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