Question

Hooke's law describes a certain light spring of unstretched length 38.0 cm. When one end is attached to the top of a door frame and a 6.00-kg object is hung from the other end, the length of the spring is 42.5 cm.

(a) Find its spring constant.
_________ kN/m

(b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 180 N. Find the length of the spring in this situation.

_________ cm

Answer 1

given
Lo = 38.0 cm = 0.380 m
L = 42.5 cm = 0.425 m

a) extension of the spring with load, x = L - Lo

= 0.425 - 0.380

= 0.045 m

let k is the spring constant of the spring.
in the equilibrium,

F_spring = F_gravity

k*x = m*g

k = m*g/x

= 6*9.8/0.045

= 1307 N/m

= 1.307 kN/m <<<<<<------------------Answer

b) let x is the extension of the spring in this case.

in the equilibrium, Fspring = F_applied

k*x = 180

x = 180/k

= 180/1307

= 0.138 m

length of the sprin, L = Lo + x

= 0.380 + 0.138

= 0.518 m

= 51.8 cm <<<<<<<<<<--------------------Answer