Answered: An inclined plane makes an angle of θ =…

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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Question

An inclined plane makes an angle of θ = 32° above the horizontal. A wooden block (m = 560 g) is placed on the plane and is connected to the top of the plane by a spring with spring constant k = 23 N/m. The spring is parallel to the surface of the plane, and friction between the block and the plane is negligible. The block is held in place with the spring at its relaxed length, and then the block is released from rest. It slides a distance d down the plane before momentarily coming to rest, and then being pulled back up the plane. What is d? The symbolic answer must be written in terms of the variables θ, m, k, and g, although not all of these variables may be needed. Note: tackle this problem using energy concepts.

Expert Solution

Step 1: Spring energy and potential energy

Write the expression for the spring energy.

$S E equals 1 half k d squared$

Write the expression for the potential energy.

$table row cell P E equals m g h end cell row cell P E equals m g left parenthesis d sin theta right parenthesis end cell end table$

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