3. Human cannonballs have been a part of circuses for years. A human cannonball with a mass of 70 kg experiences an impulse of 4.0x103 Ns for 0.35 s.
a) Calculate the force acting on the human cannonball.
b) How long was the barrel of the cannon? (Assume the force is applied only for the period of time that the cannonball is in the cannon.)
average Force = change of momentum / time = impulse / time
a) F = 4.0*10^3 / 0.35 Newtons
b) momentum at start = 0
momentum at end = 4*10^3
average momentum during trip up barrel = 2*10*3
average velocity in barrel = 2*10^3 / 70 = 28.6 m/s
28.6 m/s * 0.35 s = 10 meters long
Of course with a human you might not use gunpowder :) However you would fake it with a big spring and some smoke I suppose.
Why is the initial momentum at zero?
The initial momentum is at the base of the barrel when you explode the gunpowder. It is not moving until the explosion. It accelerates up the barrel.
Thank you ;-)
a) To calculate the force acting on the human cannonball, we can use the formula:
Impulse = Force * Time
From the given data, we know that the impulse is 4.0x10^3 N·s and the time is 0.35 seconds. Plugging these values into the formula, we can solve for the force:
4.0x10^3 N·s = Force * 0.35 s
To isolate the force, we divide both sides of the equation by 0.35 s:
Force = (4.0x10^3 N·s) / (0.35 s)
Force ≈ 11429 N
Therefore, the force acting on the human cannonball is approximately 11429 N.
b) To calculate the length of the barrel of the cannon, we need to use the concept of impulse again. The impulse is equal to the change in momentum, and momentum is given by the formula:
Momentum = Mass * Velocity
From the given data, we know the mass of the human cannonball is 70 kg. Assuming the human cannonball starts from rest in the barrel and experiences a constant force during the time it is in the cannon, we can calculate the final velocity using the formula:
Impulse = Force * Time = (Mass * Velocity) - (Mass * 0)
Since the initial velocity is 0, the equation simplifies to:
Impulse = Mass * Velocity
Plugging in the values, we get:
4.0x10^3 N·s = 70 kg * Velocity
To find the velocity, we divide both sides of the equation by 70 kg:
Velocity = (4.0x10^3 N·s) / 70 kg
Velocity ≈ 57 m/s
Finally, to calculate the length of the barrel, we can use the formula:
Length = Velocity * Time
Plugging in the values, we have:
Length = 57 m/s * 0.35 s
Length ≈ 20 m
Therefore, the length of the barrel of the cannon is approximately 20 meters.