Question

A horizontal spring with force constant k = 700 N/m is attached to a wall at one end and to a block of mass m = 2.30 kg at the other end that rests on a horizontal surface. The block is released from rest from a position 3.40 cm beyond the spring's equilibrium position. (a) If the surface is frictionless, what is the speed of the block as it passes through the equilibrium position? m/s (b) If the surface is rough and the coefficient of kinetic friction between the box and the surface is uk = 0.300, what is the speed of the block as it passes through the equilibrium position? m/s

Answer 1

By work Energy Principle,
$\Delta Energy = External Work$

As no friction is acting, external work done will be zero

$\Delta Energy = 0$

$\Delta KE +\Delta SPE= 0$

0,5m2 — 0,5k 2 = 0

When friction acts,
Work done = Frictional force * displacement (x)

$\Delta KE +\Delta SPE= -W_{f}$

$0.5mv^{2} -0.5kx^{2}= -\mu mg*x$