All practice questions

Question 1781Question →

An overflow container is filled to the brim with a specialized drilling mud that weighs $15 \text{ N}$ per liter. A solid geological core sample weighing $75 \text{ N}$ in the air is completely submerged in the mud, causing exactly $2$ liters of mud to spill into a measuring basin. Based on Archimedes' principle, what is the apparent weight of the core sample while it is fully suspended in the mud?

45 \text{ N}

30 \text{ N}

60 \text{ N}

105 \text{ N}

Show answer & explanation

Answer: $45 \text{ N}$

Answer

The apparent weight of the core sample is

45 \text{ N}

.

Archimedes' principle dictates that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. Because the core sample displaces

2

liters of mud (which weighs

15 \text{ N}

per liter), the upward buoyant force is

30 \text{ N}

. The apparent weight is the actual downward weight (

75 \text{ N}

) minus this upward buoyant force (

30 \text{ N}

), resulting in a net apparent weight of

45 \text{ N}

.

Step-by-Step Solution

1

Calculate the weight of the displaced drilling mud.

2 \text{ liters} \times 15 \text{ N/liter} = 30 \text{ N}

According to Archimedes' principle, the upward buoyant force acting on a submerged object is exactly equal to the weight of the fluid it displaces.

2

Calculate the apparent weight of the submerged core sample.

75 \text{ N} - 30 \text{ N} = 45 \text{ N}

The apparent weight is determined by subtracting the upward buoyant force from the actual downward weight of the object.

Key Concept

Apparent weight and Archimedes' principle

Question 1782Question →

A combat engineer squad needs to push a $60\text{ kg}$ supply crate up a smooth, frictionless ramp onto a platform. The platform is $2\text{ meters}$ above the ground, and the ramp is $6\text{ meters}$ long. Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , what is the ideal effort force required to push the crate up the ramp?

20\text{ N}

200\text{ N}

600\text{ N}

1200\text{ N}

Show answer & explanation

Answer: $200\text{ N}$

Answer

The required effort force is

200\text{ N}

.

The ideal mechanical advantage (IMA) of an inclined plane is calculated by dividing its length by its height (6 m / 2 m = 3). The crate's weight is its mass multiplied by gravity (60 kg × 10 m/s² = 600 N). The effort force required is the weight divided by the IMA (600 N / 3 = 200 N).

Step-by-Step Solution

1

Calculate the weight (gravitational force) of the crate.

Weight = 60\text{ kg} \times 10\text{ m/s}^2 = 600\text{ N}

Effort force must oppose the weight (force of gravity) pulling the object down, not just the mass.

2

Calculate the ideal mechanical advantage (IMA) of the ramp.

IMA = \frac{6\text{ m}}{2\text{ m}} = 3

IMA compares the length of the ramp (distance the effort is applied) to the vertical height the load is lifted.

3

Calculate the effort force.

Effort = \frac{600\text{ N}}{3} = 200\text{ N}

The inclined plane reduces the required force by a factor equal to its mechanical advantage.

Key Concept

Ideal Mechanical Advantage of Inclined Planes

Question 1783Question →

A technician replaces a standard soldering iron tip with a modified tip made of the exact same copper material. To reach into a tighter space, the new tip is designed to be twice as long and has half the cross-sectional area of the original tip. Assuming the temperature difference between the internal heating element and the wire joint remains constant, how will this modification affect the rate of conductive heat transfer to the joint?

The transfer rate will decrease to one-fourth of its original value.

The transfer rate will increase, as the longer surface promotes stronger convective heat flow to the joint.

The transfer rate will double, because the smaller tip has a lower heat capacity to overcome.

The transfer rate will increase to four times its original value, due to the inverse relationship between area and heat flow.

Show answer & explanation

Answer: The transfer rate will decrease to one-fourth of its original value.

Answer

The transfer rate will decrease to one-fourth of its original value.

