Question

A mass of 1.03 kilograms is placed on a horizontal frictionless surface against an uncompressed spring with spring constant 861.1 N/m. The mass is pushed against the spring until the spring is compressed a distance 0.36 m and then released. How high (vertically) in m does the mass rise from the original height before it stops (momentarily).

Answer 1

5.522 m

Step-by-step explanation:

Data provided:

Mass, m = 1.03 kg

spring constant, k = 861.1 N/m

Distance by which the spring is compressed, x = 0.36

Thus,

the energy stored in the spring =
`(1)/(2)kx^2`

on substituting the values, we get

the energy stored in the spring =
`(1)/(2)*861.1*0.36^2`

now,

by the conservation of energy, we have

Potential energy gained by the mass = Energy gained by the spring

or

mgh =
`(1)/(2)*861.1*0.36^2`

where,

g is the acceleration due to the gravity

h is the maximum height reached by the mass before falling

on substituting the values in the above relation, we get

1.03 × 9.81 × h =
`(1)/(2)*861.1*0.36^2`

or

h = 5.522 m