Hooke’s Law Experiment

IntroductionHook’s Law is used in designing devices that uses springs. If we have to design a kitchen scale or door locks we have to determine what force is required to produce the required displacement and also it should return to its original position when the load is removed. Thus, hooke’s law is vital in such scenario.

TheoryHookes Law states that for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load. It can be written as

Fs = -ks

where Fs is the tension in a stretched spring and s is the spring's displacement from its unstretched position. k is the elastic constant, or "spring constant."

Common Types of Spring1. Tension Spring2. Compression Spring

Tension SpringExtension springs, also known as a tension spring, are helically wound coils, wrapped tightly together to create tension. Extension springs usually have hooks, loops, or end coils that are pulled out and formed from each end of the body.

The function of an extension spring is to provide retracting force when the spring is pulled apart from its original length.

Commons use Trampoline

A trampoline uses many extension springs to create the bouncing effect. Every time someone jumps on the trampoline, the extension springs are pulled apart and force is exerted. This makes the extension spring want to go back to its original length, thus giving the inertia to fly into the air.

Procedure1. Push the crosshead above until and unless the spring becomes slack.2. Set the cell reading to zero and note the position of the double-edged pointer3. Release the cross head and let it come to rest so that the weight and the tension becomes

equal.4. Tap the equipment so that any stoppage due to friction is released and the equipment comes to

rest at the position given in point 3.5. Next note the reading of the scale pointer.6. Turn the screw on the cross head so it stretches the spring 2 mm (0.002m) and take the reading

from the Load cell.7. Repeat in 2 mm (0.002 m) steps, until you reach the end of the Crosshead travel.

Tips: The scale has two edges. Look across both of these to reduce the parallax error. To remove the pretension in the spring (if it not appropriate for your course) pull the spring by

the loops until the coils no when the spring is relaxed.

Conduct the experiment and note down its readingObserv. No Distance

(mm)

Scale Reading

(N)1 132 32 134 3.53 136 44 138 4.65 140 5.26 142 5.77 144 6.28 146 6.79 148 7.2

10 150 7.711 152 8.212 154 8.713 156 9.214 158 9.915 160 10.616 162 10.917 164 11.418 166 1219 168 12.620 170 13.221 172 13.622 174 1423 176 14.624 178 15.2

Draw the best fit curve (line). What is the trend that you observe? Linear.

132

136

140

144

148

152

156

160

164

168

172

176

0

2

4

6

8

10

12

14

16f(x) = 0.529782608695652 x + 2.45688405797102

Tension Vs Displacement

Series1Linear (Series1)

Scale Reading (mm)

Forc

e Re

cord

ed (N

)

Determine the spring constant. Using k = (y2-y1)/(x2-x1)K=0.5298 N/mm

Determine the y-intercept. What does this indicate?

That the spring is already under tension by 2.4569N

At what scale reading would the spring have no load?Displacement at no Load = 132 – 2.4569/0.5298 = 127.3626 mm

Draw the free body diagram of tension spring apparatus, demonstrating all the forces acting on it if the Load Cell shows a reading of 5 N, when it has reached an equilibrium state.

Drawn on back of page 6T

Compression

Practical Example: Pogo stick

A pogo stick is a toy that works as an exercising tool without children realizing their fun is actually healthy. A child uses his legs, abdomen and arms to operate a pogo stick with repeated movement, exercising each muscle. A pogo stick is a simple machine called a spring that uses the weight of the child pressing down on the spring to cause the spring to push the child up into the air.

Procedure

1. Take up the slack in the spring by using the screw on the crosshead until the load cell pointer just begins to move

2. Set the load cell to zero and note the position of the double-edged pointer.3. Turn the screw on the crosshead so it compresses the spring 2 mm (0.002m) and take a reading

from the Load cell.4. Repeat in 2mm (0.002 m) steps until you reach the end of the crosshead travel or when the

spring is fully compressed.

Tips: The scale has two edges. Look across both of these to reduce the parallax error.

Draw the free body diagram showing all the forces acting on the apparatus when the spring balance is showing the reading of 3 N.

Diagram drawn on back of page 7T.

Conduct the experiment and note down the observations.Observation

numberScale Reading on

Compression (mm)Scale Reading –

Intial Reading (mm)Compression

force Recorded(N)1 55 0 02 53 -2 -23 51 -4 -34 49 -6 -4.15 47 -8 -5.36 45 -10 -6.77 43 -12 -7.98 41 -14 -99 39 -16 -10.1

10 37 -18 -11.411 35 -20 -12.412 33 -22 -13.813 31 -24 -1514 29 -26 -16.215 27 -28 -17.416 25 -30 -18.417 23 -32 -19.618 21 -34 -20.6

Draw the best fit curve (line). What is the trend that you observe? Linear.

-34

-32

-30

-28

-26

-24

-22

-20

-18

-16

-14

-12

-10 -8 -6 -4 -2 0

-25

-20

-15

-10

-5

0f(x) = 1.19494324045408 x − 22.0686274509804

Compression Vs Displacement

Series1Linear (Series1)

Displacement (mm)

Forc

e Ge

nera

ted

(N)

Calculate k of the above experimentK = 1.1704 N / mm

Other Questions

The turning total length of the bolt thread is 80 mm. Count the number of revolutions a nut would take to reach from top to bottom.

What is the pitch of the bolt

How many turns would we have to provide if we have to compress the spring from 8mm to 6 mm.