Question

A glider with mass m = 0.250kg sits on a frictionless horizontal air track, connected to a spring with force constant k = 4.60 N/m . You pull on the glider, stretching the spring 0.100 m , and then release it with no initial velocity. The glider begins to move back toward its equilibrium position (x=0).A) What is the speed of the glider when it returns to ?B) What must the initial displacement of the glider be if its maximum speed in the subsequent motion is to be 2.60 ?

Answer 1

Answer:

given,

mass of the glider = 0.250 Kg

force constant = k = 4.6 N/m

x = 0.1 m

a) Using conservation of energy

     K E = PS

     $\dfrac{1}{2}mv^2 =\dfrac{1}{2}kx^2$

     $v =\sqrt{\dfrac{kx^2}{m}}$

     $v =\sqrt{\dfrac{4.6\times 0.1^2}{0.25}}$

            v = 0.428 m/s

b) now, calculation of displacement

Using conservation of energy

     K E = PS

     $\dfrac{1}{2}mv^2 =\dfrac{1}{2}kx^2$

     $x =\sqrt{\dfrac{mv^2}{k}}$

     $x =\sqrt{\dfrac{0.25\times 2.6^2}{4.6}}$

            x= 0.606 m