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Word Knowledge

The teacher made an exception and let Gina eat her snack in class.

anomaly

A case to which the rule does not apply.

Mechanical Comprehension

When all forces acting on a system cancel each other out, this is called:

equilibrium

When a system is stable or balanced (equilibrium) all forces acting on the system cancel each other out. In the case of torque, equilibrium means that the sum of the anticlockwise moments about a center of rotation equal the sum of the clockwise moments.

Mechanical Comprehension

If A = 10 ft., B = 1 ft., C = 9 ft., the green box weighs 50 lbs. and the blue box weighs 60 lbs., what does the orange box have to weigh for this lever to balance?

48.89 lbs.

In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. 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 + f_Cd_C

For this problem, this equation becomes:

50 lbs. x 10 ft. = 60 lbs. x 1 ft. + f_C x 9 ft.

500 ft. lbs. = 60 ft. lbs. + f_C x 9 ft.

f_C = \( \frac{500 ft. lbs. - 60 ft. lbs.}{9 ft.} \) = \( \frac{440 ft. lbs.}{9 ft.} \) = 48.89 lbs.

Mechanical Comprehension

A 290 lb. barrel is rolled up a 14 ft. ramp to a platform that's 2 ft. tall. What effort is required to move the barrel?

41.4 lbs.

This problem describes an inclined plane and, for an inclined plane, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance:

F_ed_e = F_rd_r

Plugging in the variables from this problem yields:

F_e x 14 ft. = 290 lbs. x 2 ft.
F_e = \( \frac{580 ft⋅lb}{14 ft.} \) = 41.4 lbs.

Mechanical Comprehension

A box is resting on a smooth floor. Static friction is present:

when an attempt is made to move the box

For any given surface, the coefficient of static friction is higher than the coefficient of kinetic friction. More force is required to initally get an object moving than is required to keep it moving. Additionally, static friction only arises in response to an attempt to move an object (overcome the normal force between it and the surface).

Math Knowledge

Simplify (5a)(2ab) - (9a²)(3b).

-17a²b

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(2ab) - (9a²)(3b)
(5 x 2)(a x a x b) - (9 x 3)(a² x b)
(10)(a¹⁺¹ x b) - (27)(a²b)
10a²b - 27a²b
-17a²b

Automotive Information

The firing order of the cylinders in an engine can be found by:

observing the order in which the intake valves open

The firing order of the cylinders in an engine is different than the cynlinder numbers and can be found by observing the order in which the intake valves open.

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:
\( W = 1 hp \times 550 \frac{ft⋅lb}{s} \times 3s = 1650 ft⋅lb \)

Mechanical Comprehension

Which of the following is not a type of bridge?

block

The six basic bridge forms are beam, truss, arch, cantilever, cable, and suspension.

General Science

In the water cycle, infiltration is most closely related to:

water table

The water then accumulates as runoff and eventually returns to bodies of water or is absorbed into the Earth (infiltration) and becomes part of the water table, an underground resevoir of fresh water.