Practical - spring motion.pptx

Spring motion

1. UNIVERSITY OF DELHI

2. Aim To study the mo tion of the spring and calculate (a) spring constant (b) g

3. APPARATUS A spring of high elasticity , a hanger with light aluminium pointer, weight hanger with slotted weights, stop clock , etc.

4. Theory The helical spring is the most commonly used mechanical spring in which a wire is wrapped in a coil that resemble a screw thread. The helical spring us suspended vertically from a rigid support. The pointer is attached horizontally to the free end of the spring. A meter scale is kept vertically in such a way that the tip of the pointer is over the divisions of the scale, but doesn’t touch the scale.

5. Spring constant can be found by two methods: (A) static method. (B) dynamic method STATIC METHOD When a load F is suspended from lower end of a spring hanging from a rigid support , it increases its length by amount x. In equilibrium during the downward movements it executes simple harmonic motion. During downward movement the body will feel a restoring force acts along the initial position of the body and Hook’s law will act i.e. Restoring force is directly proportional to ‘x’ and opposite in direction. F = - Kx ( K is spring constant ) K = Mg ( slope = x ) x M

6. Dynamic Method When a loaded spring vibrates then its oscillation time period is correlated with its spring constant. The equation of Simple Harmonic is K = 4π 2 ( M 2 – M 1 ) ( T 2 2 – T 2 1 ) Where ( T2 – T1) is slope of the graph ( M2 - M1) Gravity g is calculated by, g = 4π 2 x T 2

7. PROCEDURE DYNAMIC METHOD Place the load in the hook of the spring. Pull the load vertically to give a small displacement and then release it. The spring will do simple harmonic motion. Note down the time for 10 oscillations of the spring. Repeat the observation for the same load and find the mean time period T. Increase the load and each time note down the time for 10 vibrations and find mean time period T. Plot the graph between the load M(kg) along x axis and T² (sec) along y axis.

8. STATIC METHOD Arrange the apparatus as shown in the figure. Make sure that the aluminium pointer is close to the mirror on which the scale is etched but it does not touch the mirror Read the position of the pointer on the scale. Avoid the parallax error. Note the reading on the scale. The apparatus should be in equilibrium Increase the load on weight banger and again note the readings for different values of load when the pointer comes at rest and one by one add load. Now remove one slotted weight and note the reading when pointer comes at rest & note in unloading column and repeat this step again. After finding k, by the formula we can find g also . PROCEDURE

9. OBSERVATION TABLE Table for finding spring constant by STATIC METHOD S.no Load M (kg) Reading of pointer (m) Mean Reading(m) Extension x= (m) Spring Const. K= N Loading Unloading 1. 0.15 0.123 0.123 0.123 0.123 11.98 2. 0.2 0.164 0.166 0.165 0.165 11.91 3. 0.25 0.207 0.207 0.207 0.207 11.85 4. 0.3 0.250 0.250 0.250 0.250 11.76 5. 0.35 0.278 0.291 0.288 0.288 11.88 S.no Load M (kg) Mean Reading(m) Loading Unloading 1. 0.15 0.123 0.123 0.123 0.123 11.98 2. 0.2 0.164 0.166 0.165 0.165 11.91 3. 0.25 0.207 0.207 0.207 0.207 11.85 4. 0.3 0.250 0.250 0.250 0.250 11.76 5. 0.35 0.278 0.291 0.288 0.288 11.88 Mean value of K = = 11.88 N  

10. CALCULATION STATIC METHOD : k= N = N N N N N  

11. OBSERVATION TABLE Table for finding spring constant by DYANIMC METHOD S.No . Load M (kg) Extension spring x (m) Time for 10 oscillation (s) Period = (s) in G = m Trial 1(s) Trial 2 (s) Mean (S) 1. 0.15 0.123 7.25 7.09 7.12 0.712 0.52 9.34 2. 0.2 0.165 8.16 8.22 8.18 0.818 0.68 9.57 3. 0.25 0.207 9.10 9.16 9.09 0.909 0.83 9.84 4. 0.3 0.250 10.00 9.9 9.93 0.993 0.99 9.96 5. 0.55 0.288 10.90 10.44 10.67 1.067 1.14 10.05 S.No . Load M (kg) Extension spring x (m) Time for 10 oscillation (s) Trial 1(s) Trial 2 (s) Mean (S) 1. 0.15 0.123 7.25 7.09 7.12 0.712 0.52 9.34 2. 0.2 0.165 8.16 8.22 8.18 0.818 0.68 9.57 3. 0.25 0.207 9.10 9.16 9.09 0.909 0.83 9.84 4. 0.3 0.250 10.00 9.9 9.93 0.993 0.99 9.96 5. 0.55 0.288 10.90 10.44 10.67 1.067 1.14 10.05 Mean value of K = = 12.74 N   Mean value of g = 9.752  

12. DYNAMIC METHOD K = 4 π 2 (M 2 – M 1 )/(T 2 2 – T 2 1 ) = N = N = N = N Mean value of k = N  

13. Calculations Pointer reading for no load, x = 0 m STATIC METHOD ( K = Mg/x ) Nm -1 DYNAMIC METHOD ( K = 4 π 2 (M 2 – M 1 )/(T 2 2 – T 2 1 ) Average value of spring constant, K = 12.74 Nm -1

14. RESULT The spring constant K of the given spring, Static method, By calculation, K = 11.88 Nm -1 By graph , K = 11.88 Nm -1 Dynamic method, By calculation, K = 12.74 Nm -1 By graph, K = 12.72 Nm -1 Acceleration due to gravity by Dynamic method is, g = 9.75 ms -2

15. Percentage Error Theoretically, the value of g is, g = 9.8 ms -2 Percentage Error = |Theoretical value – observed value| × 100 Theoretical value = | 9.8 – 9.752 | × 100 9.8 = 0.49 %

16. Precautions: 1. Loading and unloading of weight must be done carefully. 2. To avoid parallax, reading should be noted when the tip of the pointer comes at rest. 3. Loading should not be done beyond elastic limit of the spring used. Sources of Error: 1. Parallax error may be present. 2. There may be estimation error present while measuring the readings of stopwatch. 3. The support may not be rigid.