Question

A 37-cm long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. Part A: What is the spring constant of the vertical spring?

Answer 1

The spring constant of the vertical spring is 269.5 N/m.

Step-by-step explanation:

To find the spring constant of the vertical spring, we can use 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.

Using the given information, the initial length of the spring is 37 cm and the compressed length is 29 cm. The change in length is 37 cm - 29 cm = 8 cm = 0.08 m.

To calculate the spring constant, we can use the formula F = k * x, where F is the force applied on the spring, k is the spring constant, and x is the displacement. In this case, the force is the weight of the physics textbook, which is given by F = m * g, where m is the mass of the textbook and g is the acceleration due to gravity (9.8 m/s^2).

So, we have F = (2.2 kg) * (9.8 m/s^2) = 21.56 N.

Now, we can substitute the known values into the formula F = k * x and solve for k: 21.56 N = k * 0.08 m. Therefore, the spring constant of the vertical spring is k = 21.56 N / 0.08 m = 269.5 N/m.