A wrench with a length of #15 cm# is used to unscrew a #5/2 cm# bolt. If a torque of #25 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?

To calculate the minimum torque needed to unscrew the bolt using the wrench, we can use the formula:

Torque = Force × Distance

First, we need to find the force required to unscrew the bolt. The force can be calculated using the formula:

Force = Friction × Distance

Given that the friction force is 25 N and the distance is the length of the wrench (15 cm), we have:

Force = 25 N

Next, we calculate the torque needed to unscrew the bolt using the force and the distance from the pivot point (fulcrum) to where the force is applied (wrench length). The distance from the pivot point to where the force is applied is the length of the wrench (15 cm), and the distance from the pivot point to where the bolt is located is the length of the bolt (5/2 cm).

Therefore, the total distance from the pivot point to where the force is applied to unscrew the bolt is:

Total distance = Wrench length + Bolt length

Total distance = 15 cm + 5/2 cm

Now, we can calculate the torque:

Torque = Force × Total distance

Substituting the values:

Torque = 25 N × (15 cm + 5/2 cm)

Torque = 25 N × (15 cm + 2.5 cm)

Torque = 25 N × 17.5 cm

Finally, converting the units to meters:

Torque = 25 N × 0.175 m

Torque = 4.375 Nm

So, the minimum torque that must be applied to the wrench to unscrew the bolt is approximately 4.375 Nm.