Question

A vertically mounted spring (k = 850 N/m) is compressed by 31.0 cm relative to its unstrained length. A mass (m = 0.24 kg) is placed at rest against the spring. When the spring is released, the mass is launched vertically in the air. How high from the release point can the mass reach? g

Answer 1

Answer:

h = 1.74m

Explanation:

Given that k = 850N/m, x = 31.0cm = 0.31m, m = 2.4kg.

The act of stretching the spring stores potential energy in the spring. On attaching a mass of 0.24kg to the spring in its stretched state and releasing it, the stored potential energy in the spring is converted into the gravitational potential of the spring.

So

1/2kx² = mgh

h = ? g = 9.8m/s²

h = 1/2×kx²×1/mg

h = 1/2×850×0.31²×1/(2.4×9.8)

h = 1.74m

Answer 2

Answer: 4.17 m

Explanation: According to the law of conservation of energy, the elastic potential energy of the elastic material is used in launching the mass hence giving the body it potential energy.

Elastic potential energy = kx²/2

Potential energy = mgh

Where m = mass of object = 0.24kg

g = acceleration due to gravity = 9.8 m/s²

h = height =?

k = spring constant = 850 N/m

x = compression = 31cm = 0.13m

kx²/2 = mgh

kx² = 2× mgh

850 ×(0.31)² = 2 × 9.8 × h

h = 850 × (0.31)²/ 2 × 9.8

h = 81.685 / 19.6

h = 4.17 m