A 5.8 g bullet leaves the muzzle of a rifle with
a speed of 306 m/s.
What total constant force is exerted on the
bullet while it is traveling down the 0.75 m
long barrel of the rifle?
vf^2=2*force/mass* distance
solve for force. change mass to kg.
To find the total constant force exerted on the bullet while it is traveling down the 0.75 m long barrel of the rifle, we can use the principle of impulse and momentum.
The impulse-momentum principle states that the change in momentum of an object is equal to the impulse applied to it. The impulse is the product of the force exerted on an object and the time interval over which the force acts. The momentum of an object is equal to the product of its mass and velocity.
In this case, the bullet leaves the muzzle of the rifle with a certain velocity, so we need to find the change in momentum. We know the mass of the bullet is 5.8 g, which is equal to 0.0058 kg, and the velocity is 306 m/s.
The change in momentum (Δp) is given by the formula:
Δp = final momentum - initial momentum
The initial momentum of the bullet is 0, as it starts from rest inside the barrel. The final momentum can be calculated using the mass and velocity of the bullet as follows:
final momentum = mass * velocity
Substituting the given values:
final momentum = 0.0058 kg * 306 m/s
Now, we can find the change in momentum:
Δp = final momentum - initial momentum
Δp = (0.0058 kg * 306 m/s) - 0
Next, recall that impulse is equal to the change in momentum:
impulse = Δp
Since the force is constant, the time interval over which the force acts is the time it takes for the bullet to travel the length of the barrel. We know the length of the barrel is 0.75 m.
The average velocity of the bullet while traveling down the barrel is equal to the distance divided by the time:
average velocity = distance / time
Rearranging the formula, we get:
time = distance / average velocity
Substituting the given values:
time = 0.75 m / average velocity
Finally, substitute the time value into the impulse formula to find the force:
impulse = force * time
Rearranging the formula, we get:
force = impulse / time
By plugging in the values of impulse and time, we can find the total constant force exerted on the bullet.