Friction help

Oct 2012
34
0
UK
A book, which may be modelled as a particle of weight 8N rests in equilibrium on a desk top inclined at 28 degree to the horizontal. ind the frictional force acting on the book. he coefficients of friction between the book and the desk top is 0.6. Determine whether the equilibrium is limiting.

No clue

F = 8 sin (28)= 3.75
R= MF
= 0.3* 3.75



but the answer given is 3.76 N and the friction is not limiting . Please help me out
 

earboth

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A book, which may be modelled as a particle of weight 8N rests in equilibrium on a desk top inclined at 28 degree to the horizontal. ind the frictional force acting on the book. he coefficients of friction between the book and the desk top is 0.6. Determine whether the equilibrium is limiting.

No clue

F = 8 sin (28)= 3.75
R= MF
= 0.3* 3.75



but the answer given is 3.76 N and the friction is not limiting . Please help me out
1. The frictional force depends on the normal force acting perpendicularly on the desk:

\(\displaystyle |\overrightarrow{F_n}|=8 N \cdot \cos(28^\circ) \cdot 0.6\approx 4.24 N\)

2. The force parallel to the surface of the desk pulling the book downwards is

\(\displaystyle |\overrightarrow{F_h}|=8 \cdot \sin(28^\circ) \approx 3.756 N\)