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Mechanical Comprehension

If A = 10 ft., B = 1 ft., C = 9 ft., the green box weighs 50 lbs. and the blue box weighs 60 lbs., what does the orange box have to weigh for this lever to balance?

48.89 lbs.

In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

50 lbs. x 10 ft. = 60 lbs. x 1 ft. + f_C x 9 ft.

500 ft. lbs. = 60 ft. lbs. + f_C x 9 ft.

f_C = \( \frac{500 ft. lbs. - 60 ft. lbs.}{9 ft.} \) = \( \frac{440 ft. lbs.}{9 ft.} \) = 48.89 lbs.

General Science

The Earth's rocks fall into three categories based on how they're formed. Which of the following is formed by the gradual depositing of small rocks?

sedimentary

The Earth's rocks fall into three categories based on how they're formed. Igneous rock (granite, basalt, obsidian) is formed from the hardening of molten rock (lava), sedimentary rock (shale, sandstone, coal) is formed by the gradual despositing and cementing of rock and other debris, and metamorphic rock (marble, slate, quartzite) which is formed when existing rock is altered though pressure, temperature, or chemical processes.

Arithmetic Reasoning

What is (z⁵)⁴?

z²⁰

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

(z⁵)⁴
z^{(5 * 4)}
z²⁰

Electronics Information

An inductor __________ changes in the electric current flowing through it.

resists

An inductor is coiled wire that stores electric energy in the form of magnetic energy and resists changes in the electric current flowing through it. If current is increasing, the inductor produces a voltage that slows the increase and, if current is decreasing, the magnetic energy in the coil opposes the decrease to keep the current flowing longer. In contrast to capacitors, inductors allow DC to pass easily but resist the flow of AC.

Word Knowledge

Celebrated most nearly means:

admired

Widely known, respected.

Shop Information

A welding rod provides:

the joining material for a weld

The joining material for a weld is called a welding or filler rod and is available in a variety of diameters and alloys for different welding tasks.

Mechanical Comprehension

Torque involves a perpendicular force applied to a lever arm that moves around a center of rotation. Increasing the length of the lever arm will do which of the following?

increase torque

Torque measures force applied during rotation: τ = rF. Torque (τ, the Greek letter tau) = the radius of the lever arm (r) multiplied by the force (F) applied. Radius is measured from the center of rotation or fulcrum to the point at which the perpendicular force is being applied. The resulting unit for torque is newton-meter (N-m) or foot-pound (ft-lb).

Word Knowledge

Pretentious most nearly means:

pompous

Making unjustified claims.

Electronics Information

The rate of flow of electrons per unit time is which of the following?

current

Current is the rate of flow of electrons per unit time and is measured in amperes (A). A coulomb (C) is the quantity of electricity conveyed in one second by a current of one ampere.

General Science

The Earth's rocks fall into three categories based on how they're formed. Which of the following is formed when existing rock is altered through pressure, temperature, or chemical processes?

metamorphic

The Earth's rocks fall into three categories based on how they're formed. Igneous rock (granite, basalt, obsidian) is formed from the hardening of molten rock (lava), sedimentary rock (shale, sandstone, coal) is formed by the gradual despositing and cementing of rock and other debris, and metamorphic rock (marble, slate, quartzite) which is formed when existing rock is altered though pressure, temperature, or chemical processes.