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Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how much weight would need to be placed at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 8 ft.?

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

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{20 lbs. \times 1 ft.}{8 ft.} \) = \( \frac{20 ft⋅lb}{8 ft.} \) = 2.5 lbs.

Mechanical Comprehension

Normal force is generally equal to the __________ of an object.

weight

Normal force arises on a flat horizontal surface in response to an object's weight pressing it down. Consequently, normal force is generally equal to the object's weight.

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.

Automotive Information

The two major types of vehicle braking systems are:

drum and disc

Brakes utlize friction to slow vehicle tires. Drum brakes employ a cast iron drum that roates with the vehicle axle. When hydraulic pressure is applied to the brake assemblies at the wheels, internal pistons expand and push brake shoes outward into contact with the brake drum slowing the rotation of the axle. More powerful disc brakes operate by pinching a rotating disc betweeen two brake pads and allow for a larger surface area to contact the disc, provide more force, and are more easily cooled.

Mechanical Comprehension

A a seesaw / teeter-totter is an example of which of the following?

first-class lever

A first-class lever is used to increase force or distance while changing the direction of the force. The lever pivots on a fulcrum and, when a force is applied to the lever at one side of the fulcrum, the other end moves in the opposite direction. The position of the fulcrum also defines the mechanical advantage of the lever. If the fulcrum is closer to the force being applied, the load can be moved a greater distance at the expense of requiring a greater input force. If the fulcrum is closer to the load, less force is required but the force must be applied over a longer distance. An example of a first-class lever is a seesaw / teeter-totter.

Word Knowledge

Thelma tended to polarize discussions rather than to encourage compromise.

divide

To break up into opposing groups.

Mechanical Comprehension

What is work?

The movement of an object by a force

Work is accomplished when force is applied to an object: W = Fd where F is force in newtons (N) and d is distance in meters (m). Thus, the more force that must be applied to move an object, the more work is done and the farther an object is moved by exerting force, the more work is done. By definition, work is the displacement of an object resulting from applied force.

Math Knowledge

Solve for b:
-5b - 3 = \( \frac{b}{-3} \)

-\(\frac{9}{14}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-5b - 3 = \( \frac{b}{-3} \)
-3 x (-5b - 3) = b
(-3 x -5b) + (-3 x -3) = b
15b + 9 = b
15b + 9 - b = 0
15b - b = -9
14b = -9
b = \( \frac{-9}{14} \)
b = -\(\frac{9}{14}\)

Word Knowledge

Exalt most nearly means:

glorify

To elevate by praise.

Word Knowledge

Diffident most nearly means:

timid

Lacking self–confidence.