Final answer:
The total correction due to sag in the tape is 97.3668 N.
Step-by-step explanation:
To calculate the total correction due to sag in the tape, we need to consider the weight of the tape and the tension in the tape at the supports. There are two sections in the tape: from 0 m to 30 m and from 30 m to 75 m. Let's calculate the correction for each section:
In the first section (from 0 m to 30 m), the tension in the tape is equal to the weight of the tape plus the tension at the support. The weight of the tape is 2.4 kg x 9.8 m/s^2 = 23.52 N. The tension at the support is equal to the pull minus the weight of the tape on that section. The weight of the tape on that section is (30 m/100 m) * 23.52 N = 7.056 N. So the tension at the support is 15 kg x 9.8 m/s^2 - 7.056 N = 142.944 N. The correction due to sag in this section is (30 m/100 m)^2 * (142.944 N)^2 / (2 * 9.8 m/s^2) = 27.8224 N.
In the second section (from 30 m to 75 m), the tension in the tape is equal to the weight of the tape plus the tension at the support. The weight of the tape is still 23.52 N. The tension at the support is equal to the pull minus the weight of the tape on that section. The weight of the tape on that section is ((75 m - 30 m)/100 m) * 23.52 N = 11.76 N. So the tension at the support is 15 kg x 9.8 m/s^2 - 11.76 N = 124.44 N. The correction due to sag in this section is ((75 m - 30 m)/100 m)^2 * (124.44 N)^2 / (2 * 9.8 m/s^2) = 69.5444 N.
Therefore, the total correction due to sag in the tape is 27.8224 N + 69.5444 N = 97.3668 N.