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Question 161Question →

A construction crew is moving several identical uniform steel I-beams. Each beam is $12$ feet long and weighs $600$ pounds. Two workers will carry each beam by supporting it from beneath at different points along its length.

Rank the following carrying configurations based on the amount of weight supported by the worker positioned on the LEFT side, from the GREATEST load to the LEAST load.

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Answer

The configuration with the greatest load on the left worker is when the left worker is 3 feet inward (400 lbs), followed by 2 feet inward (360 lbs), then both workers at extreme ends (300 lbs), and finally the least load occurs when the right worker is moved inward (200 lbs).

As a support point moves closer to a uniform object's center of gravity, it takes on a proportionally larger share of the total weight. Moving the opposite support closer to the center transfers weight away from the first support.

Step-by-Step Solution

Determine the location of the center of gravity (CG).

For a uniform

12

-foot beam, the CG is exactly in the middle at the

6

-foot mark.

The weight of a uniform object can be treated as a single downward point force acting at its center.

Establish the formula for calculating load distribution.

Load on Left Worker = Total Weight

\times

(Distance from Right Worker to CG) / (Total Distance Between Workers)

This formula balances the torques around the right worker, which acts as a fulcrum when determining the left worker's lifting force.

Calculate the left worker's load for each configuration.

Item 1:

600 \times (6 / 12) = 300

lbs.
Item 2:

600 \times (3 / 9) = 200

lbs.
Item 3:

600 \times (6 / 10) = 360

lbs.
Item 4:

600 \times (6 / 9) = 400

lbs.

Applying the formula from step 2 translates the distances into exact pounds supported.

Order the results from greatest to least.

400

lbs (Item 4),

360

lbs (Item 3),

300

lbs (Item 1),

200

lbs (Item 2).

The question requests ranking from greatest load supported by the left worker to the least.

Key Concept

Load Distribution and Balancing

Estimated Time:2m 0s

Question 162Question →

Three identical $10$ -foot planks are each placed across two sawhorses, one sawhorse at the left end (Support X) and one at the right end (Support Y). A single $60$ -pound bag of cement is placed on each plank at a different location. Rank the scenarios below based on the amount of downward force carried by Support X, from greatest to least.

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Answer

The bag closest to Support X places the greatest load on it, followed by the centered bag, while the bag closest to Support Y places the least load on Support X.

Support X must carry the largest portion of the load when the weight is closest to it. As the weight moves further away across the plank, the amount of force supported by X decreases.

Step-by-Step Solution

Understand the principle of load distribution.

The closer a weight is to a given support, the more of that weight the support must carry.

This is a basic rule of mechanical balance and levers.

Evaluate the load on Support X for the bag placed

3

feet from it.

This bag is very close to Support X, so Support X carries more than half the weight.

The distance to X is smaller than the distance to Y.

Evaluate the load on Support X for the centered bag.

This bag is exactly

5

feet from both supports, so Support X carries exactly half the weight.

A centered load is shared evenly.

Evaluate the load on Support X for the bag placed

2

feet from Support Y.

This bag is

8

feet away from Support X, so Support Y carries almost all the weight, leaving very little for Support X.

The distance to X is much larger than the distance to Y.

Key Concept

The proportion of a load carried by a support increases as the center of gravity moves closer to that support.

Question 163Question →

Water flows at a steady rate through a horizontal pipe that consists of four distinct sections with different diameters. According to Bernoulli's principle and the continuity equation, arrange the pipe sections in order of their static pressure, from the lowest static pressure to the highest static pressure.

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Answer

The correct sequence from lowest to highest static pressure is: Section W (1-inch), Section X (2-inch), Section Y (3-inch), Section Z (4-inch).

According to the continuity equation, a fluid travels faster through a narrower section of pipe. According to Bernoulli's principle, an increase in fluid velocity results in a decrease in static pressure. Therefore, the pipe sections with the smallest diameters will have the highest velocities and the lowest static pressures, while the sections with the largest diameters will have the lowest velocities and the highest static pressures.

Step-by-Step Solution

Determine the relationship between the pipe's diameter and the fluid's velocity.

The continuity equation indicates that fluid must travel faster through narrower sections to maintain a steady flow rate. Therefore, the smallest diameter has the highest velocity, and the largest diameter has the lowest velocity.

Because the volume of fluid passing through any section per second must remain constant.

