EKrackers Math Reasoning Problem - Please loook

[VandyDerm]

This involves physics-

Everyone knows the equation for elastic potential energy in a spring as:
PE = 1/2kx^2. GREAT!

So lets assume that if the PE is 100J when compressed half the distance from rest. The EK book now asks, what is the PE when compressed to 1/4 the rest length. How the hell is the answer 225J. It doesn't even make sense conceptually because less compression means less potential energy stored in the spring. Please tell me you all get 25J as your answer when you solve for k = 400. Im pissed as if I didn't know what I was doing.

thanks

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[Gavanshir]

It's assumed that the spring is compressed in the other direction! So you are actually increasing the compression not decreasing it, From 50 cm compressed to 75 cm compressed. And therefore increasing PE.

 

[nikeshp]

you are probably setting x=.25, howeveer it is compressed to 1/4 the length, so x is actually .75. that works. btw, k =800

 

[BerkReviewTeach]

It's assumed that the spring is compressed in the other direction! So you are actually increasing the compression not decreasing it, From 50 cm compressed to 75 cm compressed. And therefore increasing PE.

EXACTLY

First compression is 50cm, so U = 0.5k(.5)exp2 = 100

Second compression is 75cm, so U = 0.5k(.75)exp2 = ???

The ratio of (.75)exp2 : (.50)exp2 = 9/16 : 1/4 = 9/16 : 4/16 = 9/4

This means that the energy ratio is 9:4 = 225:100.

 

[Vihsadas]

You just got a little jumbled up in the meaning of '1/4 of rest length'. Draw a diagram next time to see just how the distance 'x' fits into the problem. 🙂