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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.

Shop Information

This tool is a(n) __________.

inside caliper

Calipers are similar to micrometers in shape but instead of measuring distances, calipers are used to transfer distances between objects. An outside caliper is used to transfer outside dimensions while an inside caliper is used to transfer inside distances. A vernier caliper is an extremely precise caliper (down to \({1 \over 1000}\) inch) that allows measuring / transferring either inside or outside dimensions.

Word Knowledge

The sociable Glenda was delighted to receive the party invitation.

genial

Inclined to seek companionship.

Math Knowledge

A cylinder with a radius (r) and a height (h) has a surface area of:

2(π r²) + 2π rh

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.

General Science

The biosphere consists of which of the following?

all of these

The biosphere is the global ecological system integrating all living beings and their relationships. This includes their interactions with the lithosphere (the rigid outer part of the earth, consisting of the crust and upper mantle), hydrosphere (all surface water), and atmosphere (the envelope of gases surrounding the planet).

General Science

A compound is a substance containing two or more different chemical elements bound together by what kind of bond?

chemical

A compound is a substance containing two or more different chemical elements bound together by a chemical bond. In covalent compounds, electrons are shared between atoms. In ionic compounds, one atom borrows an electron from another atom resulting in two ions (electrically charged atoms) of opposite polarities that then become bonded electrostatically.

Word Knowledge

Avian most nearly means:

bird–like

Relating to birds.

General Science

"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force." This describes which of Newton's laws of motion?

first

Also known as the law of inertia, Newton's first law of motion states that An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Electronics Information

Which of the following is not true about a line drop?

it is addressed by raising current and lowering voltage across the ransmission line

Electricity is delivered from power stations to customers as AC because it provides a more efficient way to transport electricity over long distances. A line drop is a decrease in voltage between two points on an electrical transmission line due to resistance in the line. A lower current and higher voltage across the line will help compensate for the line drop.

General Science

Poor balance could indicate an issue with which part of the nervous system?

cerebellum

The cerebellum is a large cluster of nerves at the base of the brain that's responsible for balance, movement, and muscle coordination.