Determine the relationship between fluid velocity and static pressure.

Bernoulli's principle states that an increase in fluid velocity occurs simultaneously with a decrease in static pressure.

The total energy in a steady, horizontal fluid flow is constant; as kinetic energy (speed) increases, pressure potential energy must decrease.

Rank the sections based on these relationships.

Since smallest diameter = highest velocity = lowest pressure, the order from lowest to highest pressure corresponds exactly to the order from smallest to largest diameter.

This allows us to arrange the sections directly by their diameter sizes: 1-inch, 2-inch, 3-inch, and 4-inch.

Key Concept

Fluid Dynamics and Bernoulli's Principle

Question 164Question →

A carpenter is sorting four wooden planks based on their lengths to construct a custom frame. The lengths of the planks, in feet, are listed below. Sequence the plank lengths from shortest to longest.

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Answer

The correct ascending sequence is

1\frac{1}{3}

feet,

1\frac{3}{8}

feet,

\frac{7}{5}

feet, and

\frac{17}{12}

feet.

To compare fractions with different denominators, they must be converted to a common denominator. The least common multiple of

3

8

5

, and

12

120

. Converting all values yields

\frac{160}{120}

\frac{165}{120}

\frac{168}{120}

, and

\frac{170}{120}

. Arranging these from smallest to largest gives the proper sequence of

1\frac{1}{3}

feet,

1\frac{3}{8}

feet,

\frac{7}{5}

feet, and

\frac{17}{12}

feet.

Step-by-Step Solution

Convert all mixed numbers to improper fractions.

1\frac{3}{8} = \frac{11}{8}

and

1\frac{1}{3} = \frac{4}{3}

Fractions must be in a consistent improper format to find a common denominator efficiently.

Find the least common multiple (LCM) for the denominators

8

12

3

, and

5

The LCM of

8

12

3

, and

5

120

A common denominator is required to directly compare the relative sizes of the fractions.

Convert each fraction to an equivalent fraction with a denominator of

120

\frac{4}{3} = \frac{160}{120}

\frac{11}{8} = \frac{165}{120}

\frac{7}{5} = \frac{168}{120}

, and

\frac{17}{12} = \frac{170}{120}

Normalizing the denominators isolates the variation to the numerators, making comparison straightforward.

Arrange the fractions by comparing their normalized numerators from smallest to largest.

160 < 165 < 168 < 170

, which corresponds to the original values

1\frac{1}{3} < 1\frac{3}{8} < \frac{7}{5} < \frac{17}{12}

The problem specifies sequencing the plank lengths from shortest to longest.

Key Concept

Ordering and Comparing Fractions

Alternative Method

Convert each fraction to its decimal equivalent:

1\frac{1}{3} \approx 1.333

1\frac{3}{8} = 1.375

\frac{7}{5} = 1.400

, and

\frac{17}{12} \approx 1.417

. The decimals can then be easily ordered from least to greatest.

Estimated Time:1m 0s

Question 165Question →

A quality control inspector is verifying the thickness of four different steel plates. Arrange the following plate thicknesses in order from thinnest to thickest.

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Answer

The correct order from thinnest to thickest is

1\frac{5}{16}

inches,

1\frac{11}{32}

inches,

1\frac{3}{8}

inches, and

\frac{23}{16}

inches.

To accurately compare these lengths, they must all be expressed with a common denominator. The lowest common denominator for 8, 16, and 32 is 32. Converting the values yields

1\frac{5}{16} = \frac{42}{32}

1\frac{11}{32} = \frac{43}{32}

1\frac{3}{8} = \frac{44}{32}

, and

\frac{23}{16} = \frac{46}{32}

. Ordering by the numerators from lowest to highest gives the sequence

1\frac{5}{16}

1\frac{11}{32}

1\frac{3}{8}

, and

\frac{23}{16}

Step-by-Step Solution

Convert all mixed numbers to improper fractions.

1\frac{3}{8} = \frac{11}{8}

;

1\frac{5}{16} = \frac{21}{16}

;

1\frac{11}{32} = \frac{43}{32}

. The fraction

\frac{23}{16}

is already in improper form.

Working with improper fractions simplifies the process of finding a common denominator.

Determine the lowest common denominator (LCD) for the fractions

\frac{11}{8}

\frac{23}{16}

\frac{21}{16}

, and

\frac{43}{32}

The LCD for 8, 16, and 32 is 32.

