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A pogo stick has a spring with a force constant of 2.50 × 104 N/m , which can be compressed 11.2 cm. what maximum height, in meters above the compressed position of the spring, can a child jump with the stick using only the maximum elastic potential energy in the spring, if the child and stick have a combined mass of 44 kg?

Respuesta :

Answer:

h = 36.4 cm

Explanation:

given,

spring constant = 2.5 x 10⁴ N/m

compressed distance = 11.2 cm = 0.112 m

mass of the child = 44 kg

maximum height = ?

by energy of conservation

[tex]K.E_i +P.E_i= K.E_f + P.E_f[/tex]

[tex]\dfrac{1}{2}kx^2 = mgh[/tex]

[tex]\dfrac{1}{2}\times 2.5 \times 10^4 \times 0.112^2 = 44\times 9.8 \times h[/tex]

[tex]\dfrac{1}{2}\times 2.5 \times 10^4 \times 0.112^2 = 44\times 9.8 \times h[/tex]

[tex]156.8 = 44 \times 9.8 \times h[/tex]

[tex]h = \dfrac{156.8}{44 \times 9.8}[/tex]

h = 0.364 m

h = 36.4 cm

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