How Is Force Calculated in a Human Cannonball Act?

[Rylynn97]

During the performance of the Bouglione circus in 1976, John Tailor was fired from a compressed-air cannon whose barrel was 20m long. Taylor emerged from the cannon at 40 m/s. If Tailor's mass was 70kg, find the force on him during the firing of the cannon.

I'm at a loss for what to do. I understand that in order to get the force I must get the acceleration first. What's the relevance of the length of the barrel to the computations? How should I proceed? Thank you! ^__^.

 

[Astronuc]

Well, force F is just mass times acceleration, or F = ma. We know the mass, so we must find the acceleration.

Now all we have to do is think of the appropriate equation of motion to use.

We know he starts at rest so v₀ = 0, he emerges from the cannon at v=40 m/s, and the distance over which he is accelerated is 20 m.

So, what equation do we use?

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

 

[ogb p]

The length of the barrel is relevant because it is the distance that Tailor traveled before being launched out of the cannon. This distance, along with the final velocity of 40 m/s, can be used to calculate the acceleration using the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is 0 m/s since Tailor was at rest in the cannon), a is the acceleration, and s is the distance traveled.

So, using the given values, we have 40^2 = 0^2 + 2a(20), which can be simplified to 1600 = 40a. Solving for a, we get a = 40 m/s^2.

Now that we have the acceleration, we can use Newton's second law of motion, F = ma, to calculate the force on Tailor during the firing of the cannon. Plugging in the mass of 70 kg and the acceleration of 40 m/s^2, we get F = (70 kg)(40 m/s^2) = 2800 N.

Therefore, the force on Tailor during the firing of the cannon was approximately 2800 Newtons. This force is likely to have caused significant acceleration and impact on Tailor's body, highlighting the physical demands and risks involved in circus acts such as this one. Further analysis and considerations, such as the direction and duration of the force, could provide a more comprehensive understanding of the impact on Tailor's body during the performance.