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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.

Automotive Information

Which of these is not necessary for combustion?

accelerant

Combustion is the burning of an air-fuel mixture to provide energy. It requires the presence of air, fuel, and a heat source to ignite the air-fuel mixture. In the internal combustion engine that powers automobiles and trucks the combustion happens inside the engine utilzing a fuel like gasoline, diesel fuel, or natural gas.

Word Knowledge

Heinous most nearly means:

odious

Shockingly evil.

Mechanical Comprehension

A = 5 ft., the green box weighs 50 lbs., and the blue box weighs 80 lbs. What does distance B need to be for this lever to balance?

3.13 ft.

In order for this lever to balance, the torque acting on side A must equal the torque acting on side B. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B

For this problem, the equation becomes:

50 lbs. x 5 ft. = 80 lbs. x d_B

d_B = \( \frac{50 \times 5 ft⋅lb}{80 lbs.} \) = \( \frac{250 ft⋅lb}{80 lbs.} \) = 3.13 ft.

Automotive Information

The fluid reservoir stores the __________ that the master cylinder uses to maintain hydraulic pressure.

brake fluid

The fluid reservoir stores the brake fluid that the master cylinder uses to maintain hydraulic pressure.

General Science

Elements in the Periodic Table of the Elements are ordered by which of the following?

atomic number

The Periodic Table of the Elements categorizes elements primarily by the number of protons in their nucleus (atomic number) and secondarily by the characteristics they exhibit.

General Science

A __________ is the smallest multi-atom particle of an element or compound that can exist and still retain the characteristics of the element or compound.

molecule

A molecule is the smallest multi-atom particle of an element or compound that can exist and still retain the characteristics of the element or compound. The molecules of elements consist of two or more similar atoms, the molecules of compounds consist of two or more different atoms.

General Science

The formula for acceleration is which of the following?

\(\vec{a} = { \vec{F} \over m }\)

Newton's second law of motion leads to the formula for acceleration which is a measure of the rate of change of velocity per unit time and, if you solve for positive acceleration, reveals how much net force is needed to overcome an object's mass. The formula for acceleration is \(\vec{a} = { \vec{F} \over m }\) or, solving for force, \(\vec{F} = m\vec{a}\).

Word Knowledge

Sadie's cowboy hat was incongruous with her black cocktail dress.

inappropriate

Not harmonious, incompatible.

Mechanical Comprehension

The principle of conservation of mechanical energy states that, as long as no other forces are applied, what will remain constant as an object falls?

total mechanical energy

As an object falls, its potential energy is converted into kinetic energy. The principle of conservation of mechanical energy states that, as long as no other forces are applied, total mechanical energy (PE + KE) of the object will remain constant at all points in its descent.