Question

A 0.2-kg block is held in place by a force that results in a 0.10-m compression of a spring beneath the block. The spring constant is 1.0 × 102 N/m. Assuming the mass of the spring is negligible compared to that of the block, to what maximum height would the block rise if the force were removed.?

Answer 1

h = 0.255 meters

Step-by-step explanation:

It is given that,

Mass of the block, m = 0.2 kg

Compression in the spring, x = 0.1 m

Spring constant of the spring,
`k=10^2\ N/m`

Let h is the maximum height reached by the block if the force were removed. Using the conservation of energy of the spring mass system as :

`mgh=(1)/(2)kx^2`

`h=(1)/(2mg)kx^2`

`h=(1)/(2* 0.2* 9.8)* 100* (0.1)^2`

h = 0.255 meters

So, the maximum height reached by the block is 0.255 meters. Hence, this is the required solution.