HOOKE's LAW
F =  K ∆x or load(N) = K . extension(m)   K is the spring constant (N/m)


The load or stress is proportional to the extension of the spring as long as
the  elastic limit has not been exceeded.
F is the load  (mass in kg x 9.8 ) the unit is newton (N) 
∆x is the stretch or extension or change in length . the unit is meter (m) 
K is a constant called the spring constant or the elastic constant. the unit is ( N/m)
 
HOME                   !!!!!!! UNITS FOR K (constant of proportionality or spring constant) is N/m not N/cm  
(or lb/in sometimes)!!!!!!
animation

DO THE LAB

One of the most basic principles related to the elasticity of solids is Hooke's law. THis law is named after Robert Hooke, who first discovered the principle in the seventeenth century while inverting the balance spring for spring driven clock. 

If you pull a spring down, with a force F  and the spring is stretched by an amount of X (the elongation) then : F = K X. The stress applied( your pulling force) is proportional to the elongation of the spring  (X) (or strain). or F = K X/  K is a constant and depends on the kind of the spring you are stretching. K is called the spring constant. THe units are N/m (or sometimes lb/in)

F / X = K                   F (in N) is the force applied (compressing or stretching) or stress
X (in m)is the change in length or elongation or strain
K is the elastic constant of the spring constant in N/m

EXERCISES       try not to look at the hints. 

1)A force of 5.00 N is applied to a spring whose elastic constant is 0.250 N/m. Find its change in length.
draw a picture.
Hints: F = K ∆x solve for ∆x

2)A force of 3.00lb stretches a spring 12.0 in. What force is required to stretch the spring 15.0 in. ?
hints: A) find the spring constant using an extension of 12 in is for a load of 3lb. the unit is lb/in
B) use hookes law F =  K  ∆ X  to solve for F.
Or you can also write a proportion: if 3lb is for 12in then ? is for 15in.


3) In a Hooke's law experiment, the following weights were attached to a spring, resulting in the following elongations ( ∆X) :
y= weight (N) x = elongation (cm)
00
50 2.0
75 3.3
105 4.2
125 5.0
150 6.0
175 7.4
225 9.5
275 11.1

A) Plot the graph of weight versus elongation.
hints: x = elongation (horizontal axis) and y = weight (vertical axis)

 B) Draw the best straight line through the data. !! do not connect the dots. Find the best fit line.
(going through the origin). don't forget title , good scale, labels...

C) find the slope of the best fit line. m = _____ N/cm.  (!! watch the units)

D) Find the equation of the best fit line: y = ___ x or weight (N) = ______ elongation (cm)

E)Using your equation,  what weight corresponds to an elongation of 7.5 cm?
hints:  if  x = 7.5 what is y ?

F)  determine the spring constant K (hint: remember: weight(N) = K (N/m)  x extension (m) )? the spring constant has unit N/m. so you need to convert N/cm to N/m !!
with 100cm = 1m.

4) What was the original length of a spring constant 96.0 N/m that is stretched to 28.0cm  by a 15.0 N weight ?
follow the steps for hints. (try without)
A) find the extension ∆x (m)  using the hookes law. F = K ∆x
B) convert the extension (change in length) in cm. ∆x = ____ cm
C) solve for xo with ∆x = x - xo  and x = 28cm. you have ∆x from B)
D) draw , comics style, the situation

 5) A force of 36.0N stretches a spring 18.0 cm. Find the spring constant (in N/m)
hint: first convert cm to meters.

6) Some students carry out an experiment to find out how a spring stretched when small loads were added to it.
A) Draw a diagram to show what is meant by the extension of the spring.
hint: draw 2 springs. one with a load and one without.

B) The results of the experiment are shown in the following table. One the readings in incorrect. CAn you find it and correct it ?
x =extension (cm) 0 2 4 6 8 10 12 14
y = load (N) 0 16 32 58 64 80 96 112

hint: the relationship between the extension (y) and the load (x) is linear so y = K x or load = K x extension and K is a constant.

C) Find the equation of the graph y versus x or load versus extension.

D) Find 
i) the extension when the load is 3N 
hint: y=3N

 ii) the load which produces an extension of 40 cm
hint: x=40cm

D) Find the spring constant K = ____ N/m (!! units) 

7) A fitness enthusiast (not me!) is using chest expanders.
THe table shows the force how the force he applies varies with the extension of the expanders.

extension (cm) 0 10 20 30
force (N) 0 40 80 120

A) Find the equation of the graph y vs x or force vs extension

B) What force would be required to stretch the expanders by 25 cm ?
hints: x = 25 cm, find y. 

D) If the force is 60N, what is the extension? What is the extension is cm.

E) Find the spring constant (!!! unit = N/m)

Here is a picture of Robert Hooke, the enemy of Newton. They hated each other.

8) During a lab, a very meticulous and diligent student did the Hooke's law experiment. She plotted Force(N) vs (elongation(cm)

Observer her graph.  How can you tell this is a best fit line ?
Can you find the spring constant K ? K = _____N/m/
Do you think tge line is going through (0,0 ) ? why?

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