Question

A vertically mounted spring (k = 750 N/m) is compressed by 35.0 cm relative to its unstrained length. A mass (m = 0.36 kg) is placed at rest against the spring. When the spring is released, the mass is launched vertically in the air. How high from release point the mass can reach?

Answer 1

Answer:

Height, h = 13.02 meters

Explanation:

It is given that,

Spring constant of the spring, k = 750 N/m

It is compressed by 35 cm relative to its unstained length, x = 35 cm = 0.35 m

Mass of the object, m = 0.36 kg

When the spring is released, the mass is launched vertically in the air. We need to find the height attained by the mass at this position. On applying the conservation of energy as :

Energy stored in the spring = change on potential energy

$\dfrac{1}{2}kx^2=mgh$

$h=\dfrac{kx^2}{2mg}$

$h=\dfrac{750\ N/m\times (0.35\ m)^2}{2\times 0.36\ kg\times 9.8\ m/s^2}$

h = 13.02 meters

So, the mass will reach a height of 13.02 meters. Hence, this is the required solution.