Question

a mass of 0.74 kg attached to a vertical spring stretches it 3.7 cm from its natural length to its equilibrium position. what is the spring constant, in n/m? round your answer to the nearest whole number.

Answer 1

To calculate the spring constant, the weight of the mass is used as the force in Hooke's Law, resulting in a spring constant of approximately 196 N/m.

Step-by-step explanation:

To find the spring constant (k), we use Hooke's Law, which states that the force (F) needed to stretch or compress a spring by some distance (x) is proportional to that distance:

F = kx

Given a mass (m) of 0.74 kg that stretches the spring 3.7 cm, we first convert this distance to meters (3.7 cm = 0.037 m). The force exerted by the mass due to gravity is its weight, which is calculated using the equation:

F = mg

where g is the acceleration due to gravity (9.81 m/s2). Substituting values we get:

F = 0.74 kg × 9.81 m/s2 = 7.2594 N

Now we can solve for the spring constant (k) using Hooke's Law:

k = F/x = 7.2594 N / 0.037 m

After performing the division, the spring constant is found to be approximately 196 N/m (rounded to the nearest whole number).