The rate of conductive heat transfer through a solid object depends directly on its cross-sectional area and inversely on its length. Halving the area cuts the flow rate by a factor of

\frac{1}{2}

, and doubling the length cuts the rate by another factor of

\frac{1}{2}

. Combining these constraints yields an overall transfer rate that is

\frac{1}{4}

of the original.

Step-by-Step Solution

1

Identify the factors affecting the rate of conductive heat transfer.

The rate is directly proportional to the cross-sectional area (

A

) and inversely proportional to the length (

L

).

Fourier's law of heat conduction defines how the physical dimensions of an object affect the flow of thermal energy.

2

Analyze the effect of halving the cross-sectional area.

Reducing the area to

\frac{1}{2}A

reduces the heat transfer rate by a factor of

\frac{1}{2}

.

There is less physical material (fewer molecules in a given cross-section) available to pass the thermal energy forward.

3

Analyze the effect of doubling the length.

Increasing the length to

2L

further reduces the heat transfer rate by a factor of

\frac{1}{2}

.

The thermal energy must travel a longer distance, which decreases the temperature gradient (the temperature drop per unit of length).

4

Combine the effects of both geometric changes.

Multiplying the two effects (

\frac{1}{2} \times \frac{1}{2}

) results in a final heat transfer rate that is

\frac{1}{4}

of the original rate.

Both dimensional modifications act concurrently to restrict the flow of heat.

Key Concept

Geometric factors in thermal conduction

Question 1784Question →

An automotive technician needs to manage heat transfer in a custom engine build. Arrange the following components based on the thermal conductivity of their primary materials, from the best heat conductor (highest rate of conduction) to the best thermal insulator (lowest rate of conduction).

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from best conductor to best insulator is: pure copper heat sink core, aluminum radiator fin, cast iron engine block, and finally fiberglass exhaust wrap.

Thermal conductivity measures how easily heat energy transfers through a solid material via direct molecular contact. Copper is the most efficient conductor among these options. Aluminum is highly efficient but slightly less conductive than copper. Cast iron conducts heat but at a significantly lower rate than aluminum. Finally, fiberglass is an engineered composite that traps air to actively block heat transfer, making it the poorest conductor and the best insulator.

Step-by-Step Solution

1

Identify the extreme ends of the thermal spectrum among the given components.

Copper is widely known as an exceptional thermal conductor, while fiberglass is specifically utilized as a thermal barrier (insulator).

Establishing the highest and lowest conductivity values makes it easier to rank the intermediate metallic materials.

2

Compare the remaining metallic components (aluminum and cast iron).

Aluminum has a much higher thermal conductivity than cast iron.

This physical property is precisely why modern vehicle radiators and high-performance cylinder heads are cast from aluminum rather than heavier iron, ensuring faster heat dissipation.

Key Concept

Relative thermal conductivity of common mechanical materials

Question 1785Question →

A sheet metal fabricator uses a custom compound lever tool to punch holes in aluminum panels. The tool consists of two connected levers:

1. The Handle (Lever A): A second-class lever with its fulcrum at the very top. The handle is $25\text{ inches}$ long overall. A vertical connecting rod is attached to this handle $5\text{ inches}$ away from the fulcrum.
2. The Punch Arm (Lever B): A first-class lever positioned horizontally. The connecting rod pulls down on one end, which is $8\text{ inches}$ away from its fulcrum. The punching die is located on the opposite side of the fulcrum, $2\text{ inches}$ away.

If the fabricator applies a perpendicular force of $24\text{ lbs}$ to the extreme end of the handle, what is the total downward force, in pounds, exerted by the punch die onto the aluminum panel?

Show answer & explanation

Answer: 480

Answer

The correct answer is

480\text{ lbs}

.

