A wrench with a length of #20 cm# is used to unscrew a #3/2 cm# bolt. If a torque of #15 Nm# is needed to overcome the friction keeping the bolt in place, what is the minimum torque that must be applied to the wrench to unscrew the bolt?

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To calculate the minimum torque needed to unscrew the bolt, we use the equation:

[ \text{Torque} = \text{Force} \times \text{Distance} ]

Given that the torque needed to overcome friction is 15 Nm and the length of the wrench is 20 cm (or 0.2 meters), we can rearrange the equation to solve for force:

[ \text{Force} = \frac{\text{Torque}}{\text{Distance}} ]

Plugging in the values:

[ \text{Force} = \frac{15 , \text{Nm}}{0.2 , \text{m}} = 75 , \text{N} ]

Now, the torque needed to unscrew the bolt depends on the distance from the point where force is applied to the center of rotation (fulcrum) of the wrench. Assuming the force is applied perpendicular to the wrench, the distance from the bolt to the fulcrum is the length of the wrench (0.2 meters).

Thus, the minimum torque needed to unscrew the bolt is:

[ \text{Torque} = \text{Force} \times \text{Distance} = 75 , \text{N} \times 0.2 , \text{m} = 15 , \text{Nm} ]

To calculate the minimum torque required to unscrew the bolt, you can use the formula:

Torque = Force × Distance

Given: Force required to overcome friction = 15 N Length of the wrench = 20 cm = 0.2 m Distance from the pivot (fulcrum) to where the force is applied = 3/2 cm = 0.015 m

The torque needed to unscrew the bolt is:

Torque = (15 N) × (0.2 m) / (0.015 m) ≈ 200 Nm