Determine the muzzle velocity of a spring-launched projectiile.

[howsockgothap]

Homework Statement

A gun that shoots a mass of 0.0046 kg uses a spring of constant 10.8 N/m. The 0.22 m spring is compressed to 0.11 m. The 0.22 m long barrel exerts a force of 0.25 N on the cork due to friction when it is fired. The spring obeys Hooke's law. The cork is projected horizontally.

The potential energy in the spring is 0.0653 J
The work done by friction on the cork is -0.0275 J

Question: What is the cork's speed in m/s at the muzzle of the gun? (Hint: Use the generalized Work-Energy Theorem)

Homework Equations

W=deltaE=1/2m(v₁-v₂)²

The Attempt at a Solution

I did the obvious and plugged in -0.0275=1/2mv₂² since v₁ is equal to zero. I ended up with an answer of 3.59 or so, but the study key our prof gave us says the answer is 4.06 m/s. Is there something wrong with my inital equation?

 

[rock.freak667]

The conversion of energy is like this

Potential energy = work done against friction + KE

So you should have KE = PE + Work done by friction. (I changed against to by, so the sign changed)

 

[howsockgothap]

Thank you, that helps very much.