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Mechanical Comprehension

If the force applied at the blue arrow over 5 ft. moves the green box 2.5 ft., what is the mechanical advantage of this lever?

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where E_d is the effort distance and R_d is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{5 ft.}{2.5 ft.} \) = 2

You might be wondering how having an effort distance of 2 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 2 times the resistance distance, the effort force must be \( \frac{1}{2} \) the resistance force. You're trading moving 2 times the distance for only having to use \( \frac{1}{2} \) the force.

Word Knowledge

Induce most nearly means:

incite

To influence or cause.

Word Knowledge

Advantageous most nearly means:

favorable

Giving an advantage.

General Science

pH is a scale that measures of how basic or acidic a solution is. A solution with a pH of 9 is:

alkaline

An acid is a substance that gives up positively charged hydrogen ions (H⁺) when dissolved in water. A base (alkaline) gives up negatively charged hydroxide ions (OH^-) when dissolved in water. pH is a scale that measures of how basic or acidic a solution is. Numbered from 0 to 14, solutions with a pH of 7 are neutral, less than 7 are acidic, more than 7 are alkaline.

Word Knowledge

Onset most nearly means:

start

Beginning.

Arithmetic Reasoning

What is \( 5 \)\( \sqrt{28} \) + \( 7 \)\( \sqrt{7} \)

17\( \sqrt{7} \)

To add these radicals together their radicands must be the same:

5\( \sqrt{28} \) + 7\( \sqrt{7} \)
5\( \sqrt{4 \times 7} \) + 7\( \sqrt{7} \)
5\( \sqrt{2^2 \times 7} \) + 7\( \sqrt{7} \)
(5)(2)\( \sqrt{7} \) + 7\( \sqrt{7} \)
10\( \sqrt{7} \) + 7\( \sqrt{7} \)

Now that the radicands are identical, you can add them together:

10\( \sqrt{7} \) + 7\( \sqrt{7} \)
(10 + 7)\( \sqrt{7} \)
17\( \sqrt{7} \)

General Science

DNA is encoded through a combination of which of the following?

nucleotides

Deoxyribonucleic acid (DNA) is the molecule that contains genetic information. DNA is encoded through a combination of nucleotides that bind together in a specific double helix pattern.

Electronics Information

The conductivity of an element depends on how many electrons occupy which electron shell?

outer

All electricity is the movement of electrons which are subatomic particles that orbit the nucleus of an atom. Electrons occupy various energy levels called shells and how well an element enables the flow of electrons depends on how many electrons occupy its outer (valence) electron shell.

General Science

The __________ nervous system controls voluntary actions.

somatic

Part of the peripheral nervous system, the somatic nervous system is made up of nerve fibers that send sensory information to the central nervous system and control voluntary actions.

Electronics Information

The valence shell of n insulator is how full of electrons?

more than half full

Insulators have valence shells that are more than half full of electrons and, as such, are tightly bound to the nucleus and difficult to move from one atom to another.