Question

In a supermarket, you place a 2.27 kg bag of oranges on a scale, and the scale starts to oscillate at .30 Hz. What is the force constant (spring constant) of the spring of the scale? A) 600 N/m B) 474 N/m C) 820 N/m D) 650 N/m E) 410 N/m

Answer 1

The force constant (spring constant) of the spring is approximately 27.03 N/m.

Step-by-step explanation:

To calculate the force constant (spring constant) of the spring, we can use Hooke's Law and the given information.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

The formula to calculate the force constant is:

k = (2πf)^2 * m

Where:

• k is the force constant (spring constant)
• f is the frequency of oscillation (0.30 Hz in this case)
• m is the mass of the object (2.27 kg in this case)

Substituting the given values into the formula:

k = (2π * 0.30)^2 * 2.27

Simplifying the equation:

k = 0.30^2 * 2.27 * 4π^2

k ≈ 0.27 * 2.27 * 39.48

k ≈ 27.03 N/m

Therefore, the force constant (spring constant) of the spring is approximately 27.03 N/m.