Question

A glider with mass m = 0.230 kg sits on a frictionless horizontal air track, connected to a spring with force constant k = 4.50 N/m . You pull on the glider, stretching the spring 0.130 m , and then release it with no initial velocity. The glider begins to move back toward its equilibrium position (x=0). What is the speed of the glider when it returns to x=0?

What must the initial displacement of the glider be if its maximum speed in the subsequent motion is to be 3.00 m/s?

Answer 1

given,

mass of glider = 0.23 Kg

spring constant = k = 4.50 N/m

spring stretched to 0.130 m

The springs potential energy =

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

`U = (1)/(2)* 4.5 * 0.13^2`

U = 0.038 J

at x = 0,the only energy will be kinetic .

`(1)/(2)mv^2=0.038`

`(1)/(2)* 0.23 * v^2=0.038`

v² = 0.3304

v = 0.575 m/s

displacement of the glider

using conservation of energy

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

`x =v\sqrt{(m)/(k)}`

`x =3* \sqrt{(0.23)/(4.5)}`

x = 0.678 m