Answered: A box is initially sliding up a 32.5 ̊…

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

A box is initially sliding up a 32.5 ̊ incline at a speed of 13.0 m/s. The coefficients of friction between the incline and the box are μk = 0.680 and μs = 0.740.

a)What is the acceleration of the box while it is sliding up the incline?

b)How far will the box travel up the inline before coming to a stop?

c)What would the coefficient of kinetic friction have to be for the box to be able to slide down the ramp at a constant speed?

Expert Solution

Step 1

Acceleration of the box sliding up the incline is

$m a = μ_{k} m g \cos θ + m g \sin θ a = μ_{k} g \cos θ + g \sin θ$

Substitute

$\begin{array}{rcl} a & = & (9.81 \frac{m}{s^{2}}) [(0.680) (\cos 32.5 °) + (\sin 32.5 °)] \\ = & 10.897 \frac{m}{s^{2}} \\ \approx & 10.9 \frac{m}{s^{2}} \end{array}$

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