A common denominator is required to accurately compare the absolute sizes of the fractions.

Convert each fraction into an equivalent fraction with a denominator of 32.

\frac{11}{8} = \frac{44}{32}

;

\frac{23}{16} = \frac{46}{32}

;

\frac{21}{16} = \frac{42}{32}

;

\frac{43}{32}

remains

\frac{43}{32}

This normalization allows for direct comparison of the numerators to determine size.

Order the numerators from smallest to largest and map them back to their original forms.

The numerators in order are

42 < 43 < 44 < 46

. This corresponds to

\frac{42}{32}

(

1\frac{5}{16}

\frac{43}{32}

(

1\frac{11}{32}

\frac{44}{32}

(

1\frac{3}{8}

), and

\frac{46}{32}

(

\frac{23}{16}

When the denominators are identical, the magnitude of the fraction is directly proportional to its numerator.

Key Concept

Comparing and Ordering Fractions

Question 166Question →

A logistics specialist is organizing four replacement fuel hoses by length. The lengths are $\frac{17}{4}$ meters, $4 \frac{3}{8}$ meters, $\frac{14}{3}$ meters, and $4 \frac{5}{12}$ meters. Arrange these hose lengths in ascending order from shortest to longest.

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Answer

The correct ascending order is

\frac{17}{4}

meters,

4 \frac{3}{8}

meters,

4 \frac{5}{12}

meters, and

\frac{14}{3}

meters.

By converting all values to mixed numbers with a common denominator of 24, the fractional parts become

\frac{6}{24}

\frac{9}{24}

\frac{10}{24}

, and

\frac{16}{24}

. Ordering these from smallest to largest provides the correct sequence.

Step-by-Step Solution

Convert the improper fractions to mixed numbers for easier comparison.

\frac{17}{4} = 4 \frac{1}{4}

and

\frac{14}{3} = 4 \frac{2}{3}

Comparing values is simpler when whole numbers and fractional parts are separated.

Identify the fractional parts to be compared.

Since all lengths share a whole number of 4, we only need to compare the fractions:

\frac{1}{4}

\frac{3}{8}

\frac{5}{12}

, and

\frac{2}{3}

The whole numbers are identical, so the overall size depends entirely on the fractional parts.

Find a common denominator for the fractions 4, 8, 12, and 3.

The least common multiple (LCM) of the denominators 4, 8, 12, and 3 is 24.

A common denominator is required to directly and accurately compare the sizes of the numerators.

Convert each fraction to an equivalent fraction with a denominator of 24.

\frac{1}{4} = \frac{6}{24}

;

\frac{3}{8} = \frac{9}{24}

;

\frac{5}{12} = \frac{10}{24}

;

\frac{2}{3} = \frac{16}{24}

This standardizes the fractions so their relative sizes are visually clear.

Order the fractions from smallest to largest based on their numerators.

\frac{6}{24} < \frac{9}{24} < \frac{10}{24} < \frac{16}{24}

, which corresponds to

\frac{17}{4} < 4 \frac{3}{8} < 4 \frac{5}{12} < \frac{14}{3}

Ordering the standardized fractions reveals the correct ascending sequence for the original lengths.

Key Concept

Comparing and ordering mixed numbers and improper fractions by finding a common denominator.

Question 167Question →

Arrange the following mathematical expressions in ascending order, from the least value to the greatest value.

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Answer

The correct order from least to greatest is:

1.2 \times 0.6

, then

0.35 + 0.38

, then

4.2 - 3.45

, and finally

0.48 \div 0.6

Each arithmetic expression must be evaluated independently applying the correct decimal rules for that specific operation. The results are

0.72

0.73

0.75

, and

0.80

. Sorting these decimal values chronologically by magnitude yields the correct ascending sequence.

Step-by-Step Solution

Evaluate the multiplication expression:

1.2 \times 0.6

0.72

Multiply the whole numbers (

12 \times 6 = 72

) and count a total of two decimal places from the factors.

Evaluate the addition expression:

0.35 + 0.38

0.73

Align the decimal points vertically and add the hundredths, then the tenths.

Evaluate the subtraction expression:

4.2 - 3.45

0.75

Rewrite

4.2

4.20

to align the decimal points properly, then subtract.

