A 22 g bullet is accelerated in a rifle barrel 43.2 cm long to a speed of 907 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
Well, well, well! Looks like we have a bullet on the move. Let's see what we can do with some energy and a dash of humor.
To find the average force exerted on the bullet while it is being accelerated, we can rely on our good ol' friend, the work-energy theorem, which states that the work done on an object equals its change in kinetic energy.
Now, we know that the kinetic energy of an object is given by the equation KE = (1/2)mv^2, where m is the mass and v is the velocity. So, let's calculate that first.
Given:
Mass of the bullet (m) = 22 g = 0.022 kg
Initial velocity (u) = 0 m/s (since the bullet starts from rest)
Final velocity (v) = 907 m/s
So, using the kinetic energy equation, we can find the change in kinetic energy:
Change in kinetic energy (ΔKE) = (1/2)m(v^2 - u^2)
Now, since the bullet starts from rest, u = 0 m/s, we can simplify the equation to:
ΔKE = (1/2)m(v^2 - 0)
ΔKE = (1/2)m(v^2)
ΔKE = (1/2)(0.022 kg)(907 m/s)^2
Now, simplify that calculation, and you'll find the change in kinetic energy.
But wait, there's more! We want to find the average force exerted on the bullet. So, we need to know the work done on the bullet, which is equal to the change in kinetic energy.
Now, the work done (W) is given by the equation W = Fd, where F is the force applied, and d is the distance covered. In this case, d is the length of the rifle barrel, which is 43.2 cm or 0.432 m.
So, we have:
W = ΔKE = Fd
Now, we can solve for the average force (F):
F = ΔKE / d
Plug in the value of ΔKE calculated earlier, and divide it by the distance covered, and voila! You'll have your answer in units of Newtons.
Now, isn't it fascinating how physics and humor can come together to solve a problem?
To find the average force exerted on the bullet while it is being accelerated, 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 can be calculated as the product of force and displacement:
Work = Force × Displacement
The change in kinetic energy of the bullet can be calculated as:
Change in Kinetic Energy = ½ × Mass × (Final Velocity^2 - Initial Velocity^2)
Given:
Mass (m) = 22 g = 0.022 kg
Length of barrel (d) = 43.2 cm = 0.432 m
Final Velocity (v) = 907 m/s
The initial velocity of the bullet can be assumed to be 0 since it starts from rest.
So, the change in kinetic energy is:
Change in Kinetic Energy = ½ × 0.022 × (907^2 - 0^2)
= 0.5 × 0.022 × (822,649)
= 9,040.994 J
Now, the work done on the bullet is equal to the change in kinetic energy, so we can write:
Work = 9,040.994 J
Finally, we can use the formula for work and the given displacement to find the average force:
Average Force = Work / Displacement
= 9,040.994 J / 0.432 m
= 20,984.152 N
Therefore, the average force exerted on the bullet while it is being accelerated is approximately 20,984.152 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 formula for work is given by W = F * d * cos(theta), where W is the work done, F is the force applied, d is the displacement, and theta is the angle between the force and displacement vectors.
In this case, the force applied is the average force exerted on the bullet, and the displacement is the length of the rifle barrel. Since the bullet is being accelerated, its initial kinetic energy is zero, and its final kinetic energy is given by KE = 1/2 * m * v^2, where m is the mass of the bullet and v is its final velocity.
Since the work done on the bullet is equal to the change in its kinetic energy, we can set up the equation:
W = KE - 0
W = 1/2 * m * v^2
To find the average force, we can rearrange the equation as:
F = W / d
Substituting the values given:
m = 22 g = 0.022 kg
v = 907 m/s
d = 43.2 cm = 0.432 m
Plugging in these values:
F = (1/2 * 0.022 kg * (907 m/s)^2) / 0.432 m
Calculating the expression:
F ≈ 2012.13 N
Therefore, the average force exerted on the bullet while it is being accelerated is approximately 2012.13 N.
F*x = 1/2*m*v^2
where F is the average force, x is the distance over which the bullet is accelerated, v is the speed, m is the mass of the bullet
F*0.432 = 1/2*22*907^2