Final answer:
The force constant of the spring is found using Hooke's law which relates force to displacement. By converting the mass of the object to force using the acceleration due to gravity and the stretch to meters, the force constant can be calculated. For a 2.10 kg mass stretching the spring 2.54 cm, the force constant is approximately 810.63 N/m.
Step-by-step explanation:
The force constant of a spring, also known as the spring constant or stiffness, is calculated using Hooke's law, which states that the force (F) needed to extend or compress a spring by some distance (x) is directly proportional to that distance. Mathematically, it is expressed as F = kx, where k is the force constant.
In this case, the student is asking to find the force constant when a 2.10 kg object is hung vertically on a spring, causing it to stretch 2.54 cm. First, we need to convert the weight of the object to newtons (N) because the weight is the force that causes the spring to stretch. This can be done using the equation F = mg, where m is the mass and g is the acceleration due to gravity (9.8 m/s2). Then, we convert the stretch distance to meters. Finally, we rearrange Hooke's law to solve for the force constant, k = F/x.
So, the calculation will be:
- Convert the mass to force in newtons: F = (2.10 kg) × (9.8 m/s2) = 20.58 N
- Convert the stretch distance to meters: 2.54 cm = 0.0254 m
- Calculate the force constant: k = F/x = 20.58 N / 0.0254 m ≈ 810.63 N/m