Question

Hooke's law describes a certain light spring of unstretched length 34.8 cm. When one end is attached to the top of a doorframe and a 8.22 kg object is hung from the other end, the length of the spring is 40.8 cm. (a) Find its spring constant. 1342.6 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 205 N. Find the length of the spring in this situation. m

Answer 1

Answer:

a) $k = 1343.6\,\frac{N}{m}$, b) $l = 0.501\,m\,(50.1\,cm)$

Explanation:

a) The Hooke's law states that spring force is directly proportional to change in length. That is to say:

$F \propto \Delta l$

In this case, the force is equal to the weight of the object:

$F = m\cdot g$

$F = (8.22\,kg)\cdot (9.807\,\frac{m}{s^{2}} )$

$F = 80.614\,N$

The spring constant is:

$k = \frac{F}{\Delta l}$

$k = \frac{80.614\,N}{0.408\,m-0.348\,m}$

$k = 1343.6\,\frac{N}{m}$

b) The length of the spring is:

$F = k\cdot (l-l_{o})$

$l = l_{o} + \frac{F}{k}$

$l=0.348\,m+\frac{205\,N}{1343.6\,\frac{N}{m} }$

$l = 0.501\,m\,(50.1\,cm)$