Typically a bullet leaves a standard 45 caliber pistol at 262 m/s. If it takes 1 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.
change in speed = 262 m/s
time = 1 * 10^-3 s
average acceleration = change in speed/change in time = 262 * 10^3 m/s^2
Force = m a = 0.016 Kg * 262 * 10^3 Newtons
Well, if we're talking about a bullet being shot out of a 45 caliber pistol, let's just say it goes pretty fast! Now, let's do some math that's faster than a speeding bullet!
To find the average acceleration, we can use the equation:
acceleration = (final velocity - initial velocity) / time
The bullet starts from rest in the barrel, so the initial velocity is 0 m/s. The final velocity is 262 m/s, and the time it takes to transverse the barrel is 1 millisecond, which is 0.001 seconds.
Using the equation, we have:
acceleration = (262 m/s - 0 m/s) / 0.001 s
Simplifying, we get an average acceleration of a whopping:
acceleration = 262,000 m/s²
That bullet's in a hurry to leave that pistol!
Now, to find the average force exerted on the bullet, we can use Newton's second law of motion:
force = mass * acceleration
The mass of the bullet is given as 16.2 grams, which we'll convert to kilograms by dividing by 1000.
mass = 16.2 g / 1000 = 0.0162 kg
Now we can calculate the force:
force = 0.0162 kg * 262,000 m/s²
And the result is:
force = 4,244.4 Newtons
That's one powerful force! But remember, this calculation assumes constant acceleration, which is not necessarily the case in real life due to various factors. Stay safe and always handle firearms responsibly, my friend!
To find the average acceleration experienced by the bullet within the gun's barrel, you can use the equation:
acceleration (a) = change in velocity (Δv) / time interval (Δt)
Given that the initial velocity (v0) of the bullet is 0 m/s (since it starts from rest within the barrel) and the final velocity (v) is 262 m/s, and the time interval (Δt) is 0.001 seconds (1 millisecond), we can calculate the change in velocity:
Δv = v - v0 = 262 m/s - 0 m/s = 262 m/s
Now, we can substitute the values into the equation to find the average acceleration:
acceleration (a) = Δv / Δt = 262 m/s / 0.001 s = 262,000 m/s^2
Therefore, the average acceleration experienced by the bullet within the gun's barrel is 262,000 m/s^2.
To find the average force exerted on the bullet, we can use Newton's second law of motion:
force (F) = mass (m) * acceleration (a)
Given that the mass (m) of the bullet is 16.2 grams (which is 0.0162 kg), and the acceleration (a) is 262,000 m/s^2, we can calculate the force:
F = 0.0162 kg * 262,000 m/s^2 = 4256.4 N
Therefore, the average force exerted on the 16.2-gram bullet within the gun's barrel is approximately 4256.4 Newtons.
To determine the average acceleration experienced by the bullet within the gun's barrel, we can use the equation for average acceleration:
Average acceleration = (Final velocity - Initial velocity) / Time
The initial velocity of the bullet is zero, as it starts from rest within the gun's barrel. The final velocity of the bullet is 262 m/s, as stated in the question. The time it takes for the bullet to traverse the barrel is 1 millisecond, which can be converted to seconds by dividing it by 1000:
Time = 1 millisecond / 1000 = 0.001 seconds
Substituting the values into the equation, we get:
Average acceleration = (262 m/s - 0 m/s) / 0.001 s
= 262,000 m/s²
Therefore, the average acceleration experienced by the bullet within the gun's barrel is 262,000 m/s².
To compute the average force exerted on the bullet, we can use Newton's second law of motion:
Force = Mass × Acceleration
The mass of the bullet is given as 16.2 grams. To convert it to kilograms, we divide it by 1000:
Mass = 16.2 g / 1000 = 0.0162 kg
Substituting the values into the equation, we get:
Force = 0.0162 kg × 262,000 m/s²
= 4232.4 N
Therefore, the average force exerted on the bullet is approximately 4232.4 Newtons.