During a circus performance, a 75-kg human cannonball is shot out of an 19-m-long cannon. If the human cannonball spends 0.94 s in the cannon, determine the average net force exerted on him in the barrel of the cannon
V = 19 m / .94 s = 20.2 m/s,
V = at,
a = V / t = 20.2 m/s / 0.94 s = 21.5 m/s^2,
F = ma = 75 kg * 21.5 m/s^2 = 1613 N.
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To determine the average net force exerted on the human cannonball in the barrel of the cannon, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
1. First, let's calculate the acceleration of the human cannonball. We can use the equation of motion:
d = v0t + (1/2)at^2,
where d is the displacement (19 m in this case), v0 is the initial velocity (0 m/s since the cannonball starts from rest), t is the time (0.94 s), and a is the acceleration.
Rearranging the equation, we have:
a = (2(d - v0t)) / t^2.
Plugging in the given values, we get:
a = (2(19 m - 0 m/s * 0.94 s)) / (0.94 s)^2
= 40.425 m/s^2.
2. Next, we can calculate the force exerted on the human cannonball using Newton's second law:
F = ma,
where F is the net force, m is the mass (75 kg in this case), and a is the acceleration we calculated in step 1.
Plugging in the values, we get:
F = 75 kg * 40.425 m/s^2
= 3031.875 N.
Therefore, the average net force exerted on the human cannonball in the barrel of the cannon is approximately 3031.875 Newtons.