Calculating Spring Stretch in Aircraft Carrier Landing

[jjd101]

Homework Statement

A 16,000 kg F-18 (jet fighter) lands at 52 m/s on an aircraft carrier, its tail hook snags the cable to slow it down. The cable is attached to a spring with a spring constant of 60,000 N/m. How far does the spring stretch to stop the jet?

Homework Equations

f=-ks
motion equations

The Attempt at a Solution

too hard to put on computer

 

[gneill]

The Attempt at a Solution

too hard to put on computer

No effort, no help!

 

[jjd101]

i tried a lot of different things, all the methods i tried didn't seem to work because it doesn't give neither time nor distance.

 

[SammyS]

Show us what you tried, so we can do a better job helping you.

 

[jjd101]

i tried taking the velocity V=m/s and setting V=deltaX/deltaT. Then i solved delta T and got deltaT=deltaX/V. I then tried substituting this into the first motion equation vf=vi+adeltaT and solving for a, then used a in another motion equation V^2 = Vi^2 +2adeltaX after all this i think i got a =36.75 and t = 1.415 which i don't think is right

 

[gneill]

i tried taking the velocity V=m/s and setting V=deltaX/deltaT. Then i solved delta T and got deltaT=deltaX/V. I then tried substituting this into the first motion equation vf=vi+adeltaT and solving for a, then used a in another motion equation V^2 = Vi^2 +2adeltaX after all this i think i got a =36.75 and t = 1.415 which i don't think is right

You're right, it's not right

As a spring stretches, the force it supplies increases. If the force is changing with distance, then so is the acceleration. If they are not constant, then you can't apply the 'usual' kinematic formulas that assume constant force or acceleration.

Problems involving springs are often best approached from a conservation of energy point of view. Kinetic and potential energy get exchanged via the spring. Do you have the formulas for kinetic energy and spring potential energy?

 

[jjd101]

KE=1/2mv2 and Us=1/2k(deltaX)^2 correct? so do i set these equal to each other?

 

[gneill]

KE=1/2mv2 and Us=1/2k(deltaX)^2 correct? so do i set these equal to each other?

Yes, you'll be setting them equal to each other. Do you know why?

 

[jjd101]

yeah i understand now, i just have trouble figuring out what equations to use. I just did it and i got distance is 26.85m. Thanks a lot i really appreciate it