How is the Barrel Length of a Human Cannon Calculated?

[Mary1910]

Human cannonballs have been a part of circuses for years. A human cannonball with a mass of 70kg experiences an impulse of 4.0 x 10^3 N•s for 0.35 s.

a) Calculate the force acting on the human cannonball.

F=(J)/(Δt)
=(4000 N•s)/(0.35s)
=11428.5 N
=1.14 x 10^4 N

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.)

Im not to sure about part b), At first I thought that I should be using F•d=ΔEk, but I don't think so. Although I don't think I know of any other formulas for this type of problem that would incorporate displacement.

Any help would be appreciated. Thank you.

 

[SammyS]

Human cannonballs have been a part of circuses for years. A human cannonball with a mass of 70kg experiences an impulse of 4.0 x 10^3 N•s for 0.35 s.

a) Calculate the force acting on the human cannonball.

F=(J)/(Δt)
=(4000 N•s)/(0.35s)
=11428.5 N
=1.14 x 10^4 N

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.)

Im not to sure about part b), At first I thought that I should be using F•d=ΔEk, but I don't think so. Although I don't think I know of any other formulas for this type of problem that would incorporate displacement.

Any help would be appreciated. Thank you.

Actually that's the average force (and that's what the question should have asked you for).

Your idea was fine! Work = ΔKE seems as reasonable as any way to do this.

 

[Mary1910]

Your idea was fine! Work = ΔKE seems as reasonable as any way to do this.

Thank you! Could you just let me know if this is correct?

b)

J=Δp
Δp=mΔv

4.0 x 10^3 N•s=70kgΔv
Δv=(4.0 x 10^3 N•s)/(70kg)
Δv=57m/s

Ek=½mvf^2-½mvi^2
=½(70kg)(57m/s)^2-½(70kg)(0m/s)^2
=113715-0
=1.14 x 10^5 J

F•d=ΔEk
d=(ΔEk)/(F)
=(1.14 x 10^5)/(1.14 x 10^4)
=10m

Therefore the barrel of the cannon is 10m

 

[SammyS]

Yes, with significant digits, it's 10m or arguably it's 10.0m