A 0.22 calibre rifle shoots a bullet of mass 1.8 g with a muzzle velocity of 500 m/s. If the barrel is 25 cm long, what is the average force exerted on the bullet while it is in the barrel?
Oh, I see we've got ourselves a projectile problem here. So, a 0.22 calibre rifle, huh? Well, it sounds like you're asking about the force exerted on the bullet while it's in the barrel.
Let's strap on our thinking caps and calculate this. We've got a bullet with a mass of 1.8 grams and a muzzle velocity of 500 m/s. But, before we continue, let's convert that bullet mass from grams to kilograms, because the metric system is just cooler that way. So, 1.8 grams is equal to 0.0018 kilograms.
Now, we need to find the time it takes for the bullet to emerge from the barrel. Since speed is distance divided by time, and the distance traveled is the length of the barrel (25 cm or 0.25 meters), we can rearrange the equation to solve for time. Time is equal to distance divided by speed. So, time is 0.25 meters divided by 500 m/s, which gives us 0.0005 seconds.
Stay with me, we're almost there. To calculate the average force exerted on the bullet, we can use the equation force equals mass times acceleration. Now, acceleration is a change in velocity over time. But since the bullet is in the barrel for such a short time, we can approximate the acceleration as the change in velocity divided by the time it takes to leave the barrel. So, the change in velocity is the final velocity (500 m/s) minus the initial velocity (0 m/s), which gives us 500 m/s.
Therefore, acceleration is 500 m/s divided by 0.0005 seconds, which gives us a whopping 1,000,000 m/s²!
Finally, we can plug in the values into the force equation: force equals 0.0018 kg times 1,000,000 m/s².
And the grand finale! The average force exerted on the bullet while it's in the barrel is approximately 1,800 Newtons.
Just remember that this is an average force, so the actual force experienced by the bullet could vary throughout its journey. But hey, if you were looking for a bang, there it is! *cue comical explosion*
To find the average force exerted on the bullet while it is in the barrel, we can use the formula for average force:
Average Force = (Change in Momentum) / (Time)
First, let's calculate the change in momentum of the bullet.
Momentum = Mass x Velocity
Given that the mass of the bullet is 1.8 g (or 0.0018 kg) and the muzzle velocity is 500 m/s, we can calculate the initial momentum:
Initial Momentum = Mass x Velocity
= 0.0018 kg x 500 m/s
Next, let's calculate the final momentum of the bullet when it exits the barrel. Since it is not specified whether the bullet accelerates or decelerates within the barrel, we will assume that the final momentum is the same as the initial momentum.
Now, we can calculate the change in momentum:
Change in Momentum = Final Momentum - Initial Momentum
= Initial Momentum - Initial Momentum
= 0
Since the change in momentum is zero, there is no change in momentum as the bullet travels through the barrel.
Lastly, we need to determine the time it takes for the bullet to travel through the barrel. We can use the formula for average speed:
Average Speed = Distance / Time
Given that the barrel length is 25 cm (or 0.25 m) and the muzzle velocity is 500 m/s, we can rearrange the formula to solve for the time:
Time = Distance / Average Speed
= 0.25 m / 500 m/s
Now that we have the change in momentum and the time, we can calculate the average force exerted on the bullet using the formula:
Average Force = Change in Momentum / Time
= 0 / (0.25 m / 500 m/s)
Since the change in momentum is zero, the average force exerted on the bullet while it is in the barrel is also zero.
To calculate the average force exerted on the bullet while it is in the barrel, we can use the principle of impulse-momentum. The impulse experienced by an object is equal to the change in momentum it undergoes.
First, let's calculate the initial momentum of the bullet as it leaves the barrel. Momentum (p) is given by the product of mass (m) and velocity (v):
Momentum = mass x velocity
p = m * v
Given that the mass of the bullet (m) is 1.8 g = 0.0018 kg and the muzzle velocity (v) is 500 m/s, we can calculate the initial momentum:
p = 0.0018 kg * 500 m/s
p = 0.9 kg⋅m/s
Now, the average force (F) exerted on the bullet can be determined by the change in momentum (∆p) divided by the time (Δt) it takes for the bullet to travel the length (l) of the barrel:
Average Force = Change in Momentum / Time
F = ∆p / Δt
The change in momentum (∆p) is equal to the final momentum minus the initial momentum. Since the bullet starts from rest inside the barrel, the final momentum is zero:
∆p = 0 - 0.9 kg⋅m/s
∆p = -0.9 kg⋅m/s
To find the time (Δt), we can use the equation for average speed:
Average Speed = Distance / Time
v_avg = l / Δt
Rearranging the equation, we can solve for Δt:
Δt = l / v_avg
Given the length of the barrel (l) as 25 cm = 0.25 m, we need to calculate the average speed (v_avg). The average speed is the distance traveled divided by the time taken, which is equal to the muzzle velocity (v) since the bullet starts from rest inside the barrel:
v_avg = v
Therefore, the time (∆t) it takes for the bullet to travel the length of the barrel is:
Δt = 0.25 m / 500 m/s
Δt = 0.0005 s
Finally, we can calculate the average force (F) exerted on the bullet:
F = ∆p / Δt
F = -0.9 kg⋅m/s / 0.0005 s
F = -1800 N
The negative sign indicates that the force acts in the opposite direction of the bullet's motion. Therefore, the average force exerted on the bullet while it is in the barrel is 1800 Newtons.
force * distance = work
so work done = .025 F
which we assume is Ke of bullet
(1/2) m v^2 = .025 F
(1/2) (.0018) (500)^2 = .025 F