In a compound lever system, the mechanical advantage of each lever multiplies sequentially to produce the final force. The handle (Lever A) provides a mechanical advantage of

25/5 = 5

. Therefore, the

24\text{ lbs}

input is multiplied by

5

, becoming

120\text{ lbs}

of force on the connecting rod. The punch arm (Lever B) provides a mechanical advantage of

8/2 = 4

. The

120\text{ lbs}

input to Lever B is then multiplied by

4

, resulting in a total output force of

480\text{ lbs}

at the punching die.

Step-by-Step Solution

1

Calculate the input torque generated by the fabricator on Lever A.

24\text{ lbs} \times 25\text{ inches} = 600\text{ in-lbs}

Torque is determined by multiplying the applied force by the perpendicular distance from the fulcrum.

2

Determine the force exerted on the connecting rod by Lever A.

600\text{ in-lbs} / 5\text{ inches} = 120\text{ lbs}

In equilibrium, the input torque equals the output torque. The rod is attached

5\text{ inches}

from the fulcrum.

3

Calculate the input torque on Lever B caused by the connecting rod.

120\text{ lbs} \times 8\text{ inches} = 960\text{ in-lbs}

The connecting rod applies

120\text{ lbs}

of force at a distance of

8\text{ inches}

from Lever B's fulcrum.

4

Calculate the final output force at the punching die.

960\text{ in-lbs} / 2\text{ inches} = 480\text{ lbs}

The punching die is

2\text{ inches}

from the fulcrum, balancing the

960\text{ in-lbs}

of torque on the opposite side.

Key Concept

Compound Lever Systems and Torque Balance

Estimated Time:1m 30s

Question 1786Question →

A technician is modifying a heavy steel sliding door that currently drags directly along a flat metal base. To significantly reduce the frictional resistance required to open and close the door, which of the following design changes would be the most effective?

Incorporating steel ball bearings or roller wheels between the door and the base.

Widening the base track so the door's weight is distributed over a larger surface area.

Increasing the total mass of the door so it carries more momentum once pushed.

Decreasing the pushing speed to minimize the reaction force from the track.

Show answer & explanation

Answer: Incorporating steel ball bearings or roller wheels between the door and the base.

Answer

Incorporating steel ball bearings or roller wheels between the door and the base.

The correct answer identifies that converting sliding friction into rolling friction (by using wheels or bearings) is one of the most effective mechanical methods to reduce resistance. Rolling friction is generally much weaker than sliding friction because the contact surfaces do not grind against each other as they move.

Step-by-Step Solution

1

Identify the type of friction currently acting on the door.

The door dragging flat against a metal track experiences kinetic (sliding) friction.

Understanding the current state helps identify how to improve the system.

2

Evaluate the options based on mechanical principles to find the best method for reducing resistance.

Adding wheels or ball bearings changes the interaction from sliding to rolling.

Rolling friction is significantly lower than sliding friction for hard materials like steel, making this the most effective mechanical improvement.

Key Concept

Rolling friction is substantially lower than sliding (kinetic) friction, which is why wheels and bearings are used in mechanical designs to reduce resistance.

Estimated Time:45s

Question 1787Question →

A small water pump uses a direct gear drive system. The driving gear, attached to an electric motor, has $20$ teeth and spins at $300\text{ rpm}$ . It meshes directly with a driven gear on the pump shaft that has $60$ teeth. What is the rotational speed of the driven gear in rpm?

Show answer & explanation

Answer: 100

Answer

100 rpm

Because the driven gear has three times as many teeth as the driving gear (

60

compared to

20

), it requires three times the effort to turn. Therefore, it will rotate at exactly one-third the speed of the driving gear. Dividing the driving speed of

300\text{ rpm}

by

3

yields

100\text{ rpm}

.

Step-by-Step Solution

1

Recall the fundamental gear relationship formula.

S_1 \times T_1 = S_2 \times T_2

The product of the speed and number of teeth of the driving gear equals the product of the speed and number of teeth of the driven gear.

2

Substitute the given values into the formula.

300 \times 20 = S_2 \times 60

We are given the driving gear speed (

300\text{ rpm}

) and teeth (

20

), along with the driven gear teeth (

60

).

