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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 0.073 m. A crank with a turning radius of 0.41 m is attached to the end of the cylinder. What minimum force directed perpendicularly to the crank handle is required to raise the bucket?

Respuesta :

Answer:

[tex]F = 75.1 N[/tex]

Explanation:

Here we know that torque due to applied force on the crank must be balanced by the torque due to weight of bucket on the cylinder

so here we know that

torque due to weight is given as

[tex]\tau_1 = r F[/tex]

[tex]\tau_1 = 0.073 \times 43 \times 9.81[/tex]

[tex]\tau_1 = 30.8 Nm[/tex]

now the torque by applied force on the crank is given as

[tex]\tau_2 = 0.41 F[/tex]

so we have

[tex]0.41 F = 30.8[/tex]

[tex]F = 75.1 N[/tex]

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