Evaluate the division expression:

0.48 \div 0.6

0.80

Multiply both numbers by

10

to make the divisor a whole number (

4.8 \div 6

), then divide.

Order the evaluated results from least to greatest.

0.72 < 0.73 < 0.75 < 0.80

Comparing the values digit by digit from the tenths place to the hundredths place establishes the correct magnitude sequence.

Key Concept

Evaluating all four basic operations with decimals and comparing their relative magnitudes.

Question 168Question →

A heavy steel block must be moved along a level track. Rank the following methods or conditions based on the amount of frictional resistance they generate, from LEAST resistance to GREATEST resistance.

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Answer

The correct order from least to greatest resistance is: floating on oil (fluid friction), moving on rollers (rolling friction), sliding continuously (kinetic friction), and overcoming the initial standstill (static friction).

Fluid friction separates the surfaces entirely, offering the least resistance. Rolling friction prevents surfaces from dragging, making it the second lowest. For the dry track, sliding (kinetic) friction is less than the static friction required to break the object's initial grip, making static friction the greatest resistance.

Step-by-Step Solution

Identify the primary type of friction acting in each scenario.

Oil film involves fluid friction; steel rollers involve rolling friction; continuous sliding involves kinetic friction; breaking free from a standstill involves static friction.

Categorizing the physical interaction is required to compare their relative magnitudes.

Determine the lowest sources of friction.

Fluid friction creates the least resistance, followed closely by rolling friction.

Fluids deform easily to allow movement and separate the surfaces entirely, while rollers prevent direct surface scraping.

Compare the resistance of a moving object versus a stationary object on the exact same dry surface.

Kinetic (sliding) friction is always less than the maximum static (standstill) friction.

Once the microscopic bonds between the resting surfaces are broken, it takes less force to keep the object moving than it did to start it.

Arrange the scenarios from least to greatest based on these physical principles.

The correct sequence is: Fluid, Rolling, Kinetic, Static.

This correctly orders the magnitudes of frictional resistance from lowest to highest.

Key Concept

Friction and Resistance

Question 169Question →

Arrange the following events in the correct chronological order for the extension stroke of a basic single-acting pneumatic cylinder:

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Answer

The correct sequence is: 1) The control valve is opened, 2) Air flows into the cylinder, 3) Pressure builds against the piston, 4) The piston rod extends.

The chronological sequence follows the fundamental transfer of energy in a pneumatic system. It begins with control (valve opening), followed by fluid transmission (air flowing into the cylinder), followed by energy accumulation (pressure building against the piston due to gas compressibility), and ends with mechanical work (piston extension).

Step-by-Step Solution

Identify the initiating control action

The control valve is opened.

A pneumatic system requires a signal or mechanical actuation to release energy from the compressor or tank.

Trace the path of the working fluid

Air enters the cylinder chamber.

Air moves from a region of higher pressure (supply) to lower pressure (cylinder) through the open valve.

Determine the physical effect inside the actuator

Pressure builds against the piston.

As air fills the confined space of the cylinder, it exerts uniform pressure on the piston face.

Identify the resulting mechanical output

The piston extends.

Once the force of the air pressure is greater than the opposing load and friction, the piston moves outward.

Key Concept

Pneumatic System Operation and Force Generation

Question 170Question →

Four solid machine parts are completely submerged in a deep vat of hydraulic fluid. Their respective masses and physical volumes are listed below. Arrange the machine parts in order from the LEAST buoyant force experienced to the GREATEST buoyant force experienced.

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Answer

The correct sequence from least to greatest buoyant force is based entirely on the objects' volumes: Machine Part 3, Machine Part 1, Machine Part 4, and Machine Part 2.

Archimedes' Principle states that the buoyant force on an object equals the weight of the fluid it displaces. Because all the machine parts are entirely submerged in the exact same hydraulic fluid, the buoyant force is determined exclusively by their physical volumes. Therefore, ordering them from least to greatest buoyant force simply requires ordering them from smallest to largest volume:

4 \text{ L}

6 \text{ L}

8 \text{ L}

, and

12 \text{ L}

Step-by-Step Solution

Identify the relevant variable for determining buoyant force on fully submerged objects.

Buoyant force depends solely on the volume of displaced fluid, not the mass of the object.

According to Archimedes' Principle, the buoyant force equals the weight of the displaced fluid. Since all parts are submerged in the same fluid, displaced volume is the only variable.