3

Solve for the driven gear speed (

S_2

).

S_2 = \frac{6000}{60} = 100\text{ rpm}

Isolating

S_2

provides the final rotational speed of the driven gear.

Key Concept

The speed of a driven gear is inversely proportional to its number of teeth compared to the driving gear.

Question 1788Question →

Match each modification made to a standard closed hydraulic lift system with its resulting effect on the output piston. Assume the applied input force remains constant unless otherwise specified.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Modifications changing the area ratio affect force and distance inversely; proportional area modifications maintain the status quo; and input distance modifications only affect output distance.

Each correct match applies Pascal's Principle (

F_2 = F_1 \times \frac{A_2}{A_1}

) and the principle of work conservation (

F_1 \times d_1 = F_2 \times d_2

). Changing the area ratio inversely affects force and distance. Changing only input distance affects fluid volume displaced, altering output distance without changing force.

Step-by-Step Solution

1

Analyze modifications changing a single piston area.

Doubling output area doubles force but halves distance; doubling input area halves force but doubles distance.

Pascal's principle states

F_2 = F_1 \times \frac{A_2}{A_1}

, and conservation of work states

d_2 = d_1 \times \frac{A_1}{A_2}

.

2

Analyze modifications changing both piston areas.

Doubling both areas keeps the ratio

A_2/A_1

constant, resulting in no change to force or distance.

The mechanical advantage depends strictly on the ratio of the areas, not their absolute sizes.

3

Analyze modifications changing only input distance.

Doubling input distance doubles output distance without affecting force.

Volume displaced (

V = A_1 \times d_1

) doubles, so output distance doubles. Force depends only on the area ratio, which is unchanged.

Key Concept

Pascal's Principle and Conservation of Energy in Hydraulics

Question 1789Question →

If a hockey puck is sliding across a perfectly frictionless sheet of ice at a constant velocity, a continuous forward force must be applied to it to keep it moving at that velocity.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because it contradicts Newton's First Law of motion. The law dictates that a moving object naturally maintains its velocity unless an external force intervenes. Since the surface is frictionless and there is no resistance to overcome, no continuous pushing force is needed to sustain the puck's motion.

Step-by-Step Solution

1

Analyze the environmental conditions described in the scenario.

The scenario specifies a 'perfectly frictionless sheet of ice', meaning there is zero opposing force of friction acting on the sliding hockey puck.

Identifying all external forces (or the lack thereof) is necessary before applying the laws of motion.

2

Apply Newton's First Law of motion to the isolated puck.

Because there are no unbalanced external forces acting on the puck along the horizontal plane, its state of motion will not change.

Newton's First Law states that an object in motion stays in motion with the same speed and in the same direction unless acted upon by a net external force.

3

Determine if a forward force is required based on the law.

A forward force would cause the puck to accelerate. Since it is moving at a 'constant velocity', no such forward force is needed.

Force is required to change velocity (accelerate or decelerate), not to maintain it in a frictionless environment.

Key Concept

In the absence of opposing forces like friction, an object moving at a constant velocity requires absolutely no applied force to maintain its state of motion.

Question 1790Question →

When a steady flow of fluid passes through a horizontal pipe that suddenly narrows in diameter, the fluid's velocity increases in the constricted section, resulting in a higher static pressure against the pipe walls.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because Bernoulli's principle dictates that as a fluid's velocity increases in a constricted horizontal pipe, its static pressure decreases, creating a low-pressure zone rather than a high-pressure one.

Step-by-Step Solution

1

Analyze the change in fluid velocity through the constriction.

Based on the continuity equation (

A_1V_1 = A_2V_2

), the fluid's velocity increases as it enters the narrower section of the pipe.

The same volume of fluid must pass through a smaller area in the same amount of time, requiring it to speed up.

2

Determine the effect of increased velocity on static pressure.

Static pressure decreases.

