Mechanical Reasoning Principles Flashcards

If gear X turns clockwise as shown by the arrow, which of the following statements is true about gears Y and Z? (Image depicts three meshed gears in a line: X, Y, Z)

Answer: Gear Y turns counter-clockwise and Gear Z turns clockwise.

When gears are meshed directly, they rotate in opposite directions. Since Gear X turns clockwise, Gear Y must turn counter-clockwise. Because Gear Y turns counter-clockwise, Gear Z, which is meshed with Y, must turn in the opposite direction, which is clockwise.

An electrician needs to lift a heavy transformer weighing 200 lbs to the top of a utility pole. Which pulley system will require the least amount of effort (force) to lift the transformer?

Answer: A system with one fixed and one movable pulley.

A single fixed pulley only changes the direction of the force and provides no mechanical advantage. A movable pulley, however, distributes the load across multiple sections of the rope. A system with one fixed and one movable pulley (a block and tackle) provides a mechanical advantage, effectively halving the force required to lift the 200 lb load (requiring approximately 100 lbs of force), which is more efficient than the other options.

A worker is using a 6-foot long crowbar as a lever to move a heavy crate. The fulcrum is placed 1 foot from the end of the crowbar touching the crate. To move the crate, where should the worker apply force to achieve the maximum mechanical advantage?

Answer: At the very end of the crowbar, 5 feet from the fulcrum.

The principle of a lever states that mechanical advantage is maximized by increasing the distance between the point where force is applied (effort) and the fulcrum. With the fulcrum 1 foot from the load, the remaining length of the lever is 5 feet. Applying force at the furthest point from the fulcrum (the very end of the bar) maximizes the effort arm, thus maximizing the mechanical advantage.

Water is being pumped through a pipe that narrows in the middle and then widens again. According to Bernoulli's principle, what happens to the water's speed and pressure in the narrow section compared to the wider sections?

Answer: The speed increases and the pressure decreases.

Bernoulli's principle states that for a fluid in motion, an increase in speed occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. In the narrow section of the pipe (a venturi), the fluid must speed up to maintain the same volume flow rate. This increase in speed results in a corresponding decrease in pressure.

Two gears are connected by a crossed drive belt. The drive gear (A) has a diameter of 10 inches and the driven gear (B) has a diameter of 5 inches. If gear A rotates clockwise, what is the motion of gear B?

Answer: Counter-clockwise at twice the speed of A.

Gears connected by a crossed belt move in opposite directions. Therefore, if gear A rotates clockwise, gear B will rotate counter-clockwise. Since gear B is smaller (half the diameter), it must rotate faster to keep up with the belt. The speed ratio is inversely proportional to the diameter ratio, so gear B will rotate at twice the speed of gear A.

A fully loaded toolbox is easier to pull up a long, gradual ramp than to lift straight up to the same height. This is because the ramp:

Answer: Increases the distance over which the force is applied, reducing the required effort.

An inclined plane (a ramp) is a simple machine that provides a mechanical advantage. While the total work done (force x distance) remains the same (ignoring friction), the ramp increases the distance over which the work is performed. This allows the required input force (effort) to be less than the force required to lift the object vertically.