A 5.7 g bullet leaves the muzzle of a rifle with a speed of 636.8 m/s. What constant force is exerted on the bullet while it is traveling down the 0.5 m length of the barrel of the rifle? Answer in units of N
force*distance=1/2 m v^2
solve for force
this assumes there are no energy lost on friction in the barrel
To find the constant force exerted on the bullet while traveling down the barrel of the rifle, we can use the equation of motion:
Force = Mass × Acceleration
We have the mass of the bullet given as 5.7 g, but we need to convert it to kilograms (kg).
1 gram (g) = 0.001 kilograms (kg)
So, the mass of the bullet in kilograms is:
5.7 g × 0.001 kg/g = 0.0057 kg
The acceleration of the bullet can be determined using the equation of motion:
Acceleration = (Final Velocity - Initial Velocity) / Time
Since the bullet starts from rest inside the barrel and leaves the muzzle with a speed of 636.8 m/s, the final velocity is 636.8 m/s and the initial velocity is 0 m/s.
The time taken to travel down the length of the barrel can be determined using the equation of motion:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Since the initial velocity is 0 m/s and the distance is 0.5 m, the equation simplifies to:
Distance = (1/2) × Acceleration × Time^2
Rearranging the equation, we get:
Time = √(2 × Distance / Acceleration)
Plugging in the values, we have:
Time = √(2 × 0.5 m / Acceleration)
Solving for acceleration:
Acceleration = 2 × 0.5 m / (Time)^2
Next, we need to determine the time it takes for the bullet to travel down the barrel. We can use the equation of motion:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Since the initial velocity is 0 m/s and the distance is 0.5 m, the equation simplifies to:
Distance = (1/2) × Acceleration × Time^2
Plugging in the values:
0.5 m = (1/2) × Acceleration × (Time)^2
Solving for time:
(Time)^2 = (0.5 m × 2) / Acceleration
Time = √(1 m / Acceleration)
Now, substitute the expression for time in terms of acceleration into the equation we obtained earlier for acceleration:
Acceleration = 2 × 0.5 m / (√(1 m / Acceleration))^2
Simplifying:
Acceleration = 1 m / (0.5 m/s)^2
Acceleration = 1 m / 0.25 m^2/s^2
Acceleration = 4 m/s^2
Now that we have the acceleration, we can calculate the force:
Force = Mass × Acceleration
Force = 0.0057 kg × 4 m/s^2
Force ≈ 0.0228 N
Therefore, the constant force exerted on the bullet while traveling down the 0.5 m length of the barrel of the rifle is approximately 0.0228 N.