Compare the volumes of all four machine parts.

The volumes are: Part 3 (

4 \text{ L}

), Part 1 (

6 \text{ L}

), Part 4 (

8 \text{ L}

), and Part 2 (

12 \text{ L}

Extracting the volume metric from each item allows for direct comparison.

Arrange the parts in ascending order based on their volume.

The correct order is Part 3, Part 1, Part 4, Part 2.

A smaller physical volume displaces less fluid, resulting in a proportionally smaller upward buoyant force.

Key Concept

For fully submerged objects, the buoyant force is directly proportional to the object's volume (which dictates the volume of fluid displaced), completely independent of the object's mass.

Question 171Question →

A block of ice at -10°C is placed in a sealed container and heated continuously until it completely turns into steam. Arrange the following events in the chronological order in which they occur.

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Answer

First the solid ice warms, then it melts at a constant temperature, next the liquid water warms, and finally it vaporizes at a constant temperature.

When heat is continuously applied to a substance, it first raises the temperature of the solid to its melting point. During the melting phase change, the temperature remains constant because the energy (latent heat) is consumed to break intermolecular bonds. Once the substance is fully melted, the temperature of the liquid rises until it reaches the boiling point. During vaporization, the temperature again remains constant as the liquid converts into a gas.

Step-by-Step Solution

Identify the initial state and the effect of heating.

The solid ice at -10°C warms up to its melting point of 0°C.

Before a phase change can occur, the substance must reach its specific transition temperature.

Determine what happens when the melting point is reached.

The ice melts at a constant temperature of 0°C.

During a phase change, added thermal energy (latent heat) is used to overcome intermolecular forces rather than increase the temperature.

Identify the effect of continued heating after the solid has completely melted.

The liquid water warms up from 0°C to its boiling point of 100°C.

Once the phase change is complete, the added energy (sensible heat) increases the kinetic energy and temperature of the liquid.

Determine what happens when the boiling point is reached.

The liquid water boils and turns into steam at a constant temperature of 100°C.

During vaporization, the added heat is again used to break intermolecular forces, so the temperature plateaus.

Key Concept

Heating Curves and Latent Heat

Question 172Question →

A scuba diver records the surrounding water pressure at four different locations in a freshwater lake. Arrange these locations in order from the LOWEST hydrostatic pressure to the HIGHEST hydrostatic pressure experienced by the diver.

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Answer

The correct order from lowest to highest hydrostatic pressure is: Location W (1 meter), Location X (4 meters), Location Y (12 meters), and Location Z (18 meters).

Hydrostatic pressure is determined by the weight of the fluid directly above an object. In a single body of water like a lake, the density of the water is constant. Therefore, the hydrostatic pressure depends entirely on the depth (

h

). Since the question asks for the order from lowest to highest pressure, the locations must be ordered from the shallowest depth to the deepest depth: 1 meter, 4 meters, 12 meters, and finally 18 meters.

Step-by-Step Solution

Recall the relationship between hydrostatic pressure and depth.

Hydrostatic pressure is calculated using the formula P = ρgh (where ρ is fluid density, g is gravity, and h is depth). Therefore, pressure increases as depth increases.

Understanding this direct relationship is required to rank the locations.

Identify the depth of each location provided in the scenario.

Location W is 1m, Location X is 4m, Location Y is 12m, and Location Z is 18m.

The depth is the only variable changing between the different locations.

Order the locations from the smallest depth to the greatest depth.

Smallest depth (1m) is Location W, followed by 4m (Location X), 12m (Location Y), and the greatest depth is 18m (Location Z).

Since pressure increases with depth, ordering from smallest to greatest depth directly corresponds to lowest to highest pressure.

Key Concept

In a fluid of uniform density, hydrostatic pressure increases proportionally with the depth of the fluid.

Question 173Question →

A large dam holds back a deep reservoir of fresh water. Three pressure sensors are installed on the submerged face of the dam at different depths: Sensor X is 10 meters below the water surface, Sensor Y is 2 meters below the water surface, and Sensor Z is 25 meters below the water surface. Arrange the sensors in order from the LOWEST hydrostatic pressure to the HIGHEST hydrostatic pressure.

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Answer

The correct order from lowest to highest hydrostatic pressure is: Sensor Y, Sensor X, and Sensor Z.

