Rotational & rolling energy, springs help

[jjd101]

Homework Statement

There are a few, help with any would be appreciated.

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?

A horizontal spring with a spring constant of 200.0 N/m is compressed 25.0 cm and used to launch a 3.00 kg block across a frictionless surface. After the block travels some distance, the block goes up a 32 degree incline that has a coefficient of friction of 0.25 between the block and the surface of the incline. How far along the incline does the block go before stopping?

A playground merry-go-round (which can be modeled as a disk) has a 3.4 m diameter, a mass of 240 kg and is rotating at 22.5 rpm. A 35 kg child running at 6.0 m/s, tangent to and in the same direction as the merry-go-round is turning, jumps on the outer edge. Ignoring any friction, what is the angular velocity in rpm after the child jumps on?

An 800 g, 40.0 cm diameter hollow sphere is rolling along at 4 m/s when it comes to a 25 degree incline. Ignoring any friction, how far along the incline does it roll before it stops and reverses its direction?

A ball on a 6.5 m long string swings down and wraps around a post that is 4.0 m below the post the string is attached to. If the ball is released level with the post to which it is attached, what will be the velocity of the ball when it is at its highest point over the lower post?

Homework Equations

K rolling=1/2Iw^2 + 1/2Mv^2
F=-k(DELTAx)

The Attempt at a Solution

My attempts for these problems are too difficult to transfer from paper to computer.

 

[anathema]

However, I can give some general advice for solving these types of problems.
First, make sure you understand the concepts and equations involved. Review any relevant material from your class or textbook.
Next, write down what you know and what you are trying to find. This will help you organize your thoughts and determine what equations to use.
Then, carefully choose your reference frame and draw a free body diagram to help you visualize the problem.
Finally, use the appropriate equations and plug in your known values to solve for the unknown. Don't forget to include units in your final answer!
If you are still having trouble, try breaking the problem into smaller parts and solving each part separately. Also, don't be afraid to ask for help from your classmates, teacher, or a tutor. Good luck!