OBJECTIVE : 1. To determine the validity of Hooke’s law for two helical springs with different spring constants. THEORY : An important property of solids is their "stretchiness" or "squeeziness," which is called their elasticity. In the case of many solids, the amount of stretch or squeeze is proportional to the force causing the stretch or squeeze. This relationship can be expressed as: F
x
which is read as "force is proportional to stretch (or squeeze)". To change this expression into an equation, a constant of proportionality must be included. The expression ends up taking the form: Fs = -k x where k is the constant of proportionality (in this case, the spring constant). The value for k depends on the material being stretched or squeezed. This equation expresses what has come to be known as Hooke's Law. ***Your problem in this experiment is to see if the spring on the apparatus obeys Hooke's Law, and find the value of k for your spring.*** The spring potential energy, PEspring or Us , can be written as Us = ½ k x2 APPARATUS : 1. A tripod base 2. A barrel base 3. A support rod, square 4. A right angle clamp 5. Cursors, 1 pair 6. A weight holder f. slotted weights 7. 2 slotted weight, 10 g, black 8. 2 slotted weight, 10 g, silver bronze 9. A slotted weight, 50 g, black 10. 2 slotted weight, 50 g, silver bronze 11. A helical spring, 3 N/m 12. A helical spring, 20 N/m 13. A meter scale (±0.1 cm) 14. A holding pin
Figure 1
Figure 2
PROCEDURE : 1. The experimental set-up to measure the spring constants is shown in Figure1 2. To start with, submit the helical spring to no stress. 3. The equilibrium position of the spring, xo (set the sliding pointer to the lower end of the spring) is determined. The length of the spring, lo is recorded. 4. A mass on the helical spring is inserted using the weight holder and the slotted weight. The elongation of the spring, Δl is recorded (refer Figure 2) 5. The mass is increased on the helical spring in steps of 10 g, until reach the maximum mass of 200 g. 6. All the values of elongation, Δl and load, F is tabulated. 7. A graph of F against Δl is plotted. 8. From the graph, the spring constant, k and its uncertainty is determined. 9. The above steps is repeated for the other helical spring.
Observation :
Helical spring, 20 N/m Mass of Load (g)
Load, F (N)
Initial length, Lo (m)
Final length, L (m)
Change of length, ΔL (m)
Extension, - =Δ
Initial/0
0
0.635
0.445
0.190
0
20
0.196
0.635
0.437
0.198
0.008
40
0.392
0.635
0.427
0.208
0.018
60
0.587
0.635
0.417
0.218
0.028
80
0.785
0.635
0.407
0.228
0.038
100
0.981
0.635
0.397
0.238
0.048
120
1.177
0.635
0.387
0.248
0.058
140
1.373
0.635
0.377
0.258
0.068
160
1.570
0.635
0.367
0.268
0.078
180
1.766
0.635
0.357
0.278
0.088
200
1.962
0.635
0.347
0.288
0.098
Table 1.0
A graph of F against Δl 2.5
2
1.5 Experimental 1
0.5
0 0
Graph 1.0
0.008 0.018 0.028 0.038 0.048 0.058 0.068 0.078 0.088 0.098
Helical spring, 3 N/m Mass of Load (g)
Load, F (N)
Initial length, Lo (m)
Final length, L (m)
Change of length, ΔL (m)
Extension, - =Δ
Initial/0
0
0.895
0.725
0.170
0
20
0.196
0.895
0.663
0.232
0.062
40
0.392
0.895
0.595
0.300
0.130
60
0.587
0.895
0.530
0.365
0.195
80
0.785
0.895
0.466
0.429
0.259
100
0.981
0.895
0.401
0.494
0.324
120
1.177
0.895
0.335
0.560
0.390
140
1.373
0.895
0.273
0.622
0.452
160
1.570
0.895
0.209
0.686
0.516
180
1.766
0.895
0.144
0.751
0.581
200
1.962
0.960
0.149
0.811
0.641
Table 2.0
A graph of F against Δl 2.5 2 1.5 Experimental
1 0.5 0 0
0.062 0.13 0.195 0.259 0.324 0.39 0.452 0.516 0.581 0.641
Graph 2.0
Calculation :
(For Helical Spring 20 N/m)
To find Load,
To find spring constant,
F=W=mg
k=F/x
For example, if mass=20 g which is 0.02 kg
k= (0.196) / (0.008)
F= (0.02) (9.81) = 0.196 N
= 24.5 N/m
DISCUSSION : 1. The slope of the Force versus Elongation Graph is determined. 2. Two types of helical spring has been used : 20N/m and 3N/m 3. Table 1.0 is related to the graph 1.0. Based on the Data Table 1.0, while table 2.0 is related to the graph 2.0, the spring constant can be find by using the equation as follows: F = -kx k = -F / x
4. We found that the spring constant is actually the slope of the graph force versus stretch. 5. When the force increases, the stretch of the spring also increases and vise versa. 6. Based on the experiment, we found that the spring constant for both data is quite same but different with the slope as shown in the both graph. 7. This is because of the mass or the force that we applied to the spring. The graph plots the force that is the weight of the load. These differences will make the measurement for the spring constant also change as the equation also shows that the force is proportional to the elongation. Reliability : 1. Systematic error Occurs because of faulty equipment and some of the equipment have not been properly calibrated to fit the experiment. In this experiment, the systemic errors can be happen when student use a meter stick with zeros errors. This error will make the reading of the result become higher or become lower than the real result. The spring that has been use are not in a good condition also will make the spring constant is different between one and another. The oscillation of the spring may also be interrupt by the air and this will cause the spring swing after a while either than oscillation.
2. Parallax error Occurs due to our eyes are not perpendicular with the scale of the apparatus. In this experiment, the parallax errors occur when someone who manages to read the data are not concern about the amount and decimal places when they do the calculation. The person who is handling to measure the length of the spring are not concern about their eyes while reading the measurement.
Modification 1. Systemic error Make sure that all the equipment that are going to be use are in good condition and have been properly calibrated to fit the experiment. Make sure the person who manages to add the mass into the hanger are not stretches the spring. Make sure that there are very small of air resistance during the experiment to prevent the spring from swinging and let it on only oscillation. 2. Parallax error Make sure that the eyes are perpendicular to the scale of the measurement instruments to avoid this type of error. Make sure that we take the record in two or three decimal places in data reading so that the data will be more accurate. CONCLUSION : Based on the experiment, we can conclude that the elongation of the spring depends on the stiffness of the spring. We can determine the stiffness of the spring is the spring constant. The bigger the spring constant, the shorter the elongation of the spring. The experiment is related to the theories.
