During a circus performance, a 67.2-kg human cannonball is shot out of a 17.1-m-long cannon. If the human cannonball spends 0.772 s in the cannon, determine the average net force exerted on him in the barrel of the cannon.
Assume a constant acceleration rate in the cannon. The average speed while going out is 17.1/0.772 = 22.15 m/s
The exit speed is twice that: 44.3 m/s
Impulse = Force*time = Momentum change
= (Mass)*(exit velocity)
Force = (Mass)(exit velocity)/time
To determine the average net force exerted on the human cannonball, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
First, let's calculate the acceleration of the human cannonball while inside the cannon. We can use the kinematic equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
The initial velocity, u, is 0 m/s since the human cannonball starts from rest. The final velocity, v, can be calculated using the equation v = s/t, where s is the displacement and t is the time.
The displacement, s, is the length of the cannon, so s = 17.1 m.
Using the equation v = s/t, we can solve for v:
v = 17.1 m / 0.772 s ≈ 22.16 m/s
Now that we have the final velocity of the human cannonball, we can calculate the acceleration using the equation v = u + at. Rearranging the equation to solve for acceleration, we get:
a = (v - u) / t
Substituting the values we know, we have:
a = (22.16 m/s - 0 m/s) / 0.772 s ≈ 28.7 m/s²
Now that we have the acceleration, we can calculate the average net force exerted on the human cannonball using Newton's second law of motion:
force = mass × acceleration
Substituting the known values, we have:
force = 67.2 kg × 28.7 m/s² ≈ 1925 N
Therefore, the average net force exerted on the human cannonball in the barrel of the cannon is approximately 1925 Newtons.