A 20 g bullet is accelerated in a rifle barrel
95.3 cm long to a speed of 801 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 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:
Work = Change in Kinetic Energy.
In this case, the work done on the bullet while it is being accelerated is the force exerted on the bullet multiplied by the distance over which the force is applied. So, we can write:
Work = Force × Distance.
Since the bullet is being accelerated, its initial kinetic energy is zero, and its final kinetic energy is given by:
KE_final = (1/2) × mass × velocity^2.
The change in kinetic energy is then:
ΔKE = KE_final - KE_initial = (1/2) × mass × velocity^2.
Substituting this into the work-energy equation, we have:
Work = Force × Distance = ΔKE.
Now let's plug in the given values:
Mass of the bullet, m = 20 g = 0.02 kg.
Velocity of the bullet, v = 801 m/s.
Distance, d = 95.3 cm = 0.953 m.
Substituting these values into the equation, we have:
Force × 0.953 m = (1/2) × 0.02 kg × (801 m/s)^2.
Simplifying the right side of the equation gives:
Force × 0.953 m = 641.2788 kg·m^2/s^2.
To solve for the force, we divide both sides of the equation by 0.953 m:
Force = 641.2788 kg·m^2/s^2 / 0.953 m.
Calculating this gives:
Force ≈ 672.66 N.
Therefore, the average force exerted on the bullet while it is being accelerated is approximately 672.66 Newtons.