Answer to Question #252968 in Mechanics | Relativity for Ellea

Question #252968

 A 5.0 kg block is on a horizontal surface. The coefficient of static friction between the block and the surface is 0.6. A frame of 20 N is applied to the block and acts at an angle of 300 above the horizontal. Is the block in equilibrium? Show the free-body diagram. 


1
Expert's answer
2021-10-18T17:42:07-0400

The block will be in equlibrium if Fframe,x<Fs.fr..F_{frame, x} < F_{s.fr.}. Let's calculate both forces:


Fframe,x=Fframecosθ=20 Ncos30=17.32 N,F_{frame, x}=F_{frame}cos\theta=20\ N\cdot cos30^{\circ}=17.32\ N,Fs.fr.=μs.fr.N=μs.fr.(mgFframesinθ),F_{s.fr.}=\mu_{s.fr.}N=\mu_{s.fr.}(mg-F_{frame}sin\theta),Fs.fr.=0.6(5 kg9.8 ms220 Nsin30)=23.4 N.F_{s.fr.}=0.6\cdot(5\ kg\cdot9.8\ \dfrac{m}{s^2}-20\ N\cdot sin30^{\circ})=23.4\ N.

As we can see from calculations, Fframe,x<Fs.fr.F_{frame, x} < F_{s.fr.}, therefore, the block is in equilibrium.


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