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Mechanical Comprehension

If the green box weighs 30 lbs. and is 8 ft. from the fulcrum, how much force would need to be applied at the blue arrow to balance the lever if the arrow's distance from the fulcrum is 9 ft.?

26.67 lbs.

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 R_b, our missing value, and plugging in our variables yields:

R_b = \( \frac{R_ad_a}{d_b} \) = \( \frac{30 lbs. \times 8 ft.}{9 ft.} \) = \( \frac{240 ft⋅lb}{9 ft.} \) = 26.67 lbs.

Mechanical Comprehension

Friction between two or more solid objects that are not moving relative to each other is called:

static friction

Static friction is friction between two or more solid objects that are not moving relative to each other. An example is the friction that prevents a box on a sloped surface from sliding farther down the surface.

General Science

Which of the following represents the largest value?

1 ML

Mega (M) is 10⁶, kilo (k) is 10³, centi (c) is 10^-2, milli (m) is 10^-3 so 1 ML represents the largest value.

Mechanical Comprehension

The mass of an object correlates to the size of the object but ultimately depends on:

the object's density

Mass is a measure of the amount of matter in an object. In general, larger objects have larger mass than smaller objects but mass ultimately depends on how compact (dense) a substance is.

Word Knowledge

Appalling most nearly means:

dreadful

Inspiring dismay or disgust.

Electronics Information

The hertz is a unit of measurement for:

frequency

The hertz is a unit of measurement for frequency.

Math Knowledge

A(n) __________ is to a parallelogram as a square is to a rectangle.

rhombus

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

Electronics Information

Capacitors connected in series produce __________ capacitance compared to capacitors connected in parallel.

less

Capacitors store electricity and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors connected in series produce less capacitance than capacitors connected in parallel.

General Science

Which of the following is not true about mass and weight?

mass depends on the location where it is measured

Mass is the amount of matter something has while weight is the force exerted on an object's mass by gravity. So, although a person's mass doesn't change when going from the Earth to the Moon, their weight will decrease because the force of the Moon's gravity is much less than that of Earth.

Mechanical Comprehension

The mechanical advantage of a third class lever is always:

less than one

A third class lever is designed to multiply distance and speed at the expense of effort force. Because the effort force is greater than the resistance, the mechanical advantage of a third class lever is always less than one.

An example of a third class lever is a broom. The fulcrum is at your hand on the end of the broom, the effort force is your other hand in the middle, and the resistance is at the bottom bristles. The effort force of your hand in the middle multiplies the distance and speed of the bristles at the bottom but at the expense of producing a brushing force that's less than the force you're applying with your hand.