Question

A block of mass m=0.4 kg starts from rest and slides down a frictionless ramp, before hitting a spring of spring constant k = 300 N/m placed on a horizontal surface. When the block is at the height of 1.5m above the ground, its velocity is 2m/s. What is the maximum compression of the spring? Take g=9.8 m/s^2.

Answer 1

Maximum spring compression is 0.21 m

Solution:

As per the question:

Mass of the block, M = 0.4 kg

Spring constant, k = 300 N/m

Height of the block, h = 1.5 m

Velocity of the block, v = 2 m/s

Now,

By conservation of energy:

`PE + KE = E_(spring)` (1)

where

PE = Potential energy = Mgh

KE = Kinetic Energy =
`(1)/(2)Mv^(2)`

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

Now, using eqn (1) to calculate maximum compression 'x' of the spring:

`Mgh + (1)/(2)Mv^(2) = (1)/(2)kx^(2)`

`0.4* 9.8* 1.5 + (1)/(2)* 0.4* (2)^(2) = (1)/(2)* 300x^(2)`

`x^(2) = 0.0445`

x = 0.21 m