typically a bullet leaves a standard 45 caliber pistol at 262 m/s. if it takes i millisecond to transverse the barrel, determine the average acceleration experienced by the 16.2 gram bullet within the gun's barrel and then compute the average force exerted on it
Vfinal = sqrt(2aX)
X = barrel length
Solve for average acceleration, a.
Avg. Force = M*(average acceleration)
Typically a bullet leaves a standard 45 caliber pistol (5.0 inch barrel) at a speed of 262 m/s. If it takes 1 ms to traverse the barrel, determine the average acceleration by the 16.2 g bullet within the gun and then compute the average force Exerted on it
To determine the average acceleration experienced by the bullet within the gun's barrel, we can use the following equation:
a = (vf - vi) / t
where:
a = average acceleration
vf = final velocity of the bullet
vi = initial velocity of the bullet
t = time taken to traverse the barrel
Given that the initial velocity vi is 0 m/s (since the bullet starts from rest) and the final velocity vf is 262 m/s, and the time taken to traverse the barrel is 1 millisecond (which is equal to 0.001 seconds), we can substitute these values into the equation:
a = (262 m/s - 0 m/s) / 0.001 s
a = 262,000 m/s^2
Thus, the average acceleration experienced by the bullet within the gun's barrel is 262,000 m/s^2.
To compute the average force exerted on the bullet, we can use Newton's second law of motion:
F = m * a
where:
F = force exerted
m = mass of the bullet
a = average acceleration
Given that the mass of the bullet is 16.2 grams (which is equal to 0.0162 kg), and the average acceleration is 262,000 m/s^2, we can substitute these values into the equation:
F = 0.0162 kg * 262,000 m/s^2
F = 4,244 N (rounded to three significant figures)
Therefore, the average force exerted on the 16.2 gram bullet within the gun's barrel is approximately 4,244 Newtons.
To find the average acceleration experienced by the bullet within the gun's barrel, we can use the formula:
Average acceleration = (change in velocity) / (time taken)
First, let's convert the velocity from m/s to m/ms (millimeters per millisecond) for consistency:
262 m/s = 262,000 mm/s
Next, convert the time from milliseconds to seconds:
1 millisecond = 0.001 seconds
Now, we can calculate the change in velocity:
Change in velocity = final velocity - initial velocity
In this case, the bullet's velocity changes from 0 m/ms to 262,000 mm/s in 1 millisecond. Therefore, the change in velocity is:
Change in velocity = 262,000 mm/s - 0 m/ms = 262,000 mm/s
Plugging in the values, we get:
Average acceleration = (262,000 mm/s) / (0.001 s)
= 262,000,000 mm/s^2 (since acceleration is measured in mm/s^2)
Now, let's calculate the average force exerted on the bullet while it is inside the barrel. To do this, we can use Newton's second law of motion, which states:
Force = mass x acceleration
The mass of the bullet is given as 16.2 grams, but we need to convert it to kilograms:
16.2 grams = 0.0162 kg
Plugging in the values, we get:
Average force = (0.0162 kg) x (262,000,000 mm/s^2)
= 4,244,400 N (since force is measured in Newtons)
Therefore, the average acceleration experienced by the bullet within the gun's barrel is 262,000,000 mm/s^2, and the average force exerted on it is 4,244,400 Newtons.