Question

An elevator car of mass 790 kg falls trom rest 3.00 m. hits a buffer spring, and then travels an additional 0.410 m, as it compresces the spring by a madimum of 0.410 m. What is th force: constant of the spring?

Answer 1

The force constant of the spring is approximately 19210 N/m.

Step-by-step explanation:

The force constant of a spring can be determined using Hooke's law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. In this case, the elevator car compresses the spring by a maximum of 0.410 m, and we know the mass of the car is 790 kg. From this information, we can calculate the force constant of the spring.

Using Hooke's law, we have:

F = -kx

Where F is the force exerted by the spring, k is the force constant, and x is the displacement from the equilibrium position. Solving for k:

k = -F/x

Substituting the known values:

k = -mg/x

k = -(790 kg)(9.8 m/s^2)/(0.410 m)

k ≈ -19210 N/m

Since force constants are typically positive, we can take the absolute value of the result:

k ≈ 19210 N/m

Therefore, the force constant of the spring is approximately 19210 N/m.