During a circus performance, a 64-kg human cannonball is shot out of an 17-m-long cannon. If the human cannonball spends 0.99 s in the cannon, determine the average net force exerted on him in the barrel of the cannon.
Force=mass*acceleration
where acceleration=changevelocity/time
but change velocity=Vf-0, or 2*avgvelocity=2*distance/time
solve for force.
force=mass*2*distance/time^2
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 object's mass multiplied by its acceleration.
Step 1: Find the acceleration of the human cannonball in the barrel of the cannon.
The formula to calculate acceleration is: acceleration = change in velocity / time taken.
Since the human cannonball starts from rest and is shot out of the cannon, its final velocity will be given by: final velocity = distance traveled / time taken.
Using the equation of motion, s = ut + (1/2)at^2, where u is the initial velocity (0), s is the distance traveled (17 m), t is the time taken (0.99 s), and a is the acceleration, we can solve for the acceleration:
17 = 0(0.99) + (1/2)a(0.99)^2
17 = (1/2)a(0.99)^2
a = (2 * 17) / (0.99)^2
a ≈ 36.86 m/s^2
Step 2: Calculate the net force exerted on the human cannonball.
Using Newton's second law of motion, we can calculate the net force:
net force = mass × acceleration
net force = 64 kg × 36.86 m/s^2
net force ≈ 2362.24 N
Therefore, the average net force exerted on the human cannonball in the barrel of the cannon is approximately 2362.24 N.