Bernoulli's principle states that for a horizontal flow, an increase in the speed of the fluid occurs simultaneously with a decrease in static pressure.

3

Evaluate the statement's claim against the established physical principles.

The statement claims static pressure increases, which contradicts the actual outcome (a decrease in static pressure).

The inverse relationship between fluid velocity and static pressure confirms the statement is false.

Key Concept

Bernoulli's principle and the continuity equation for incompressible fluids.

Estimated Time:45s

Question 1791Question →

A heavy machinery technician needs to slightly lift a generator weighing $1000\text{ lbs}$ to slide a permanent leveling mount underneath it. To do this, the technician drives a solid steel wedge under the edge of the generator. If the technician can apply a maximum driving effort of $200\text{ lbs}$ and the wedge has a penetration length of $20\text{ inches}$ , what is the maximum thickness the wedge can be to successfully lift the load? (Assume an ideal system with no friction.)

100\text{ inches}

4\text{ inches}

5\text{ inches}

0.25\text{ inches}

Show answer & explanation

Answer: $4\text{ inches}$

Answer

The maximum thickness the wedge can be is

4\text{ inches}

.

To find the maximum thickness, first determine the required mechanical advantage (MA) by dividing the load force (

1000\text{ lbs}

) by the effort force (

200\text{ lbs}

), which equals 5. Because the MA of an ideal wedge is equal to its length divided by its thickness, you divide the length (

20\text{ inches}

) by the MA (

5

). This calculation yields a maximum thickness of

4\text{ inches}

.

Step-by-Step Solution

1

Calculate the required Mechanical Advantage (MA) for the task.

MA = \frac{\text{Load Force}}{\text{Effort Force}} = \frac{1000\text{ lbs}}{200\text{ lbs}} = 5

The mechanical advantage determines how much the simple machine must multiply the input force to overcome the load.

2

Relate the mechanical advantage to the geometry of the wedge.

MA = \frac{\text{Length}}{\text{Thickness}} \Rightarrow 5 = \frac{20\text{ inches}}{\text{Thickness}}

In an ideal wedge, the ratio of the input distance (penetration length) to the output distance (vertical lift or thickness) equals the mechanical advantage.

3

Solve the equation for the maximum thickness.

\text{Thickness} = \frac{20\text{ inches}}{5} = 4\text{ inches}

Rearranging the formula isolates the unknown variable. A wedge thicker than

4\text{ inches}

would provide an MA of less than 5, making the

200\text{ lbs}

effort insufficient to lift the generator.

Key Concept

Mechanical Advantage of Wedges

Question 1792Question →

In a structural assembly, two overlapping metal plates are fastened together by a single rivet. When opposing forces pull the plates parallel to their surfaces in opposite directions, what type of stress is primarily applied to the rivet?

Tensile stress

Shear stress

Compressive stress

Torsional stress

Show answer & explanation

Answer: Shear stress

Answer

The correct answer is shear stress.

The correct answer is shear stress because the pulling forces act parallel to the overlapping surfaces. This load causes the metal plates to try to slide across one another, attempting to slice the rivet in half at the exact plane where the two plates meet.

Step-by-Step Solution

1

Analyze the orientation of the forces relative to the fastener and the metal plates.

The pulling forces are acting parallel to the flat surfaces of the overlapping metal plates.

The direction of the applied load determines the specific type of stress experienced by the fastener.

2

Determine the mechanical effect of these parallel forces on the rivet.

The forces cause the plates to try to slide past each other, creating a slicing action across the middle of the rivet.

Visualizing how the plates interact with the rivet helps identify the failure mode.

3

Match the physical effect to the correct engineering terminology.

A force that attempts to cut or slice a material parallel to its cross-section is defined as shear stress.

This confirms the engineering definition of the load being applied.

Key Concept

Identifying load types and shear stress in mechanical joints.

