Lab Hooke's Law

Results:

From the data collected, Force applied to the spring can be calculated:

𝐹 = 𝑚𝑔 = 50𝑔 × 1𝑔1000 𝑘𝑔 ×9. 8 𝑚/𝑠 2

= 0. 49 𝑁

From this result, table and figure below will showed the value of force applied to the

spring and the displacement of spring from equilibrium during eight different masses:

Data Table 1: The force applied to the spring and the displacement of spring from

equilibrium during eight different masses with the spring constant slider value of 3

# Added mass

(g)

Force applied to the

spring (N)

Displacement of spring from

equilibrium (m)

0 0 0 0

1 50 0.49 0.09

2 75 0.735 0.13

3 100 0.98 0.17

4 125 1.225 0.21

5 150 1.47 0.25

6 200 1.96 0.33

7 250 2.45 0.415

8 300 2.94 0.495

Figure 1: The force applied to the spring and the displacement of spring from

equilibrium during eight different masses with the spring constant slider value of 3

From the data, the slope of the trendline is the result of the calculation:

k = (2.94N – 0N) / (0.495m – 0m) = 5.94 (N/m)

Then, the total work done can be calculated according to Trendline and integration:

𝑊 = 12 𝑘𝑥 2

= 12 ×5. 94×(0. 495 𝑚) 2

= 0. 7277 𝐽

Beside, the work done can also be calculated by the data collected:

𝑊1 = 𝐹

𝑛 +𝐹

𝑛+1

2( ) 𝑥𝑛+1 − 𝑥𝑛( ) = 0𝑁+0.49𝑁2( ) . 09𝑚 − 0𝑚( ) = 0. 0221 𝐽 With the eight masses, the total work done is the sum of that. Table below will showed

the value of the work done base on the calculation by the data collected:

Table 2: the value of the work done base on the calculation by the data collected

# Added mass (g) Work Done (J)

0 0 0

1 50 0.0221

2 75 0.0245

3 100 0.0343

4 125 0.0441

5 150 0.0539

6 200 0.1372

7 250 0.1874

8 300 0.2156

TOTAL 0.7191

Then, from this record, there is a percent different between the two values:

%𝐷𝑖𝑓𝑓 = 𝑇𝑟𝑒𝑛−𝐷𝑎𝑡𝑎| |𝐴𝑣𝑒𝑟𝑎𝑔𝑒 ×100% = 0.7277𝐽−0.7191 𝐽| |

0.7277𝐽+0.7191 𝐽| | 2

×100% = 1. 19 %

Finally, from those calculation, table 3 will describe the result:

Table 3: Work done through different calculation and the percent different between

two value

Spring Constant #1 from slope of trendline: k = 5.94

Work done according to Trendline and

integration 0.7277 (J)

Work done according to data and

summation 0.7191 (J)

Percent difference between the two values 1.19 %

This data can be compared to the result of the other students named Doriane Perlise

Lienou Kamto. Table below will show the record: