United States Physics 1 With Calculus

[GreenPrint]

Homework Statement

See attachment.

In the system shown below, the spring is initially at its equilibrium length, L, and the block has a velocity down the ramp of 5 m/s. At the point where the block stops and turns around, the spring has a length of L + ΔL. Calculate ΔL. The ramp is frictionless, the spring constant is k = 4 N/m, the block's mass is 2 kg, and θ = 10 degrees.

Homework Equations

The Attempt at a Solution

See attachment.

I got about 3.492 meters. This problem sort of made me think more than I expected and I just wanted to make sure that my work looked reasonable and if my answer is correct possibly.

 

[Delphi51]

I have exactly the same as you for the first two lines.
I substituted numeric values at that point and got
2x² - 3.4x - 25 = 0 (using x in place of the delta L)
and x = 4.49.
Likely I made a mistake somewhere but it might be worth your checking your work by running it through this way.

 

[Simon Bridge]

Your opening argument says the initial kinetic energy and the change in gravitational potential energy gets stored in the spring. (It helps get full marks if you say so on the paper you hand in.)

I like that you took it one stage at a time, you simplified the general equation before substituting the numbers, and you did a dimensional analysis to make sure you got the right units out the end. Thus you have every reason to feel confident about your method.

Some pointers:
It helps to write notes about your reasoning on your paper - you have room to do that to the right of your equations.

First line you want to write "conservation of energy" or "KE and gravity gets stored in the spring"... something that shows the method.
Second line: "in standard form"
Third line: "quadratic equation".

Across the bottom - write out the answer using the words from the question:
"At the point where the block stops and turns around, the length of the spring has increased by 3.49m."

I don't know if you are expected to keep track of the significant figures and decimal places through the calculation. The mass of the block is only given to 1sig.fig.

Caveat: I did not actually crunch the numbers.

 

[GreenPrint]

Hm interesting. I think my number crunching was correct. I just wanted to make sure my process was correct and like you said I have no reasonable doubt to do so but I just wanted to make sure. Thanks for looking at my work.

 

[Delphi51]

I should work through your calc line by line to try to find the discrepancy, but your solution is SO long! Far better for you to work through my two liner and find the mistake there (if it is there). Run that quadratic through your calculator.

 

[GreenPrint]

grr hold up my calculator is bad

 

[Delphi51]

I hate fancy calculators! I have my quadratic solution in a spreadsheet. Just drop a, b, and c into it and the answers pop up. I don't think there is an error in that part of my calc.

 

[GreenPrint]

I think it's suppose to be

-2x² + 3.4x + 25?

 

[GreenPrint]

I found my mistake it's suppose to be the square root of 211.584 not 111.584