Answer to Question #123766 in Physics for Dr. Horus

Question #123766
A body of mass 2kg lie on a rough plane which is inclined at 23° to the horizontal. A force of 20N is applied to the body parallel to and up the plane. If the body accelerate at 1.5m/s^2. Calculate the coefficient of friction between the body and the plane.
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Expert's answer
2020-06-24T11:21:10-0400

Let's apply the Newton's Second Law of Motion in projections on axis xx- and yy:


Fx=max,\sum F_x = ma_x,Fy=may=0,\sum F_y = ma_y = 0,FapplmgsinθFfr=ma,(1)F_{appl} - mgsin \theta - F_{fr} = ma, (1)Nmgcosθ=0,(2)N - mgcos \theta = 0, (2)FapplmgsinθμN=ma,F_{appl} - mgsin \theta - \mu N = ma,N=mgcosθ,N = mgcos \theta,Fapplmgsinθμmgcosθ=ma.F_{appl} - mgsin \theta - \mu mgcos \theta = ma.

From this equation we can find the coefficient of friction between the body and the plane:


μ=Fapplmgsinθmamgcosθ,\mu = \dfrac{F_{appl} - mgsin \theta - ma}{mgcos \theta},μ=20 N2 kg9.8 ms2sin232 kg1.5 ms22 kg9.8 ms2cos23=0.52.\mu = \dfrac{20 \ N - 2 \ kg \cdot 9.8 \ \dfrac{m}{s^2} \cdot sin23^{\circ} - 2 \ kg \cdot 1.5 \ \dfrac{m}{s^2}}{2 \ kg \cdot 9.8 \ \dfrac{m}{s^2} \cdot cos23^{\circ}} = 0.52.

Answer:

μ=0.52.\mu = 0.52.


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