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

Answer

given,

mass of glider = 0.23 Kg

spring constant = k = 4.50 N/m

spring stretched to 0.130 m

The springs potential energy =

 $U = \dfrac{1}{2}kx^2$

 $U = \dfrac{1}{2}\times 4.5 \times 0.13^2$

        U = 0.038 J

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

 $\dfrac{1}{2}mv^2=0.038$

 $\dfrac{1}{2}\times 0.23 \times v^2=0.038$

         v² = 0.3304

         v = 0.575 m/s

displacement of the glider

      using conservation of energy

 $\dfrac{1}{2}mv^2=\dfrac{1}{2}kx^2$

 $x =v\sqrt{\dfrac{m}{k}}$

 $x =3\times \sqrt{\dfrac{0.23}{4.5}}$

        x = 0.678 m