Question

A glider with mass m = 0.8 kg sits on a frictionless air track. It is connected to a massless spring with force constant k = 30 N/m. The glider is initially at x=0, and the spring is relaxed. You then hit the glider with a hammer, which gives it an initial velocity of υ0 = 8 m/s in the positive x direction. At what x positions will the speed of the glider be zero?

Answer 1

Answer:

The position is

$d_{o}=1.706m$

Explanation:

The kinetic energy of the motion is

$E_{K}=\frac{1}{2}*m*v^2$

$E_{K}=\frac{1}{2}*0.8kg*8(\frac{m}{s})^2$

$E_{K}=25.6 J$

So apply the conservation of energy the force of the spring is the same of the kinetic energy

$F_{s}=\frac{1}{2}*k*d^2$

$F_{s}=E_{K}$

$25.6=\frac{1}{2}*30\frac{N}{m}*d_{o}^2$

Solve to do

$d_{o}=\sqrt{\frac{2*25.6J}{30\frac{N}{m}}}$

$d_{o}=1.706m$