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# Hook's law experiment (instructor)

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### Hook's law experiment (instructor)

1. 1. Hooke’s Law ExperimentIntroductionHook’s Law is used in designing devices that uses springs. If we have to design a kitchen scale or doorlocks we have to determine what force is required to produce the required displacement and also itshould return to its original position when the load is removed. Thus, hooke’s law is vital in suchscenario.TheoryHookes Law states that for relatively small deformationsofanobject,thedisplacementor size of thedeformationisdirectlyproportionaltothedeforming force or load. Under theseconditionstheobjectreturnsto its original shape and size upon removaloftheload. It can be written as Fs = -kswhereFs is the tension in a stretched spring and s is the springs displacement from its unstretchedposition. k is the elastic constant, or "spring constant."Common Types of Spring 1. Tension Spring 2. Compression SpringTension SpringExtension springs, also known as a tension spring, are helically wound coils, wrapped tightly together tocreate tension. Extension springs usually have hooks, loops, or end coils that are pulled out and formedfrom each end of the body.The function of an extension spring is to provide retracting force when the spring is pulled apart from itsoriginal length.Commons useTrampoline
2. 2. A trampoline uses many extension springs to create the bouncing effect. Every time someone jumps onthe trampoline, the extension springs are pulled apart and force is exerted. This makes the extensionspring want to go back to its original length, thus giving the inertia to fly into the air.Procedure 1. 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 pointer 3. 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.
3. 3. Conduct the experiment and note down its reading Observ. Scale No Distance Reading (mm) (N) 1 132 3 2 134 3.5 3 136 4 4 138 4.6 5 140 5.2 6 142 5.7 7 144 6.2 8 146 6.7 9 148 7.2 10 150 7.7 11 152 8.2 12 154 8.7 13 156 9.2 14 158 9.9 15 160 10.6 16 162 10.9 17 164 11.4 18 166 12 19 168 12.6 20 170 13.2 21 172 13.6 22 174 14 23 176 14.6 24 178 15.2
4. 4. Draw the best fit curve (line). What is the trend that you observe? Linear. Tension Vs Displacement 18 16 y = 0.529x + 2.456 14 Force Recorded (N) 12 10 8 Series2 6 Linear (Series2) 4 2 0 132 136 140 144 148 152 156 160 164 168 172 176 Scale Reading (mm)Determine the spring constant. Using k = (y2-y1)/(x2-x1)K=0.5298 N/mmDetermine the y-intercept. What does this indicate?That the spring is already under tension by 2.4569NAt what scale reading would the spring have no load?Displacement at no Load = 132 – 2.4569/0.5298 = 127.3626 mmDraw the free body diagram of tension spring apparatus, demonstrating all the forces actingon it if the Load Cell shows a reading of 5 N, when it has reached an equilibrium state.Drawn on back of page 6T
5. 5. CompressionPractical Example: Pogo stickA pogo stick is a toy that works as an exercising tool without children realizing their fun isactually healthy. A child uses his legs, abdomen and arms to operate a pogo stick with repeatedmovement, exercising each muscle. A pogo stick is a simple machine called a spring that usesthe weight of the child pressing down on the spring to cause the spring to push the child up intothe 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 springbalance is showing the reading of 3 N.Diagram drawn on back of page 7T.
6. 6. Conduct the experiment and note down the observations. Observation Scale Reading on Scale Reading – Compression number Compression (mm) Intial Reading (mm) force Recorded(N) 1 55 0 0 2 53 -2 -2 3 51 -4 -3 4 49 -6 -4.1 5 47 -8 -5.3 6 45 -10 -6.7 7 43 -12 -7.9 8 41 -14 -9 9 39 -16 -10.1 10 37 -18 -11.4 11 35 -20 -12.4 12 33 -22 -13.8 13 31 -24 -15 14 29 -26 -16.2 15 27 -28 -17.4 16 25 -30 -18.4 17 23 -32 -19.6 18 21 -34 -20.6
7. 7. Draw the best fit curve (line). What is the trend that you observe? Linear. Compression Vs Displacement Displacement (mm) -28 -34 -32 -30 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 y = 1.194x - 22.06 -5 Force Generated (N) -10 Series2 Linear (Series2) -15 -20 -25Calculate k of the above experimentK = 1.1704 N / mm
8. 8. Other QuestionsThe turning total length of the bolt thread is 80 mm. Count the number of revolutions a nut would taketo reach from top to bottom.What is the pitch of the boltHow many turns would we have to provide if we have to compress the spring from 8mm to 6 mm.