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A 25 kg child bounces on a pogo stick. The pogo stick has a spring with spring constant 2.0x10^4 N/m. When the child makes a nice big bounce, he finds that at the bottom of the bounce he is accelerating upwards at 9.8 m/s^2. How much is the spring compressed?

Respuesta :

Answer:

the spring is compressed by x = 2.45 cm

Explanation:

As we know that at the bottom of the bounce the net force on the child is given as

[tex]F_s - mg = ma[/tex]

here we know that

[tex]F_s = kx[/tex]

now we will have

[tex]kx - mg = ma[/tex]

[tex](2.0 \times 10^4) x = m( g + a)[/tex]

[tex](2 \times 10^4) x = 25(9.8 + 9.8)[/tex]

[tex]x = 0.0245 m[/tex]

so the spring is compressed by x = 2.45 cm