Springs, friction, angles, and energy

  • #1
i have been given the following problem from everyone's favorite, mastering physics.
"The Great Sandini is a circus performer with mass 60.0 kg who is shot from a cannon (actually a spring gun). You don't find many men of his caliber, so you help him design a new gun. This new gun has a very large spring with a very small mass and a force constant of 1400 N/m that he will compress with a force of 4800 N. The inside of the gun barrel is coated with Teflon, so the average friction force will be only 35.0 N during the distance of 4.90 m that he moves in the barrel. At what speed will he emerge from the end of the barrel, a distance 2.60 m above his initial rest position?"

Now, i used hooke's law to find the distance he will travel while still touching the spring.
F = k * x
4800 N = 1400 N/m * x
3.43 m = x
Then, i used the conservation of energy theorem,
Potential(i) + Kinetic(i) + W(friction) = Potential(f) + Kinetic(f)
1/2*k*x^2 + 1/2*m*v^2 + (F*d) = m*g*h + 1/2*m*v^2
1/2*(1400)*(3.43)^2 + 1/2*(60)*(0)^2 + (35)(4.9) = (60)*(9.8)*(2.6) + 1/2*(60)*v^2
8240 J + 172 J = 1530 J +30*v^2
229 m^2/s^2= v^2
15.1 m/s = v

I submitted this answer to mastering physics and it told me i was close and that i may have made a rounding or significant figures error. i submitted 15.2 just to check, and i got the same feedback, maybe it's 15.0?
I think i may have done hooke's law wrong, and that in fact the distance should be twice what i found, using F*x = 1/2*k*x^2, but i only have one attempt left and i want to be sure. Using the second spring potential energy formula and plugging it into the conservation of energy theorem, my answer is 32.4 m/s.
 

Answers and Replies

  • #2
NateTG
Science Advisor
Homework Helper
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There's something wrong with the way that you've set up the equation. Make sure you've got the right signs (i.e. plus or minus) on everything, and that everything is on the correct side of the equation.
 
  • #3
ok, so i've just checked my notes and the absolute value of friction should be on the other side of the equation.
Potential(i) + Kinetic(i) = Potention(f) + Kinetic(f) + |W(friction)|

with that, i come out with 14.8 m/s as my final answer.
is that right?
 

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