A 0.40 kg mass vibrates at the end of a horizontal spring along a frictionless surface reaching a maximum speed of 0.50m/s If the maximum displacement of the mass is 0.11 m, what is the spring constant? (8.3N/m)

Question

A 0.40 kg mass vibrates at the end of a horizontal spring along a frictionless surface reaching a maximum speed of 0.50m/s If the maximum displacement of the mass is 0.11 m, what is the spring constant? (8.3N/m)

Answer 1

Here's how to solve this problem:**1. Understand the relationship between maximum speed, maximum displacement, and spring constant.**In simple harmonic motion (SHM) with a spring, the maximum speed (v_max) and maximum displacement (A) are related to the spring constant (k) and mass (m) by the following equation:v_max = √(k/m) * A**2. Rearrange the equation to solve for k:**k = (v_max² * m) / A²**3. Plug in the given values:*** v_max = 0.50 m/s* m = 0.40 kg* A = 0.11 mk = (0.50² * 0.40) / 0.11²**4. Calculate the spring constant:**k = (0.25 * 0.40) / 0.0121k = 0.1 / 0.0121k ≈ 8.26 N/m**5. Round to the appropriate number of significant figures:**Since the given values have two significant figures, the answer should also have two significant figures.k ≈ 8.3 N/mTherefore, the spring constant is approximately 8.3 N/m.

Question

A 0.40 kg mass vibrates at the end of a horizontal spring along a frictionless surface reaching a maximum speed of 0.50m/s If the maximum displacement of the mass is 0.11 m, what is the spring constant? (8.3N/m)

Solution

Answer