Question

A pogo stick has a spring with a spring constant of 2.5×104 N/m, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?

a) 0.58 m
b) 0.78 m
c) 0.98 m
d) 1.18 m

Answer 1

The maximum height a child can jump on a pogo stick using only the energy in the spring is approximately 0.58 m.

Step-by-step explanation:

To find the maximum height a child can jump on a pogo stick using only the energy in the spring, we can use the conservation of mechanical energy. The spring potential energy at maximum compression will be equal to the gravitational potential energy at maximum height:

PEspring = mtotal * g * hmax

Where PEspring is the spring potential energy, mtotal is the total mass of the child and the stick, g is the acceleration due to gravity (9.8 m/s2), and hmax is the maximum height.

Solving for hmax gives:

hmax = PEspring / (mtotal * g)

Plugging in the given values:

hmax = (0.5 * k * x2) / (mtotal * g)

Where k is the spring constant and x is the compression distance.

Substituting the values:

hmax = (0.5 * (2.5x104) * (0.12)2) / (40 * 9.8)

hmax ≈ 0.58 m