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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.

Word Knowledge

Regale most nearly means:

entertain

To amuse.

Automotive Information

What cylinder arrangement would be most common in a four cylinder front-wheel drive vehicle?

inline

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.

Math Knowledge

What is the area of a circle with a radius of 2?

4π

The formula for area is πr²:

a = πr²
a = π(2²)
a = 4π

General Science

Menstruation occurs when:

the ovum fails to become fertilized

If the ovum fails to become fertilized, the lining of the uterus sloughs off during menstruation. From puberty to menopause, this cycle of menstruation repeats monthly (except during pregnancy).

Shop Information

Which type of screwdriver has a straight slot in the top?

slotted

Screwdrivers come in many different handle, shaft, and tip configurations for use in a wide variety of applications. Screwdrivers are classified by their tip which is shaped to fit a corresponding screw head. Common tips are slotted (flat) and Phillips (x-shaped).

General Science

Examples of tertiary consumers include:

sharks

Tertiary consumers eat primary consumers and secondary consumers and are typically carnivorous predators. Tertiary consumers may also be omnivores. Examples include wolves, sharks, and human beings.

Math Knowledge

If c = 9 and x = 8, what is the value of 2c(c - x)?

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

2c(c - x)
2(9)(9 - 8)
2(9)(1)
(18)(1)
18

General Science

In the heart, the __________ artery and vein manage blood flow to the lungs.

pulmonary

The two largest veins in the body, the venae cavae, pass blood to the right ventricle which pumps the blood to the lungs through the pulmonary artery. Blood picks up oxygen in the lungs and returns it to the left atrium via the pulmonary vein.

General Science

Heat is always transferred from __________ to __________ environments.

warmer, cooler

Heat is always transferred from warmer to cooler environments and conduction is the simplest way this transfer can occur. It is accomplished through direct contact between materials and materials like metals that transfer heat efficiently are called conductors while those that conduct heat poorly, such as plastic, are called insulators.