Question

Mr. Rosario jumps on a Pogo stick which contains a spring. As he jumps up he was in the air about 2m high, the spring was compressed 1.5m. If Mr. Rosario's mass was 60kg, what is the k constant?

Answer 1

The spring constant is 1045.3 N/m.

Given data:

The vertical distance traveled is h=2 m.

The compression in the spring is x=1.5 m.

The mass of Rosario is m=60 kg.

The formula for the elastic potential energy stored in the spring is givne by,

`\text{EPE}=(1)/(2)kx^2`

Here, k is the spring constant.

The formula for the gravitational potential energy gained by the person is given by,

`\text{GPE}=\text{mgh}`

Here, g is the gravitational acceleration.

Applying the conservation of energy.

As the total of spring remains constant; therefore, the amount of gain in gravitational potential energy will be equal to the elastic potential energy of the spring. It can be applied as,

`\begin{gathered} EPE=GPE \\ (1)/(2)kx^2=mgh \\ k=(2mgh)/(x^2) \\ k=(2(60kg)((9.8m)/(s^2))(2m))/((1.5m)^2) \\ k=(1045.3kg)/(s^2)*\frac{1\text{ N/m}}{(1kg)/(s^2)} \\ k=1045.3\text{ N/m} \end{gathered}`

Thus, the spring constant is 1045.3 N/m.