Calculating the spring constant involving energy

[rbailey5]

Homework Statement

A 142 g ball is dropped from a height of 62.2 cm above a spring of negligible mass. The ball compresses the spring to a maximum displacement of 4.35501 cm. acceleration due to gravity is 9.8. Calculate the the spring force constant K.

Homework Equations

Hooke's law: F=-kx and the potential energy of the spring is given by mg(h+x) because total displacement involves the compression distance x as well as the height of the ball

The Attempt at a Solution

So I got mg(h+x)=-kx,
-mg(h+x)/x=k
(-.142*9.8*(.622+.435501))/.435501=k but I keep getting the wrong answer. What am I doing wrong am I supposed to use PE=1/2kx^2 instead?

 

[Doc Al]

So I got mg(h+x)=-kx,

You can't set an energy term equal to a force term.

What am I doing wrong am I supposed to use PE=1/2kx^2 instead?

Yes.

 

[rbailey5]

ok so you get -(mg(h+x)*2)/x^2=k,

-(2*.142*9.8*(.622+.435501)/.435501^2=k

 

[Doc Al]

ok so you get -(mg(h+x)*2)/x^2=k,

-(2*.142*9.8*(.622+.435501)/.435501^2=k

Get rid of that minus sign. And be careful when converting cm to m: 4.35 cm = 0.0435 m.

 

[rbailey5]

sweet thanks!