Question

In order to unscrew the tapped faucet a, a plumber uses two pipe wrenches as shown. By exerting a 40-lb force on each wrench, at a distance of 10 in. from the axis of the pipe and in a direction perpendicular to the pipe and to the wrench, the plumber prevents the pipe from rotating, and thus avoids loosening or further tightening the joint between the pipe and the tapped elbow c. Determine (a) the angle u that the wrench at a should form with the vertical if elbow c is not to rotate about the vertical, (b) the force-couple system at c equivalent to the two 40-lb forces when this condition is satisfied?

Answer 1

The question relates to the calculation of torque, which is the cross product of the radius vector and the force vector. To avoid rotating the elbow while unscrewing a faucet, the wrench must be positioned to produce counteracting torques. Increasing the lever arm with a pipe over the wrench handle increases the torque for the same force.

Step-by-step explanation:

The question concerns the physics concept of torque, which is a measure of the force causing an object to rotate. The torque (τ) is calculated by the cross product of the radius vector (R) from the pivot point to the point where the force is applied, and the force vector (F), which is τ = R × F. When a plumber uses two pipe wrenches to unscrew a faucet using a 40-lb force at a distance of 10 inches from the axis, they create a torquing effect.

To prevent the elbow from rotating, the wrench at point a should be positioned such that the forces exerted by both wrenches produce torques that cancel each other out. The magnitude of the torque is the force multiplied by the perpendicular distance to the pivot axis. As the force is applied perpendicularly, the full magnitude of the force contributes to the torque.

Putting a length of pipe over the handle of a wrench increases the radius (R), thereby increasing the torque for the same amount of applied force. This provides greater mechanical advantage to loosen a very tight bolt, although it may also increase the risk of breaking the bolt due to the increased force.