Hydrostatic pressure is determined by the density of the fluid, gravity, and the depth of the fluid. Because the fluid (fresh water) is consistent across all sensors, the pressure depends entirely on the depth. The sensor closest to the water's surface (Sensor Y at 2 meters) experiences the least amount of downward force from the water column above it, giving it the lowest pressure. The sensor furthest down (Sensor Z at 25 meters) experiences the most force, resulting in the highest pressure.

Step-by-Step Solution

Identify the relationship between depth and hydrostatic pressure.

Hydrostatic pressure increases as the depth of the fluid increases.

The formula for hydrostatic pressure,

P = \rho g h

, demonstrates that pressure (

P

) is directly proportional to depth (

h

Compare the vertical depths of the three sensors.

Sensor Y is at 2 meters, Sensor X is at 10 meters, and Sensor Z is at 25 meters.

Determining the relative depths is required to compare the relative pressures.

Order the sensors based on depth to find the sequence from lowest to highest pressure.

Lowest pressure is at Sensor Y, followed by Sensor X, and the highest is at Sensor Z.

Because the question asks for the order from lowest to highest pressure, the items must be arranged from the shallowest depth to the deepest depth.

Key Concept

Hydrostatic pressure in a fluid increases proportionally with depth.

Question 174Question →

A heavy steel crate must be moved across a horizontal concrete floor. Rank the following conditions based on the magnitude of frictional resistance opposing the applied force, from LEAST resistance to GREATEST resistance.

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Answer

The correct sequence from least to greatest frictional resistance is: using wheels (rolling friction), sliding on oil (fluid friction), sliding at a constant speed (kinetic friction), and pushing just prior to movement (static friction).

Frictional resistance follows a predictable hierarchy based on how surfaces interact. Rolling friction is the lowest because there is no sliding action. Fluid friction is next, as the fluid layer prevents solid-to-solid contact. Dry kinetic (sliding) friction is higher because the solids scrape directly against each other. Finally, static friction is the highest because the microscopic peaks and valleys of the stationary surfaces have settled deeply into one another.

Step-by-Step Solution

Identify the type of friction present in each condition.

Wheels = rolling friction; Oil = fluid friction; Sliding = kinetic friction; Stationary just before moving = static (breakaway) friction.

Different physical mechanisms govern resistance in each scenario.

Compare rolling friction to all forms of sliding friction.

Rolling friction is ranked lowest (least resistance).

Rolling mechanisms are specifically designed to eliminate the dragging forces characteristic of sliding.

Evaluate the lubricated surface against the dry surfaces.

Fluid friction is ranked second lowest.

Lubricants separate the solid surfaces, drastically reducing resistance compared to dry contact, but generally offer more resistance than precision wheel bearings.

Compare the two dry conditions: moving at constant speed vs. about to move.

Kinetic friction is ranked third, and static friction is ranked highest.

The coefficient of static friction is typically greater than the coefficient of kinetic friction for the same materials; it takes more force to start an object moving than to keep it moving.

Key Concept

Types of Friction (Static, Kinetic, Rolling, Fluid)

Question 175Question →

In a controlled thermodynamic test, a pure substance in a solid state is placed in a sealed piston-cylinder device and subjected to a steady, constant input of thermal energy until it becomes a superheated gas. Arrange the following molecular behaviors and thermal observations in the correct chronological order as the total enthalpy of the system increases.

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Answer

The correct chronological sequence corresponds to the standard heating curve: sensible heating of the solid, latent heat of fusion (melting), sensible heating of the liquid, latent heat of vaporization (boiling), and sensible heating of the gas.

The correct sequence maps perfectly to the five distinct segments of a standard thermodynamic heating curve. Initially, the solid undergoes sensible heating (kinetic energy increases). Upon reaching the melting point, the temperature plateaus as latent heat of fusion breaks the lattice. Next, the resulting liquid undergoes sensible heating until it reaches its boiling point. A second plateau occurs as latent heat of vaporization separates the molecules entirely. Finally, the completely gaseous substance undergoes sensible heating, increasing its temperature further.

Step-by-Step Solution

Identify the initial physical state and the ultimate final state of the substance.

The substance begins as a solid and ends as a superheated gas.

The stem specifies starting with a solid state and heating it continuously into a superheated gas state.

Determine the sequence of phase changes occurring as constant thermal energy is added.

