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Mechanical Comprehension

Two gears are connected and the larger gear drives the smaller gear. The speed of rotation will __________ and the torque will __________.

increase, decrease

Connected gears of different numbers of teeth are used together to change the rotational speed and torque of the input force. If the smaller gear drives the larger gear, the speed of rotation will be reduced and the torque will increase. If the larger gear drives the smaller gear, the speed of rotation will increase and the torque will be reduced.

Mechanical Comprehension

If the handles of a wheelbarrow are 2.5 ft. from the wheel axle and the load is concentrated at a point 1.0 ft. from the axle, how many pounds of load will a 130 lbs. force lift?

325

This problem describes a second-class lever and, for a second class lever, the effort force multiplied by the effort distance equals the resistance force multipied by the resistance distance: F_ed_e = F_rd_r. In this problem we're looking for resistance force:
\( F_r = \frac{F_e d_e}{d_r} \)
\( F_r = \frac{130 \times 2.5}{1.0} \)
\( F_r = \frac{325.0}{1.0} \)
\( F_r = 325 \)

Word Knowledge

Iridescent most nearly means:

shimmering

Having a lustrous or attractivve quality.

Mechanical Comprehension

If the green arrow in this diagram represents 420 ft⋅lb of work, how far will the box move if it weighs 140 pounds?

3 ft.

The Law of Work states that the work put into a machine is equal to the work received from the machine under ideal conditions. In equation form, that's:

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 420 ft⋅lb and the resistance force is 140 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
420 ft⋅lb = 140 lbs. x d_resistance
d_resistance = \( \frac{420ft⋅lb}{140 lbs.} \) = 3 ft.

General Science

Small rocks shed by asteroids and comets that reach the earth are called:

meteorites

Smaller rocks shed by asteroids and comets are called meteoroids. When these rocks reach Earth's atmosphere, they burn up in the mesosphere and become meteors. If a meteor manages to reach the Earth, it is called a meteorite.

General Science

Scalar quantities are fully described by which of the following?

a magnitude only

Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction. In contrast, scalar quantities are quantities that are fully described by a magnitude only. A variable indicating a vector quantity will often be shown with an arrow symbol: \(\vec{v}\)

Arithmetic Reasoning

If a car travels 45 miles in 3 hours, what is the average speed?

15 mph

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)
speed = \( \frac{45mi}{3h} \)
15 mph

General Science

As part of digestion, the liver produces bile which breaks down:

fat

The liver produces bile which emulsifies (separates) fat.

Word Knowledge

"heed my advice," the fortuneteller warned Sebastian when he tried to ignore her prophecy.

mind

To pay attention to.

Mechanical Comprehension

If the green box weighs 20 lbs. and is 1 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. force need to be applied to balance the lever?

0.29 ft.

To balance this lever the torques at the green box and the blue arrow 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 green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

Solving for d_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{20 lbs. \times 1 ft.}{70 lbs.} \) = \( \frac{20 ft⋅lb}{70 lbs.} \) = 0.29 ft.