Did I do this question correctly?

  • Thread starter andgabbana
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In summary: So you don't need to calculate the kinetic energy, work, etc.In summary, a human cannonball with a mass of 70kg experienced an impulse of 4.0x10^3 N*s for 0.35s. This resulted in a force of 11428.57N acting on the cannonball. Assuming the force was only applied while the cannonball was in the cannon, the barrel of the cannon was approximately 5.7m long. An alternative solution is to calculate the average velocity using the final velocity and time interval, and then use this to calculate the displacement of the cannonball.
  • #1
andgabbana
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I just want to make sure I know I'm on the right track...

A human cannonball with a mass of 70kg experiences an impulse of 4.0x10^3 N*s for 0.35s

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.)a) J = F (delta t)
4.0x10^3 = F (0.35)
F = 11428.57

b) J = delta P = 4.0x10^3
delta P = mv(f) - mv(i)
4.0x10^3 = 70 * V(f)
V(f) = 57m/s

E(k) = 0.5[mV(f)] - 0 ----- because it was at rest
=0.5(70 x 57)
=1995

F d = E(k)
11428.57 x d = 1995
d = 5.72m

therefore it was 5.7m long?
 
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  • #2
andgabbana said:
I just want to make sure I know I'm on the right track...

A human cannonball with a mass of 70kg experiences an impulse of 4.0x10^3 N*s for 0.35s

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.)a) J = F (delta t)
4.0x10^3 = F (0.35)
F = 11428.57

b) J = delta P = 4.0x10^3
delta P = mv(f) - mv(i)
4.0x10^3 = 70 * V(f)
V(f) = 57m/s

E(k) = 0.5[mV(f)] - 0 ----- because it was at rest
=0.5(70 x 57)
=1995

F d = E(k)
11428.57 x d = 1995
d = 5.72m

therefore it was 5.7m long?
[itex]E_k_i_n=\frac{1}{2}mv^2[/itex]. You forgot to square!

Other than that you are certainly on the right track. What you are doing is right in principle.

By the way, there is an alternative shorter answer to the problem. You know that there was a constant force acting on the mass, and you know the final velocity, so you can calculate the average velocity. You also know [itex]\Delta t[/itex] so you can calculate [itex]\Delta x[/itex].
 
  • #3


I cannot confirm if you have done the question correctly without seeing your calculations and assumptions. However, based on the given information and your calculations, it seems that you have correctly calculated the force acting on the human cannonball and the length of the barrel of the cannon. However, it may be helpful to specify the units for the length (meters) in your final answer. Additionally, it would be important to consider the assumptions made in your calculations and ensure they are reasonable and accurate. Overall, it appears that you are on the right track, but it is always important to double check your work and make sure all assumptions and units are accounted for.
 

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