The sequence must be: Solid heating -> Melting into liquid -> Liquid heating -> Boiling into gas -> Gas heating.

According to the principles of thermodynamics, a substance alternates between raising its temperature (sensible heat) and changing its phase at a constant temperature (latent heat).

Map the provided molecular descriptions to each stage of the heating curve.

Lattice vibration (solid heating) -> Fusion plateau (melting) -> Free-flowing fluid heating (liquid heating) -> Vaporization plateau (boiling) -> Expanding gas (gas heating).

Molecular kinetic energy (temperature) increases during sensible heating, whereas potential energy (breaking bonds) increases during phase change plateaus.

Key Concept

During continuous heating, a substance alternates between sensible heating (where kinetic energy and temperature increase) and latent heating (where temperature plateaus because thermal energy is used to break intermolecular bonds during phase changes).

Question 176Question →

A logistics technician is tasked with repositioning a large, heavy equipment pod across a flat warehouse floor. Rank the following movement scenarios in order from the greatest magnitude of frictional resistance to the least magnitude of frictional resistance.

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Answer

The correct sequence from greatest to least resistance is: breaking the pod loose from a standstill (static friction), sliding continuously on a dry floor (kinetic friction), sliding continuously on a greased floor (lubricated friction), and moving the pod on wheeled dollies (rolling friction).

In mechanical systems, friction types follow a general hierarchy of resistance. Static friction (starting motion) is the highest because surfaces settle and interlock. Kinetic friction (dry sliding) is lower than static but still high due to direct surface scraping. Introducing a lubricant reduces this direct contact, lowering resistance further. Finally, replacing sliding motion with rolling motion (using wheels) typically offers the lowest resistance because the contact point rolls over the surface rather than dragging across it.

Step-by-Step Solution

Evaluate the resistance when starting motion from a dead stop.

Identified as static friction.

Static friction must be overcome to initiate movement and is typically the strongest resistive force between two unlubricated solid surfaces.

Evaluate the resistance when sliding continuously on a dry surface.

Identified as dry kinetic (sliding) friction.

Kinetic friction opposes ongoing motion and is generally weaker than static friction for the same surfaces.

Evaluate the effect of adding grease to the sliding surfaces.

Identified as lubricated boundary or fluid friction.

Lubricants physically separate the solid surfaces, reducing direct contact and thus lowering the resistance compared to dry sliding.

Evaluate the resistance when wheels are introduced.

Identified as rolling friction.

Rolling friction involves rolling rather than dragging, which requires significantly less force to maintain motion than sliding.

Order the scenarios by the magnitude of frictional force from highest to lowest.

Static friction > Dry kinetic friction > Lubricated sliding friction > Rolling friction.

This sequence follows fundamental mechanical principles regarding types of resistance.

Key Concept

Types and Magnitudes of Mechanical Friction

Estimated Time:45s

Question 177Question →

A mechanic is securing a critical structural joint using a drilled bolt, a castellated nut, and a cotter pin. Arrange the following steps in the correct chronological order to properly install and lock this fastener assembly according to standard mechanical practices.

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Answer

The correct sequence is to first clean and inspect the components, apply the initial baseline torque, check the hole alignment, tighten the nut further if necessary to align the slots, and finally install and secure the cotter pin.

Proper installation of a castellated nut and cotter pin requires a strict sequence. First, components must be cleaned for accurate torque application. Second, the nut is tightened to the specified baseline torque to achieve the necessary joint tension. Third, alignment is checked. Fourth, because the nut's slots and the bolt's drilled hole rarely align perfectly at the exact baseline torque, standard mechanical practice dictates tightening the nut slightly further until alignment is achieved; backing off the nut is strictly prohibited as it would compromise the minimum required clamping force. Finally, the cotter pin is inserted and its prongs are bent to provide a positive mechanical lock against vibration.

Step-by-Step Solution

Identify the prerequisite step before any fastener assembly.

Cleaning and inspecting the threads is placed first.

Damaged or dirty threads can lead to false torque readings and subsequent joint failure.

Determine the action that provides the primary clamping force.

Threading the nut and applying the initial specified torque is placed second.

The joint must be secured to its baseline tension before any locking mechanism is engaged.

Evaluate what must be checked before installing the positive locking mechanism.

Checking the alignment of the nut's slots and the bolt's hole is placed third.

