Question

A 3.00-kg object is fastened to a light spring, with the intervening cord passing over a pulley. The pulley is frictionless, and its inertia may be neglected. The object is released from rest when the spring is unstretched. The ends of a cord hang over the sides of a pulley attached to the ceiling. The left end of the cord is attached to the top of a vertical spring with spring constant k. The bottom of the spring is attached to the flat ground. The right end of the cord is attached to a hanging spherical object with mass 3.00 kg. (a) If the object drops 14.8 cm before stopping, find the spring constant of the spring. N/m (b) If the object drops 14.8 cm before stopping, find the speed of the object when it is 5.20 cm below its starting point.

Answer 1

a.) k = 198.65 N/m

b.) v = 1.68 m/s

Step-by-step explanation:

a.)

F = kx

k= F/x

k = 3*9.8 / 0.148 = 198.65 N/m

b.)

Potential Energy Lost=Kinetic Energy +Spring energy stored

mgh=1/2 mv^2+1/2 k x^2

3*9.8*(0.148-0.052) = 1/2 * 3 * v^2 + 1/2* 198.65* (0.148-0.052)²

3/2 * v^2 = 1.872

v = 1.68 m/s