During a circus performance, a 77-kg human cannonball is shot out of an 20-m-long cannon. If the human cannonball spends 0.91 s in the cannon, determine the average net force exerted on him in the barrel of the cannon.
He is accelerated out of the cannon at a rate "a" given by
20 = (a/2) t^2 , where t = 0.91 s
Therefore
a = 48.3 m/s^2
Use F = m*a
for the average force F, in newtons.
F = 3719 N
To determine the average net force exerted on the human cannonball inside the barrel of the cannon, we can use Newton's second law of motion:
F = m * a
Where:
F is the net force exerted on the object
m is the mass of the object
a is the acceleration
First, we need to find the acceleration of the human cannonball inside the cannon. We can use the equation of motion:
s = ut + (1/2)at^2
Where:
s is the distance traveled
u is the initial velocity
t is the time
In this case, the distance traveled is 20 m (given). The initial velocity can be calculated using the equation:
u = (s - ut) / t
Given that the time spent in the cannon is 0.91 s, we can substitute the values into the equation:
u = (20 m - 0 * 0.91 s) / 0.91 s
u = 20 m / 0.91 s
u ≈ 21.98 m/s
Next, we can calculate the acceleration by rearranging the equation of motion:
a = 2(s - ut) / t^2
Substituting the values:
a = 2(20 m - 21.98 m/s * 0.91 s) / (0.91 s)^2
a = 2(20 m - 20.0718 m) / 0.8281 s^2
a = 2(-0.0718 m) / 0.8281 s^2
a ≈ -0.1735 m/s^2
Since the cannonball is being shot out, the acceleration is negative as it opposes the motion.
Finally, we can calculate the average net force using Newton's second law:
F = m * a
F = 77 kg * (-0.1735 m/s^2)
F ≈ -13.376 N
Therefore, the average net force exerted on the human cannonball in the barrel of the cannon is approximately -13.376 N. The negative sign indicates that the force is opposite to the direction of motion.