### Problem StatementA box with 15 kg of mass slides down an inclined plane that is 1.5 m high and 3.6 m along the inclined plane. Due to friction, the box reaches 4.3 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with a 600 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction.### QuestionWhen the box is temporarily stopped by the spring, how much is the spring compressed in meters?**Hint:** Start from the bottom of the inclined plane since you know the speed of the box there. Not all values must be used.### ExplanationTo solve this problem, the concepts of kinetic energy and elastic potential energy will be applied. 1. **Determine the kinetic energy of the box at the bottom of the incline:** The kinetic energy (KE) of the box can be calculated using the formula: \[ KE = \frac{1}{2} m v^2 \] Where: - \( m \) is the mass of the box (15 kg) - \( v \) is the velocity of the box at the bottom (4.3 m/s) Substituting the values: \[ KE = \frac{1}{2} \times 15 \, \text{kg} \times (4.3 \, \text{m/s})^2 \] \[ KE = \frac{1}{2} \times 15 \times 18.49 \] \[ KE = \frac{1}{2} \times 277.35 \] \[ KE = 138.675 \, \text{J} \] 2. **Set the kinetic energy equal to the elastic potential energy stored in the spring:** The elastic potential energy (PE_spring) stored in a compressed spring can be given by: \[ PE_{\text{spring}} = \frac{1}{2} k x^2 \] Where: - \( k \) is the spring constant (600 N/m) - \( x \) is the compression of the spring (to be determined) Since the box comes to a

Given: spring constant, k = 600 N/m speed of box at the bottom, v = 4.3 m/s mass of box, m = 15 kg…

A box with 15 kg of mass slides down an inclined plane that is 1.5 m high and 3.6 m along the inclined plane. Due to friction the box reaches 4.3 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with 600 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction When the box is temporarily stopped by the spring, how much is the spring compressed in m? Hint: start from the bottom of the inclined plane since you know the speed of the box there. Not all values must be used.

A box with 15 kg of mass slides down an inclined plane that is 1.5 m high and 3.6 m along the inclined plane. Due to friction the box reaches 4.3 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with 600 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction When the box is temporarily stopped by the spring, how much is the spring compressed in m? Hint: start from the bottom of the inclined plane since you know the speed of the box there. Not all values must be used.

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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