How Does Spring Compression Relate to Energy Changes?

[hello478]

Homework Statement

what is percentage efficiency of transfer of KE from child to PE in spring

Relevant Equations

energy equations

part d- ii and iii
ii) my answer is
300-140/300 *100
ke at y = 300
and spring energy at max compression is 140

iii) e is directly proportional to x^2
so it increases exponentially
is my explanation correct?

 

[haruspex]

ii) my answer is
300-140/300 *100

I assume you mean (300-140)/300*100%. But 300J - 140J is the energy lost, not the energy retained.

iii) e is directly proportional to x^2
so it increases exponentially
is my explanation correct?

That's quadratic, not exponential. Exponential would be $E\propto e^x$

 

[hello478]

I assume you mean (300-140)/300*100%. But 300J - 140J is the energy lost, not the energy retained.

That's quadratic, not exponential. Exponential would be $E\propto e^x$

so then what would be the energy retained? only 140??

oh yeah, sorry i forgot, i meant quadratic

 

[haruspex]

so then what would be the energy retained? only 140??

Yes. What you calculated could be called the inefficiency.

 

[hello478]

Yes.

thank you!!!