During a circus performance, a 74.8-kg human cannonball is shot out of a 18.0-m-long cannon. If the human cannonball spends 0.844 s in the cannon, determine the average net force exerted on him in the barrel of the cannon.
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:
Force = mass × acceleration
First, let's calculate the acceleration of the human cannonball using the following formula:
acceleration = change in velocity / time
Since the cannonball starts from rest and travels a distance of 18.0 m in 0.844 s, we can use the equation of motion:
distance = initial velocity × time + 0.5 × acceleration × time^2
Since the initial velocity is 0 (starting from rest), we can simplify the equation to:
distance = 0.5 × acceleration × time^2
Rearranging the equation to solve for acceleration, we get:
acceleration = (2 × distance) / (time^2)
Substituting the given values, we have:
acceleration = (2 × 18.0 m) / (0.844 s)^2
Now we can calculate the acceleration of the human cannonball.
acceleration = (2 × 18.0 m) / (0.844 s)^2 = 49.7 m/s^2
Next, we can determine the force by multiplying the mass of the cannonball (74.8 kg) by the acceleration we just calculated.
Force = mass × acceleration = 74.8 kg × 49.7 m/s^2
Calculating the force using the given values, we find:
Force = 3,713.56 N
Therefore, the average net force exerted on the human cannonball in the barrel of the cannon is approximately 3,713.56 Newtons.