Final answer:
The force constant of a spring can be calculated using Hooke's Law. For this scale, each 1.0 cm length corresponds to a mass difference of 100 g. To find the force constant, we can use the formula k = F / x, where F is the applied force and x is the displacement of the spring. For a 10.0 kg load that stretches the spring by 8.00 cm, the force constant is found to be 1225 N/m.
Step-by-step explanation:
The force constant of a spring is a measure of how stiff or strong the spring is. It is denoted by the symbol k and is determined by Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
To find the force constant, we can use the formula:
k = F / x
where F is the applied force and x is the displacement of the spring.
In this case, if each 1.0 cm length along the scale corresponds to a mass difference of 100 g, we can use this information to determine the force applied to stretch the spring by 8.00 cm for a 10.0 kg load:
Force = mass * acceleration due to gravity = 10.0 kg * 9.8 m/s^2 = 98 N
Using the formula for force constant, we have:
k = 98 N / 8.00 cm = 1225 N/m
Therefore, the value of the spring constant is 1225 N/m.