Question

Hooke's law describes a certain light spring of unstretched length 32.1 cm. When one end is attached to the top of a doorframe and a 7.94 kg object is hung from the other end, the length of the spring is 42.4 cm. (a) Find its spring constant. .7554 Correct: Your answer is correct. 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 178 N. Find the length of the spring in this situation. .7923 Incorrect: Your answer is incorrect.

Answer 1

Answer:

$0.75623\ \text{kN/m}$

$55.6\ \text{cm}$

Explanation:

m = Mass of object = 7.94 kg

g = Acceleration due to gravity = $9.81\ \text{m/s}^2$

x = Change in length of the spring = $(42.4-32.1)\ \text{cm}$

F = Force on the spring

Force of gravity on the object and the force on the spring will be equal

$mg=kx\\\Rightarrow k=\dfrac{mg}{x}\\\Rightarrow k=\dfrac{7.94\times 9.81}{0.424-0.321}\\\Rightarrow k=756.23\ \text{N/m}$

The spring constant is $756.23\ \text{N/m}=0.75623\ \text{kN/m}$

F = 178 N

Force on spring is given by

$F=kx\\\Rightarrow x=\dfrac{F}{k}\\\Rightarrow x=\dfrac{178}{756.23}\\\Rightarrow x=0.235\ \text{m}=23.5\ \text{cm}$

The length of the spring will be $32.1+23.5=55.6\ \text{cm}$.