Final answer:
The spring constant needed for a spring scale where each 1.5 cm corresponds to a mass difference of 0.10 kg is approximately 65.33 N/m, calculated by using Hooke's Law with the force provided by the mass and gravity.
Step-by-step explanation:
To calculate the spring constant for the scale, we need to use Hooke's Law, which can be expressed as F = kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring (stretch or compression) from its equilibrium position.
In this problem, we know that a 1.5 cm length on the scale corresponds to a 0.10 kg mass difference. Using the acceleration due to gravity (9.8 m/s2), we can find the force (weight) that a mass of 0.10 kg would exert:
F = mass × gravity
F = 0.10 kg × 9.8 m/s2
F = 0.98 N
Since 1.5 cm is equal to 0.015 meters:
k = F/x
k = 0.98 N / 0.015 m
k = 65.33 N/m
Therefore, the value of the spring constant that would make each 1.5 cm corresponding to a 0.10 kg mass difference is approximately 65.33 N/m.