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Mechanical Comprehension

If a 25 lbs. weight is placed 3 ft. from the fulcrum at the blue arrow and the green box is 6 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?

12.5 lbs.

To balance this lever the torques on each side of the fulcrum 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 left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.

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

R_a = \( \frac{R_bd_b}{d_a} \) = \( \frac{25 lbs. \times 3 ft.}{6 ft.} \) = \( \frac{75 ft⋅lb}{6 ft.} \) = 12.5 lbs.

Math Knowledge

Solve 3c + 2c = 9c - 9x + 8 for c in terms of x.

1\(\frac{5}{6}\)x - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

3c + 2x = 9c - 9x + 8
3c = 9c - 9x + 8 - 2x
3c - 9c = -9x + 8 - 2x
-6c = -11x + 8
c = \( \frac{-11x + 8}{-6} \)
c = \( \frac{-11x}{-6} \) + \( \frac{8}{-6} \)
c = 1\(\frac{5}{6}\)x - 1\(\frac{1}{3}\)

Word Knowledge

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

irritation

The state of being irritated.

General Science

Examples of primary consumers include:

cows

Primary consumers (herbivores) subsist on producers like plants and fungus. Examples are grasshoppers, cows, and plankton.

General Science

Small rocks shed by asteroids and comets that reach the earth are called:

meteorites

Smaller rocks shed by asteroids and comets are called meteoroids. When these rocks reach Earth's atmosphere, they burn up in the mesosphere and become meteors. If a meteor manages to reach the Earth, it is called a meteorite.

Automotive Information

Which of the following is not a common vehicle cylinder arrangement?

vertical

Cylinder number and arrangement depends on the purpose of the engine. Smaller (four and six cylinder) engines in front-wheel drive vehicles often use an inline design which orients cylinders vertically over the crankshaft and aligns them in a row. Other common orientations are a horizontal/opposed design which places cylinders flat facing each other with the crankshaft between them and a V-type design common in six and eight cylinder engines that features one cylinder head per block of cylinders oriented at a 60 to 90 degree angle to each other with the crankshaft at the bottom of the V.

Shop Information

Which of the following is not an advantage of using a tape measure over using a ruler?

measure with more accuracy

Rulers are used to both measure distance and to draw straight lines. Tape measures are flexible rulers useful for measuring longer distances and in tighter spaces. Rulers and tape measures provide similarly accurate measurements.

Word Knowledge

The flighty Caroline could not be troubled with mundane tasks such as paying her bills.

commonplace

Practical, ordinary.

General Science

An endoskeleton (internal skeleton) is a charateristic of __________ animals, including humans.

vertebrate

An endoskeleton (internal skeleton) is a charateristic of vertebrate animals, including humans.

General Science

All surface water is part of the:

hydrosphere

The biosphere is the global ecological system integrating all living beings and their relationships. This includes their interactions with the lithosphere (the rigid outer part of the earth, consisting of the crust and upper mantle), hydrosphere (all surface water), and atmosphere (the envelope of gases surrounding the planet).