What is the length of the stretched version of the spring, if a 40 g mass hangs vertically on the spring, with a spring constant of 30 N/m? Assume that when the spring is in the relaxed state it has a length of 20 cm. Draw a picture

I don't understand how to do this question.

1 Answer
Jan 11, 2018

21 cm

Explanation:

Hooke's Law tells us that the extension of the spring is directly proportional to the stretching force:

#sf(F=kx)#

x is the extension

F is the force

We need to convert 40 g to kg by dividing by 1000#rArr# 0.04 kg

The force is given by:

#sf(F=mg=0.04xx9.81=0.3924color(white)(x)N)#

#:.##sf(0.3924=30xxx)#

#sf(x=0.3924/30=0.01308color(white)(x)m)#

This is the extension so the new length will be:

#sf(0.20 + 0.01308 = 0.21308color(white)(x) m)#

#sf(=21.3color(white)(x)cm)#

I'll leave you to draw the picture.