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

`0.75623\ \text{kN/m}`

`55.6\ \text{cm}`

Step-by-step 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=(mg)/(x)\\\Rightarrow k=(7.94* 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=(F)/(k)\\\Rightarrow x=(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}`.