Block m1 = 9 kg and lies on an incline plane with a coefficient of kinetic friction of 0.15. m1 is connected to mass m2 by a massless rope passing over a pulley. As m2moves down, determine the acceleration of m1 up the incline, given θ = 250 and m1= m2.

From the diagram, the net force exerted on the block m1 is, T-fk-m1gsinθ=m1aT-μkm1gcosθ-m1gsinθ=m1a…

Answered: Block m1 = 9 kg and lies on an incline…

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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Block m₁ = 9 kg and lies on an incline plane with a coefficient of kinetic friction of 0.15. m₁is connected to mass m₂by a massless rope passing over a pulley. As m₂moves down, determine the acceleration of m₁ up the incline, given θ = 25⁰ and m₁= m₂.

Expert Solution

Step 1

From the diagram, the net force exerted on the block $m_{1}$ is,

$\begin{array}{rcl} T - f_{k} - m_{1} g \sin θ & = & m_{1} a \\ T - μ_{k} m_{1} g \cos θ - m_{1} g \sin θ & = & m_{1} a \end{array}$ ...... (1)

From the diagram, the net force exerted on the block $m_{2}$ is,

$\begin{array}{rcl} m_{2} g - T & = & m_{2} a \\ T & = & m_{2} g - m_{2} a \end{array}$ ...... (2)

Substitute the equation (2) in equation (1).

$\begin{array}{rcl} m_{2} g - m_{2} a - μ_{k} m_{1} g \cos θ - m_{1} g \sin θ & = & m_{1} a \\ m_{2} g - μ_{k} m_{1} g \cos θ - m_{1} g \sin θ & = & m_{1} a + m_{2} a \\ m_{2} g - μ_{k} m_{1} g \cos θ - m_{1} g \sin θ & = & a (m_{1} + m_{2}) \\ a & = & \frac{m_{2} g - μ_{k} m_{1} g \cos θ - m_{1} g \sin θ}{m_{1} + m_{2}} \end{array}$

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