The cotter pin requires a clear, unobstructed path through both components.

Determine the correct procedure if the locking holes are not perfectly aligned.

Tightening the nut further until the next slot aligns is placed fourth.

Loosening the nut would compromise the minimum required clamping force (tension) on the joint, so it must only be tightened.

Identify the final locking step.

Inserting and bending the cotter pin is placed fifth.

This provides a positive mechanical lock, completing the assembly process.

Key Concept

Proper installation sequence and torque application for positive-locking fasteners (castellated nuts and cotter pins).

Question 178Question →

Place the following operational stages of a basic reciprocating air compressor in their proper sequential order, starting with the introduction of fresh air into the system.

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Answer

The correct operational sequence begins with the intake of ambient air, followed by the sealing of the inlet valve, then the compression of the trapped air, and finally the discharge of the pressurized air into the tank.

A basic reciprocating compressor operates in a continuous four-stage loop: it draws air in (intake), seals the chamber, squeezes the air into a smaller volume to build pressure (compression), and then pushes that pressurized air out to a tank (discharge).

Step-by-Step Solution

Identify the starting point of the pneumatic cycle.

The cycle must begin by drawing ambient air into the empty cylinder.

An air compressor needs a fresh supply of air to perform any mechanical work.

Determine the necessary condition for compression.

The inlet valve must close to seal the chamber.

If the chamber is not sealed, upward movement of the piston would simply push the air back out instead of compressing it.

Identify the actual compression action.

The piston moves up to decrease the internal volume.

Decreasing the volume of the sealed gas increases its pressure.

Identify the final stage of the cycle.

The outlet valve opens to release the compressed air.

The system must transfer the high-pressure air into the storage tank for future use.

Key Concept

Reciprocating compressor cycle and basic application of Boyle's Law

Question 179Question →

Momentum is defined as the product of an object's mass and its velocity ( $p = mv$ ). Arrange the following vehicles in order of their total momentum, from the lowest to the highest.

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Answer

The correct sequence from lowest to highest momentum is: motorcycle, bus, car, and finally the truck.

The correct sequence is found by multiplying each vehicle's mass by its velocity and then ordering the products from smallest to largest: motorcycle (

10,000

), bus (

25,000

), car (

30,000

), and truck (

36,000

Step-by-Step Solution

Recall the formula for calculating momentum.

p = m \times v

Momentum requires multiplying the mass of the object by its velocity.

Calculate the momentum for the motorcycle.

400 \text{ kg} \times 25 \text{ m/s} = 10,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the first vehicle.

Calculate the momentum for the bus.

5,000 \text{ kg} \times 5 \text{ m/s} = 25,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the second vehicle.

Calculate the momentum for the car.

1,500 \text{ kg} \times 20 \text{ m/s} = 30,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the third vehicle.

Calculate the momentum for the truck.

3,000 \text{ kg} \times 12 \text{ m/s} = 36,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the fourth vehicle.

Order the resulting values from lowest to highest.

10,000 < 25,000 < 30,000 < 36,000

The question requires arranging the vehicles in ascending order based on their momentum.

Key Concept

The total momentum of a moving object is directly proportional to both its mass and its velocity.

Estimated Time:1m 0s

Question 180Question →

A mechanic needs to loosen a severely rusted, seized steel nut from a steel bolt using an oxyacetylene torch. To successfully utilize the principles of thermal expansion to remove the fastener, arrange the following procedural steps and physical responses in their correct chronological sequence.

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Answer

The correct sequence is to first apply concentrated heat to the nut, which causes the nut to expand. Then, you must apply the wrench before the heat transfers to the bolt, allowing the nut to break free due to the temporary clearance.

For thermal expansion to loosen a seized assembly, the outer component (the nut) must be heated rapidly so it expands before the inner component (the bolt) has time to absorb the heat and expand as well. This creates a temporary difference in size that breaks the mechanical bind.

Step-by-Step Solution

Identify the component that needs to expand.

The outer component (the nut) must be heated.

Heating the outer ring increases its inner diameter, while heating the inner pin (bolt) would make it tighter.

Consider the rate of heat transfer.

Heat must be applied rapidly and the nut turned quickly.

If heat conducts into the bolt, the bolt will also expand, eliminating the beneficial clearance created by heating the nut.

Key Concept

Thermal Expansion in Mechanical Assemblies

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