Verifying Process for Block & Spring Problem

[I am Inquisitive]

I have this problem, and I'd just like to make sure if the process I used to achieve an answer is correct.

A 0.25-kg block is dropped straight downward onto a vertical spring. The spring constant of the spring is 58 N/m. The block sticks to the spring, and the spring compresses 0.15 m before coming to a momentary halt. What is the speed of the block just before it hits the spring?

So I use this equation to solve it: PEg (graviational potential energy) + KE0 (initial kinetic energy) + PEe0 (initial elastic potential energy) = PEg2 + KEf + PEef.

And there would be no initial elastic potential energy, no final kinetic energy and no final gravitational potential energy, thus leaving me with:

KE0 + PEg = PEef, which expanded would be:

1/2 mv^2 + mgh = 1/2kh (or x)^2

Plug in the numbers accordingly..

1/2 (.25)(v^2) + (.25)(9.8)(.15) =1/2(58)(.15)^2

which gives me an answer of 1.51 m/s.

Is what I'm doing right?

 

[lippyka]

Yes, your process is correct. You used the correct equation and plugged in the given values correctly. The answer of 1.51 m/s is correct.

 

[kyle8921]

Based on the information provided, it appears that your process and calculations are correct. However, to verify your answer, you could also use the conservation of energy principle, which states that the total energy of a system remains constant. In this case, the initial energy (kinetic and potential) of the block is equal to the final energy (elastic potential) of the block-spring system.

Using this principle, the equation would be:

KE0 + PEg = PEef

1/2 mv^2 + mgh = 1/2 kh^2

Where h is the maximum compression of the spring (0.15 m in this case).

Solving for v, we get v = √(2gh) = √(2*9.8*0.15) = 1.51 m/s, which is the same answer you obtained using your method.

Overall, it is important to double check your calculations and use multiple methods to verify your answer in order to ensure accuracy in scientific research.