Question

A mass of 4.8 kg is dropped from a height of 4.84 meters above a vertical spring anchored at its lower end to the floor. If the spring has a height of 82 cm and a constant of 24 N/cm, how far, to the nearest tenth of a cm, is the spring compressed?

Answer 1

45.6 cm

Step-by-step explanation:

Let x (m) be the length that the spring is compressed. We know that when we drop the mass from 4.84 m above and compress the springi, ts gravitational energy shall be converted to spring potential energy due to the law of energy conservation

`E_g = E_p`

`mgh = 0.5kx^2`

where h = 4.84 + x is the distance from the dropping point the the compressed point, and k = 24N/cm = 2400N/m is the spring constant, g = 9.81 m/s2 is the gravitational acceleration constant. And m = 4.8 kg is the object mass.

`4.8*9.81(4.84 + x) = 0.5 * 2400 * x^2`

`47.088x + 227.906 = 1200x^2`

`1200x^2 - 47.088x - 227.906 = 0`

`x = 0.456m` or 45.6 cm