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A wooden bucket filled with water has a mass of 43 kg and is attached to a rope that is wound around a cylinder with a radius of 0.063 m. A crank with a turning radius of 0.44 m is attached to the end of the cylinder. What minimum force directed perpendicularly to the crank handle is required to raise the bucket?

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usmanbiu

Answer:

60.34 N    

Explanation:

mass of water (m) = 43 kg

radius of cylinder (r) = 0.063 m

radius of crank (d) = 0.44 m

acceleration due to gravity (g) = 9.8 m/s^{2}

For the crank to raise the bucket, the force directed perpendicular to the crank must exert a torque which will be equal to the torque exerted by the weight of the water.

torque of water = torque of crank

where

  • torque of water = mgr = 43 x 9.8 x 0.063 = 26.55 Nm
  • torque of crank = mgr x sin θ = Fr x sinθ (mg = force (F))

        θ = 90° since the crank is perpendicular to the cylinder.

        torque of crank = F x 0.44 x sin 90 = 0.44 F

  • substituting the above into the equation we have

       26.55 = 0.44F

       F = 26.55 / 0.44 = 60.34 N         Â