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Mechanical Comprehension

If the green box weighs 55 lbs. and is 3 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. weight need to be placed to balance the lever?

2.36 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_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{55 lbs. \times 3 ft.}{70 lbs.} \) = \( \frac{165 ft⋅lb}{70 lbs.} \) = 2.36 ft.

Electronics Information

Longer the electrical wires mean _______________ voltage drop.

greater

Electrical wires have a certain amount of resistance per foot. A longer wire means more resistance and a greater voltage drop.

Automotive Information

Too much fuel results in a __________ air-fuel mixture that burns quicker and cooler.

rich

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.

Electronics Information

Inductance is a factor in which of the following?

an AC circuit

Inductance is a property of an AC circuit (or a component in an AC circuit) that quantifies resistance to changes in current. The current in an AC circuit is continuously changing and inductive reactance (the opposition to change) depends both on the inductance of the circuit or component and the rate at which the current is changing.

Arithmetic Reasoning

If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 14 - 6 = 8 new staff for the busy season.

Automotive Information

For inline cylinder arrangements in an engine, how are the cylinders numbered?

sequentially from the front of the engine to the back

Inline cylinder arrangements number cylinders sequentially (1, 2, 3, ...) front to rear.

Word Knowledge

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

bitter

Marked by deep ill–will.

Mechanical Comprehension

Coplanar forces:

act in a common plane

Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.

General Science

Arteries carry __________ blood at __________ pressure.

oxygenated, high

Veins carry blood back to the heart from the body. While arteries are thick-walled because they carry oxygenated blood at high pressure, veins are comparatively thin-walled as they carry low-pressure deoxygenated blood. Like the heart, veins contain valves to prevent blood backflow.

Mechanical Comprehension

How much work can a 1 hp engine do in 3 seconds?

1650 ft⋅lb

Horsepower (hp) is a common measure of power output for complex machines. By definition, a 1 hp machine does 550 ft⋅lb of work in 1 second: 1 hp = 550 ft⋅lb/s. Substituting the variables for this problem gives us:
\( W = 1 hp \times 550 \frac{ft⋅lb}{s} \times 3s = 1650 ft⋅lb \)