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Mechanical Comprehension

What is the mechanical advantage of this inclined plane if the length of the ramp is 24 ft. and the height of the green box is 8 ft.?

The mechanical advantage (MA) of an inclined plane is the effort distance divided by the resistance distance. In this case, the effort distance is the length of the ramp and the resistance distance is the height of the green box:

MA = \( \frac{d_e}{d_r} \) = \( \frac{24 ft.}{8 ft.} \) = 3

Word Knowledge

Her excellent lecture illuminated the complicated subject of nuclear physics.

elucidate

To make clear.

Mechanical Comprehension

The green box weighs 10 lbs. and a 35 lbs. weight is placed 3 ft. from the fulcrum at the blue arrow. How far from the fulcrum would the green box need to be placed to balance the lever?

10.5 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_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{35 lbs. \times 3 ft.}{10 lbs.} \) = \( \frac{105 ft⋅lb}{10 lbs.} \) = 10.5 ft.

Shop Information

The primary difference between a claw and a ball-peen hammer is which of the following?

their non-striking end

The most common striking tool is the hammer and the most common variety of hammer is the claw hammer. The claw hammer has two ends, one to drive nails and one to remove nails. Ball-peen hammers replace the claw with a rounded end that's used to round off the edges of metal pins and make gaskets.

General Science

The transfer of heat by the circulation or movement of the heated parts of a liquid or gas is called:

convection

Convection is the transfer of heat by the circulation or movement of the heated parts of a liquid or gas. Examples of heat transfer by convection include water coming to a boil on a stove, ice melting, and steam from a cup of coffee.

General Science

The hottest of Earth's atmospheric layers is which of the following?

thermosphere

Temperatures again increase with altitude in the thermosphere which is the hottest (4,530 °F / 2,500 °C) atmospheric layer due to direct exposure to the Sun's radiation. However, the gas in this layer is highly diluted so even though the atoms of gas may be very high in temperature, there are too few of them to effectively transfer much heat.

General Science

Cirrus clouds are thin, wispy clouds composed of ice crystals. At what elevation to cirrus clouds form?

high-altitude

Cirrus clouds are thin, wispy high-altitude clouds composed of ice crystals that originate from the freezing of supercooled water droplets. Cirrus clouds generally occur in fair weather and point in the direction of air movement at their elevation.

Math Knowledge

Which types of triangles will always have at least two sides of equal length?

equilateral and isosceles

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

Electronics Information

Which of the following will increase the magnetic field produced by the electric current in a wire?

wind the wire into a coil

A moving electric current produces a magnetic field proportional to the amount of current flow. This magnetic field can be made stronger by winding the wire into a coil and further enhanced if done around an iron containing (ferrous) core.

General Science

DNA is encoded through a combination of which of the following?

nucleotides

Deoxyribonucleic acid (DNA) is the molecule that contains genetic information. DNA is encoded through a combination of nucleotides that bind together in a specific double helix pattern.