How far will the trampoline compress when a person jumps on it?

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The discussion centers on calculating the compression of a trampoline when a person jumps on it. The initial compression is 0.08 m, and the person jumps to a height of 0.26 m. The key equations involve potential energy (PE) and elastic potential energy (U), with the relationship mgh + mgx = ½kx² being critical for solving the problem. Participants express confusion over the correct application of these equations and the heights involved. Ultimately, the problem requires solving a quadratic equation to find the total compression of the trampoline upon landing.
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Homework Statement



A spring-like trampoline dips down 0.08 m when a particular person stands on it. If this person jumps up to a height of 0.26 m above the top of the trampoline, how far with the trampoline compress when the person lands?

I am very lost! Please help!

Homework Equations



F=kx

U= .5 * k * x^2

PE= mgh

The Attempt at a Solution

PE = U

m * 9.8 * .18 = .5 * k * .18^2
 
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Well initially when the person is standing, weight = spring force or mg = (0.08)k.

So mg/k = 0.8

Now in mgh = 1/2 kx ^2, you can divide by k.
 
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.08k = .5 * k * x^2

.08= .5 x^2

.16= x^2

x= .40

but it marked it wrong
 
lollikey said:
.08k = .5 * k * x^2

.08= .5 x^2

.16= x^2

x= .40

but it marked it wrong

Because you are equating spring force to energy

Your equation is PE = U or mgh= ½kx2
 
.08k *.26 = .5 * k * x^2
.0208 = .5 * x^2
.0146 = x^2
x = .2039

am I using the wrong height?

.08k * h = .5 * k * .26^2
.08 * h = .0338
h = .4225

none of these are right
 
Last edited:
lollikey said:
.08k *.26 = .5 * k * x^2
.0208 = .5 * x^2
.0146 = x^2
x = .2039

am I using the wrong height?

.08k * h = .5 * k * .26^2
.08 * h = .0338
h = .4225

none of these are right

Right initially the spring is compressed 0.08 m so that mg = 0.08k

Now as the person falls, they will travel a distance 'h' to the point where they just hit the trampoline and they will continue to now compress the spring a distance 'x'. The total of these are then converted into the elastic potential energy of the spring.

So now you have mgh + mgx = ½kx2.

You will have a quadratic to solve in x.
 
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