Water is drawn from a well in a bucket tied to the end of a rope whose other end wraps around a cylinder of mass 50 kg and diameter 25 cm.As you turn this cylinder with a crank,the rope raises the bucket.If the mass of a bucket of water is 20 kg,what torque must you apply to the crank to raise the bucket of water at a constant speed? A)24 N · m B)2.5 N · m C)80 N · m D)2.4 $\times$ 10³ N · m E)49 N · m

Question

Quizplus · Accepted Answer

To raise the bucket at a constant speed, the torque applied must counteract the torque due to the weight of the bucket. The torque ($\tau$) is given by $\tau = rF$, where $r$ is the radius of the cylinder and $F$ is the force applied. The force due to the weight of the bucket is $F = mg$, where $m = 20 \, \text{kg}$ is the mass of the bucket with water and $g = 9.8 \, \text{m/s}^2$ is the acceleration due to gravity. The radius of the cylinder is half of its diameter, so $r = 0.25 \, \text{m} / 2 = 0.125 \, \text{m}$. Thus, $\tau = 0.125 \, \text{m} \times 20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 24.5 \, \text{N} \cdot \text{m}$, which rounds to $24 \, \text{N} \cdot \text{m}$ for the purposes of this question.

Water Is Drawn from a Well in a Bucket Tied ×\times×

Water Is Drawn from a Well in a Bucket Tied $\times$