A 12 g bullet is accelerated in a rifle barrel 69.2 cm long to a speed of 864 m/s.
Use the work-energy theorem to find the average force exerted on the bullet while it is being accelerated.
Answer in units of N.
To find the average force exerted on the bullet, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the bullet is given by:
work = force * distance
In this case, the distance is the length of the barrel, which is 69.2 cm (or 0.692 m). The work done on the bullet will be equal to the change in its kinetic energy.
The initial kinetic energy of the bullet is zero (since it starts from rest), and the final kinetic energy can be calculated using the mass and final velocity of the bullet.
The kinetic energy of an object is given by the equation:
kinetic energy = (1/2) * mass * velocity^2
Given that the mass of the bullet is 12 grams (or 0.012 kg) and the final velocity is 864 m/s, we can calculate:
final kinetic energy = (1/2) * 0.012 kg * (864 m/s)^2
Now, the work done on the bullet will be equal to the change in its kinetic energy:
work = final kinetic energy - initial kinetic energy
work = [(1/2) * 0.012 kg * (864 m/s)^2] - 0
Therefore, the work done on the bullet is equal to the final kinetic energy only.
Now, to find the average force exerted on the bullet, we divide the work by the distance:
average force = work / distance
Substituting the values we have:
average force = [(1/2) * 0.012 kg * (864 m/s)^2] / 0.692 m
Now, we can calculate the average force using a calculator:
average force ≈ 6,060.8 N
Therefore, the average force exerted on the bullet while it is being accelerated is approximately 6,060.8 Newtons.