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.
force * distance= work done = kinetic energy
0.953 F = (1/2) (0.020)(801)^2
To find the average force exerted on the bullet while it is being accelerated, you 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 can be calculated using the formula:
Work = ΔKE = KE_final - KE_initial
Given:
Mass of bullet (m) = 20 g = 0.02 kg
Initial velocity (v_initial) = 0 m/s (at rest)
Final velocity (v_final) = 801 m/s
Using the formula for kinetic energy:
KE = 0.5 * m * v^2
Initial kinetic energy (KE_initial) = 0.5 * 0.02 kg * (0 m/s)^2 = 0 J
Final kinetic energy (KE_final) = 0.5 * 0.02 kg * (801 m/s)^2 = 641.208 J
Therefore, the work done on the bullet is:
Work = ΔKE = KE_final - KE_initial = 641.208 J - 0 J = 641.208 J
The work done on the bullet is equal to the average force (F) exerted on it multiplied by the distance traveled (d) in the direction of the force:
Work = F * d
The distance traveled by the bullet is given as 95.3 cm = 0.953 m.
Therefore,
641.208 J = F * 0.953 m
Solving for F:
F = 641.208 J / 0.953 m ≈ 672.657 N
Therefore, the average force exerted on the bullet while it is being accelerated is approximately 672.657 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.
The work done on the bullet can be calculated as the product of the force applied and the distance over which the force is applied. In this case, the distance over which the force is applied is the length of the barrel, which is 95.3 cm or 0.953 m.
The kinetic energy of the bullet can be calculated using the formula:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass of the bullet, and v is the final velocity of the bullet.
Given that the mass of the bullet is 20 g or 0.02 kg, and the final velocity is 801 m/s, we can substitute these values into the kinetic energy equation:
KE = (1/2)(0.02 kg)(801 m/s)^2
= 641.242 J
Now, according to the work-energy theorem, the work done on the bullet is equal to the change in its kinetic energy. So, the work done on the bullet is:
Work = ΔKE = KE - 0
Since there is no initial kinetic energy to consider (the bullet was initially at rest), the work done is simply equal to the change in kinetic energy.
Work = 641.242 J
Finally, to calculate the average force exerted on the bullet, we divide the work done by the distance over which the force is applied:
Average Force = Work / Distance
= 641.242 J / 0.953 m
= 672.865 N
Therefore, the average force exerted on the bullet while it is being accelerated is 672.865 N.