A 19 g bullet is accelerated in a rifle barrel
70.6 cm long to a speed of 506 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
force*distance=1/2 m vf^2
To find the average force exerted on the bullet while it is being accelerated, we can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The work done on the bullet is equal to the force exerted on it multiplied by the distance over which the force is applied. In this case, the distance is the length of the rifle barrel, which is 70.6 cm = 0.706 m.
The initial kinetic energy of the bullet is zero because it starts from rest. The final kinetic energy can be calculated using the formula:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the bullet, and v is the final velocity of the bullet.
Plugging in the values given in the problem:
m = 19 g = 0.019 kg (convert grams to kilograms)
v = 506 m/s
KE = (1/2) * 0.019 * (506)^2
Now, we can calculate the work done on the bullet:
Work = KE - 0 (initial kinetic energy is zero)
Finally, we can use the work done and the distance to calculate the average force using the formula:
Work = Force * distance
Rearranging the formula, we get:
Force = Work / distance
Plugging in the values we have calculated:
Force = (KE - 0) / 0.706
Calculate the value of KE first, then substitute it into the formula above to find the average force exerted on the bullet while it's being accelerated.