Maximum distance an object travels when released by a spring force.

[Yankeedogg]

1. A block of mass 0.247 kg is placed on top of a light, vertical spring of force constant 5 050 N/m and pushed downward so that the spring is compressed by 0.109 m. After the block is released from rest, it travels upward and then leaves the spring. To what maximum height above the point of release does it rise? (Round your answer to two decimal places.)



2. Not sure how to set up an equation to solve for the distance.

The Attempt at a Solution

 

[Simon Bridge]

Welcome to PF;
That's a problem that gives many students pause.

Not sure how to set up an equation to solve for the distance.

... hint: conservation of energy.

 

[rude man]

Is that 0.109m compressed from the relaxed position before the weight is placed, or is it after the weight is placed? Need to find out, especially since the answer calls for 2 decimal-place accuracy.
.

 

[Yankeedogg]

Rude Man, the question is posted exactly how i received it.

 

[Yankeedogg]

I got it. Yc=kx^2/2mg+Ya where k=5050N/m, x=.109, m=0.247kg, g=9.8m/s^2 and Ya= 0m because Ya is where the spring returns to its resting position and Yb is where the spring is compressed to 0.109m. Therefore, the maximum height above the spring the object reaches is 12.39m.

Equation was taken from k= 2mg (Yc-Ya)/x^2

 

[Simon Bridge]

How did you come to choose that equation?
(i.e. did you understand the problem?)

 

[Yankeedogg]

From a similar problem on an example in my textbook.

 

[rude man]

Rude Man, the question is posted exactly how i received it.

Then you should ask. I admit it doesn't make too much difference since the spring is so strong and the mass so light - but to 2 decimal points I think it might well.

Mr Bridge, what are you assuming?

 

[Simon Bridge]

@Yankeedog: so that's a "no" then? You do not understand why the similar problem was solved using that relation? Then how do you know it's the right one?

Did you try applying conservation of energy to help you understand the problem?
Do you see what difference rude man's observation makes to the answer?

@rude man: I try not to assume - unless donkeys are involved.

 

[rude man]

Got it (I heard it on Benny Hill)!. But - how will you handle the OP if he/she comes up with a numerical answer?

 

[Simon Bridge]

how will you handle the OP if he/she comes up with a numerical answer?

OP did - post #5 ;)