kg (from Step 1), and we need to find the value of M (combined mass of the bullet and the wooden block).
By adding the mass of the bullet and the mass of the wooden block, we get:
M = mass of bullet + mass of wooden block
M = 0.03 kg + 0.002 kg
Now we have all the values needed to calculate the speed (V) of the block just after impact.