**Problem:**A mass of 0.78 kg is initially traveling across a horizontal surface. It then reaches a spring with a fixed end having a spring constant of 114 N/m that is positioned horizontally and initially at equilibrium. If the initial speed of the mass is 3.63 m/s as it contacts the spring, what is the speed of the mass after compressing the spring by 0.156 m, given that the coefficient of kinetic friction between the surfaces is 0.61?**Solution:**1. **Identify Given Data:** - Mass (m): 0.78 kg - Spring constant (k): 114 N/m - Initial speed (v_i): 3.63 m/s - Compression distance (x): 0.156 m - Coefficient of kinetic friction (μ_k): 0.612. **Calculate Forces:** - Friction force \( F_f = \mu_k \times m \times g \) - Spring force \( F_s = \frac{1}{2} k x^2 \)3. **Apply Work-Energy Principle:** - Initial kinetic energy \( KE_i = \frac{1}{2} m v_i^2 \) - Work done by friction \( W_f = F_f \times x \) - Final kinetic energy \( KE_f = KE_i - F_s - W_f \)4. **Solve for Final Speed:** The final expression for the final speed \( v_f \) can be derived from the energy balance equation: \[ \frac{1}{2} m v_f^2 = KE_i - W_f - F_s \] \[ v_f = \sqrt{\frac{2(KE_i - W_f - F_s)}{m}} \] Using computation, the final speed \( v_f \) is approximately 2.79 m/s.**Conclusion:**The speed of the mass after compressing the spring by 0.156 m, considering the friction, is approximately 2.79 m/s.

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A mass of 0.78 kg is is initially traveling at across a horizontal surface. It then reaches a spring with a fixed end having a spring constant of 114 N/m that is positioned horizontally and initially at equilibrium. If the initial speed of the mass is 3.63 as it contacts the spring, what is the speed of the mass after compressing the by 0.156 m if the coefficient of kinetic friction is between the surfaces is 0.61 ? 2.79

A mass of 0.78 kg is is initially traveling at across a horizontal surface. It then reaches a spring with a fixed end having a spring constant of 114 N/m that is positioned horizontally and initially at equilibrium. If the initial speed of the mass is 3.63 as it contacts the spring, what is the speed of the mass after compressing the by 0.156 m if the coefficient of kinetic friction is between the surfaces is 0.61 ? 2.79

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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