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Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. force need to be applied to balance the lever?

0.29 ft.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{20 lbs. \times 1 ft.}{70 lbs.} \) = \( \frac{20 ft⋅lb}{70 lbs.} \) = 0.29 ft.

General Science

The dwarf planet Pluto is located where?

in the Kuiper Belt

The Kuiper Belt is similar to the asteroid belt but much larger. Extending beyond the orbit of Neptune, it contains objects composed mostly of frozen methane, ammonia, and water. Most notably, the Kuiper Belt is home to Pluto, a dwarf planet that, until a 2006 reclassification, was considered the ninth planet of the solar system.

General Science

Neurons are part of the __________ nervous system.

peripheral

The nervous system consists of the brain and spinal cord (central nervous system) and the peripheral nervous system which is the network of nerve cells (neurons) that collect and distribute signals from the central nervous system throughout the body.

Math Knowledge

When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).

supplementary, vertical

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).

Mechanical Comprehension

Drag is a type of:

friction

Drag is friction that opposes movement through a fluid like liquid or air. The amount of drag depends on the shape and speed of the object with slower objects experiencing less drag than faster objects and more aerodynamic objects experiencing less drag than those with a large leading surface area.

General Science

An element in the physical state of __________ maintains a constant volume and shape.

solid

An element in a solid state has atoms or molecules that are constricted and do not move freely. Solids maintain a constant volume and shape and exist at a lower temperature than liquids or gases.

Automotive Information

Which of the following is a relay that connects the battery to the starter motor when the ignition key is turned?

solenoid

The cylindrical solenoid is a relay that safely connects the high amperage battery to the starter motor when the ignition key is turned. This current then allows the engine to turn at a high enough speed to start.

Word Knowledge

The longer Jorge waited in line at the ticket counter, the more his exasperation grew.

irritation

The state of being irritated.

Arithmetic Reasoning

Solve for \( \frac{5!}{6!} \)

\( \frac{1}{6} \)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)

Mechanical Comprehension

A wedge converts force applied to its blunt end into force __________ its inclined surface.

perpendicular to

The wedge is a moving inclined plane that is used to lift, hold, or break apart an object. A wedge converts force applied to its blunt end into force perpendicular to its inclined surface. In contrast to a stationary plane where force is applied to the object being moved, with a wedge the object is stationary and the force is being applied to the plane. Examples of a wedge include knives and chisels.