A 28 g bullet is traveling at 414 m/s when it strikes a block of wood. If the block of wood exerts a force of 50,000 N opposing the motion of the bullet, how far will the bullet penetrate the block of wood?
F = ma, so a = 50000/0.28
Now recall that the distance traveled is
s = v^2/(2a)
To determine how far the bullet will penetrate the block of wood, we can use the principle of work-energy.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The work done by the force opposing the motion of the bullet will cause a decrease in the bullet's kinetic energy, ultimately bringing it to rest.
First, let's calculate the initial kinetic energy of the bullet using the formula:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the bullet (m) = 28 g = 0.028 kg
Velocity of the bullet (v) = 414 m/s
Plugging in the values, we have:
Kinetic Energy = (1/2) * 0.028 kg * (414 m/s)^2
Next, using the work-energy principle, we equate the work done by the block of wood to the change in kinetic energy of the bullet:
Work done = Change in kinetic energy
The work done by the block of wood opposing the motion can be calculated using the formula:
Work done = Force * Distance
Given:
Force (F) = 50,000 N (opposing force exerted by the block of wood)
To find the distance penetrated, we rearrange the equation as:
Distance penetrated = Work done / Force = Change in kinetic energy / Force
Now, let's calculate the work done:
Work done = Force * Distance penetrated
Since the block of wood brings the bullet to rest, the change in kinetic energy is equal to the initial kinetic energy of the bullet.
Therefore, we can rewrite the distance penetrated equation as:
Distance penetrated = Initial kinetic energy / Force
Plugging in the values, we have:
Distance penetrated = (1/2) * 0.028 kg * (414 m/s)^2 / 50,000 N
Calculating this equation will give us the distance penetrated by the bullet into the block of wood.