A gun is fired and a 56g bullet is accelerated to a muzzle speed of 130m/s .
Part A
If the length of the gun barrel is 0.60m , what is the magnitude of the accelerating force? (Assume the acceleration to be constant.)
vf^2=vi^2+2ad
solve for a.
then, force=mass*a
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To find the magnitude of the accelerating force, we can use the concept of impulse and momentum. The impulse of a force acting on an object is defined as the product of the force and the time it acts. In this case, the accelerating force acting on the bullet will produce an impulse that changes the momentum of the bullet.
Since the acceleration is assumed to be constant, we can use the equation:
F = m * Δv / Δt
where F is the force, m is the mass of the bullet, Δv is the change in velocity, and Δt is the time taken to achieve that change in velocity.
In this case, the mass of the bullet (m) is given as 56g (0.056 kg), and the change in velocity (Δv) is the final muzzle speed of 130 m/s.
However, we need to find the time taken (Δt) to accelerate the bullet to this final velocity.
To find the time, we can use the formula:
Δt = Δd / v
where Δd is the distance traveled by the bullet, and v is the average velocity during that distance. In this case, Δd is given as the length of the gun barrel, which is 0.60 m.
Since the bullet is accelerated from rest to the muzzle speed, the average velocity (v) can be calculated as half of the final speed:
v = 0.5 * 130 m/s = 65 m/s.
Now we can find the time taken (Δt):
Δt = 0.60 m / 65 m/s = 0.00923 s.
Now that we have the mass of the bullet (0.056 kg), the change in velocity (130 m/s), and the time (0.00923 s), we can plug these values into the formula for force (F = m * Δv / Δt):
F = 0.056 kg * (130 m/s - 0 m/s) / 0.00923 s
F = 0.056 kg * 130 m/s / 0.00923 s
F ≈ 790 N.
Therefore, the magnitude of the accelerating force is approximately 790 Newtons.