1) A 500 kg sled is pulled along a horizontal surface at uniform speed by a rope that makes an angle of 30 degrees above the horizontal. Find mu if the tension in the rope is 200 N.

Verified Answer :

As the velocity is constant, the result of the forces in the sled is zero. If \(T_x\) is the horizontal component of the traction and \(F_{at}\) is the frictional force:

\(F_R=0\iff T_x=F_{at}\iff T\cos30^o=\mu N\iff \\\\ T\cos30^o=\mu P\iff 200\cdot\dfrac{\sqrt3}{2}=\mu (500\cdot10)\iff 100\sqrt3=5000\mu\\\\\mu=\dfrac{100\sqrt3}{5000}\iff \mu=\dfrac{\sqrt3}{50}\Longrightarrow\boxed{\mu\approx0,035}\)

Coefficient of friction ( mu) is 0.035

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