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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.

Automotive Information

The stoichiometric ratio is approximately:

14.7:1

The stoichiometric ratio defines the proper ratio of air to fuel necessary so that an engine burns all fuel with no excess air. For gasoline fuel, the stoichiometric ratio is about 14.7:1 or for every one gram of fuel, 14.7 grams of air are required. Too much air results in a lean air-fuel mixture that burns more slowly and hotter while too much fuel results in a rich mixture that burns quicker and cooler.

Word Knowledge

Franklin hoped to defeat his adversary in the afternoon's tennis match.

opponent

One who opposes or resists.

General Science

Sound travels fastest through which of the following media?

metal

The speed of a sound wave will vary with the medium. Sound travels fastest through media that has particles that are very close together, like metal. Thus, it travels faster through water than through air and doesn't travel at all through a vacuum (there are no particles in empty space to vibrate).

Word Knowledge

Turmoil most nearly means:

chaos

Extreme confusion, agitation.

Mechanical Comprehension

When it comes to force, mass and acceleration have what kind of relationship?

linear

Newton's Second Law of Motion states that "The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object." This Law describes the linear relationship between mass and acceleration when it comes to force and leads to the formula F = ma or force equals mass multiplied by rate of acceleration.

Word Knowledge

His incredible perception made him the best detective on the force.

cognition

Capacity for seeing or understanding.

Mechanical Comprehension

When all forces acting on a system cancel each other out, this is called:

equilibrium

When a system is stable or balanced (equilibrium) all forces acting on the system cancel each other out. In the case of torque, equilibrium means that the sum of the anticlockwise moments about a center of rotation equal the sum of the clockwise moments.

Math Knowledge

For this diagram, the Pythagorean theorem states that b² = ?

c² - a²

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c²= a² + b² or, solved for c, \(c = \sqrt{a + b}\)

Automotive Information

Engine oil viscosity is rated using the format XW-XX with the number preceding the W indicating viscosity at __________ ℉ and the XX indicating viscosity at __________ ℃.

0, 100

The primary component of the lubrication system is engine oil. Engines require oil blends with different thickness (viscosity) and additives depending on their operating conditions. Viscosity is rated using the format XW-XX with the number preceding the W (winter) rating the oil’s viscosity at 0 ℉ (-17.8 ℃) and the XX indicating viscosity at 100 ℃.