Question

A 40 kg child uses a pogo stick to bounce up and down. The spring constant, k, of the toy equals 8,550 N/m.

By how much would the spring be compressed by the child if she simply balanced herself vertically on the pedals of the stick? (Give your answer in cm.)

How much energy (in J) is stored in the spring under the circumstances?

Answer 1

A) 4.58 cm

B) 8.97 J

Explanation:

A)

When the child is balanced on the spring, the weight of the child (downward force) is balanced by the restoring force of the spring (upward force). Therefore, we can write:

$W=F\\mg=kx$

where:

m = 40 kg is the mass of the child

$g=9.8 m/s^2$ is the acceleration due to gravity

k = 8,550 N/m is the spring constant

x is the compression of the spring, with respect to the equilibrium position

Solving for x, we find:

$x=\frac{mg}{k}=\frac{(40)(9.8)}{8550}=0.0458 m = 4.58 cm$

So, the spring is compressd by 4.58 cm.

B)

The elastic potential energy stored in a compressed spring is given by

$E=\frac{1}{2}kx^2$

where

k is the spring constant

x is the compression of the spring

In this problem, we have:

k = 8550 N/m (spring constant)

x = 0.0458 m (compression)

So, the elastic energy stored is:

$E=\frac{1}{2}(8550)(0.0458)^2=8.97 J$

Answer 2

Hooks Law states that the force needed to compress the spring is directly proportional to the distance.  The spring compressed by the child is 4.58 cm and the energy in the spring is 8.97 J.

Hooks Law of spring:

It states that the force needed to compress or stretch the spring is directly proportional to the distance.

$\bold {F = K\times X}$

Where

F - force = $\bold {m\times g}$ = $40\times 9.8$ = 392 N

K - spring constant =  8,550 N/m.

X - distance = ?

So, $\bold{X = \frac{F}{K}}$

Now put the values,

$\bold {X= \frac{392N }{8550N/m} }\\\\\bold {X= 4.58 cm }$

Formula for potential energy in the compressed spring,

$\bold{E = \frac{1}{2}K x^2 }$

Put the values in the formula,

$\bold{E = \frac{1}{2}8550 \times 4.58^2 }\\\\\bold{E = 8.97 J}$

Therefore, the spring compressed by child is 4.58 cm and the energy in the spring is 8.97 J.

To know more about energy of compressed spring, refer to the link:

https://brainly.com/question/12644717