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?
grtrthrt
45
To find the impact velocity of the bullet, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity:
Momentum = mass × velocity
In this case, we have two objects involved in the collision: the bullet and the block of wood. Let's denote the mass of the bullet as mbullet and its impact velocity as vbullet. The mass of the block of wood is given as 10 kg, and its final velocity after the collision is given as 0.30 m/s.
Before the collision, the bullet is moving horizontally with some initial velocity, which we need to find. Since the bullet is fired horizontally into the block, we can assume there is no vertical motion involved, which means the vertical component of the bullet's velocity is zero. However, we don't know the exact initial velocity or the direction, so we will denote it as vbullet_initial.
Using the conservation of momentum, we can write the equation:
Total momentum before collision = Total momentum after collision
(mbullet × vbullet_initial) + (mwood × 0) = (mbullet × vbullet) + (mwood × 0.30 m/s)
Since the vertical component of velocity for both objects is zero, we can ignore it in our calculations.
Now, let's substitute the given values into the equation:
(5.40 g × vbullet_initial) + (10 kg × 0) = (5.40 g × vbullet) + (10 kg × 0.30 m/s)
Note that we need to convert the mass of the bullet from grams to kilograms, as the unit for mass in the SI system is kilograms. 1 g = 0.001 kg.
(0.0054 kg × vbullet_initial) + (10 kg × 0) = (0.0054 kg × vbullet) + (10 kg × 0.30 m/s)
Simplifying the equation:
0.0054 kg × vbullet_initial = 0.0054 kg × vbullet + 3 kg·m/s
Now, we can isolate vbullet in the equation:
0.0054 kg × vbullet_initial - 0.0054 kg × vbullet = 3 kg·m/s
0.0054 kg × (vbullet_initial - vbullet) = 3 kg·m/s
Dividing both sides of the equation by 0.0054 kg:
vbullet_initial - vbullet = 3 kg·m/s / 0.0054 kg
vbullet_initial - vbullet = 555.5556 m/s
Finally, let's solve for vbullet by subtracting vbullet_initial from both sides of the equation:
vbullet = vbullet_initial - 555.5556 m/s
The impact velocity of the bullet is equal to the initial velocity of the bullet minus 555.5556 m/s.