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Mechanical Comprehension

What is the power output of a 9 hp engine that's 85% efficient?

4207.5 \( \frac{ft⋅lb}{s} \)

\( Efficiency = \frac{Power_{out}}{Power_{in}} \times 100 \)
Solving for power out: \( P_{o} = \frac{E \times P_{i}}{100} \)
Knowing that 1 hp = 550 \( \frac{ft⋅lb}{s} \), P_i becomes 9 hp x 550 \( \frac{ft⋅lb}{s} \) = 4950 \( \frac{ft⋅lb}{s} \)
\( P_{o} = \frac{E \times P_{i}}{100} = \frac{85 \times 4950 \frac{ft⋅lb}{s}}{100} \) \( = \frac{420750 \frac{ft⋅lb}{s}}{100} \) = 4207.5 \( \frac{ft⋅lb}{s} \)

Word Knowledge

Trevor decided to freeze the surplus chili for next week's tailgate party.

surfeit

Excess.

General Science

Stratus clouds are __________clouds characterized by horizontal layering with a broad flat base.

low-altitude

Clouds are categorized based on their shape, size, and altitude. Stratus clouds are low-altitude clouds characterized by horizontal layering with a broad flat base. When stratus clouds occur on the ground the result is fog.

Word Knowledge

The impenitent criminal received a harsh penalty, but his remorseful accomplice was released.

obdurate

Lacking remorse.

Mechanical Comprehension

The green box weighs 10 lbs. and a 35 lbs. weight is placed 3 ft. from the fulcrum at the blue arrow. How far from the fulcrum would the green box need to be placed to balance the lever?

10.5 ft.

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 d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{35 lbs. \times 3 ft.}{10 lbs.} \) = \( \frac{105 ft⋅lb}{10 lbs.} \) = 10.5 ft.

General Science

Blood is circulated throughout the body via:

arterioles

The aorta is the body's largest artery and receives blood from the pulmonary vein via the left ventricle. From there, blood is circulated through the rest of the body through smaller arteries called arterioles that branch out from the heart. Finally, blood is delivered to bodily tissues through capillaries.

Mechanical Comprehension

What is the first step to solving a problem where multiple forces are acting on an object?

calculate the net force

In mechanics, multiple forces are often acting on a particular object and, taken together, produce the net force acting on that object. Like force, net force is a vector quantity in that it has magnitude and direction.

General Science

The hottest of Earth's atmospheric layers is which of the following?

thermosphere

Temperatures again increase with altitude in the thermosphere which is the hottest (4,530 °F / 2,500 °C) atmospheric layer due to direct exposure to the Sun's radiation. However, the gas in this layer is highly diluted so even though the atoms of gas may be very high in temperature, there are too few of them to effectively transfer much heat.

Word Knowledge

The rancorous competition between the two chess clubs actually ended in a brawl.

bitter

Marked by deep ill–will.

Math Knowledge

The dimensions of this cube are height (h) = 7, length (l) = 7, and width (w) = 7. What is the surface area?

294

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 7 x 7) + (2 x 7 x 7) + (2 x 7 x 7)
sa = (98) + (98) + (98)
sa = 294