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The friction coefficient is c1=0.2 between two bodies A,B. The friction coefficient is c2=0.18 between body B and the ground. If mass mA=0.5kgr and mB=1kgr , what is the minimum force P so that the two bodies start sliding?(we consider that there is no friction at the rope).

**Solution**

If T1 is the friction force for A, the equilibrium for the body A is

ΣFX=0→T1-F1=0 (1)

ΣFY=0→N1-mA*g=0 (2)

And because the body A starts to move

T1=c1*N1 (3)

For the body B the equilibrium is

ΣFX=0→P-F-T1-T2=0 (4)

ΣFY=0→N2-mA*g-N1=(5)

And because the body B starts to move

T2=c2*N2 (6)

With the acceleration of gravity g=10m/sec2

We solve (1),(2),(3),(4),(5),(6)

P=4.7N

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