Question 1793Question →

A cargo crate has a weight of $4,900 \text{ N}$ on Earth (where $g = 9.8 \text{ m/s}^2$ ). It is sliding across a frictionless floor at a velocity of $12 \text{ m/s}$ when it hits a padded wall. If the crate comes to a complete stop in $0.6 \text{ s}$ , what is the average impact force exerted on the crate during this collision?

98,000 \text{ N}

10,000 \text{ N}

3,600 \text{ N}

25 \text{ N}

Show answer & explanation

Answer: $10,000 \text{ N}$

Answer

The average impact force is

10,000 \text{ N}

.

To find the average impact force, we use the impulse-momentum theorem (

F\Delta t = m\Delta v

) or Newton's second law (

F = ma

). First, we must convert the weight to mass by dividing by the acceleration due to gravity:

4,900 \text{ N} / 9.8 \text{ m/s}^2 = 500 \text{ kg}

. Next, we calculate the acceleration by dividing the change in velocity by the impact time:

12 \text{ m/s} / 0.6 \text{ s} = 20 \text{ m/s}^2

. Multiplying the mass by the acceleration gives the force:

500 \text{ kg} \times 20 \text{ m/s}^2 = 10,000 \text{ N}

.

Step-by-Step Solution

1

Calculate the mass of the crate from its weight.

m = \frac{W}{g} = \frac{4,900 \text{ N}}{9.8 \text{ m/s}^2} = 500 \text{ kg}

Newton's laws and momentum calculations require mass, not weight.

2

Calculate the crate's change in velocity.

\Delta v = 12 \text{ m/s} - 0 \text{ m/s} = 12 \text{ m/s}

The crate comes to a complete stop, so the total change in velocity is its initial velocity.

3

Calculate the crate's acceleration (or deceleration) during the impact.

a = \frac{\Delta v}{\Delta t} = \frac{12 \text{ m/s}}{0.6 \text{ s}} = 20 \text{ m/s}^2

Acceleration is the change in velocity divided by the time it takes to change.

4

Calculate the average impact force using Newton's Second Law.

F = m \times a = 500 \text{ kg} \times 20 \text{ m/s}^2 = 10,000 \text{ N}

Force equals mass times acceleration. (Alternatively, impulse

F\Delta t = \Delta p

yields the same result:

F = \frac{500 \times 12}{0.6} = 10,000 \text{ N}

).

Key Concept

The impulse-momentum theorem and the distinction between mass and weight.

Question 1794Question →

An aerospace engineering team is modifying the solid metal thermal struts that connect a heat-generating electronics module to a cooling radiator. Match each proposed design modification with its specific physical effect on the rate of conductive heat transfer through the strut, assuming the temperature difference remains constant.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Changing to copper increases conductivity; using parallel struts doubles the area; increasing length halves the transfer rate; and machining a hollow core reduces the cross-sectional area.

The rate of conductive heat transfer through a solid object is determined by its material's thermal conductivity, the cross-sectional area perpendicular to the heat flow, and the length of the pathway. Adjusting these physical parameters directly alters the heat flow according to proportional relationships.

Step-by-Step Solution

1

Recall the variables that govern the rate of conductive heat transfer.

Identify that the rate of heat transfer depends directly on thermal conductivity (

k

) and cross-sectional area (

A

), and inversely on length (

L

).

Understanding these relationships is necessary to evaluate how physical dimensional or material changes affect thermal performance.

2

Evaluate the material change.

Switching from stainless steel to copper significantly increases the thermal conductivity (

k

).

Different metals have different inherent abilities to conduct heat, and copper is a highly efficient conductor compared to steel alloys.

3

Evaluate the dimensional and geometric changes.

Two struts double the area (

A

). Doubling length increases distance (

L

). A hollow core removes solid metal, reducing area (

A

).

Translating physical modifications into their corresponding mathematical variables reveals their exact impact on the heat flow rate.

Key Concept

Variables in Fourier's Law of Heat Conduction

Question 1795Question →

A maintenance team needs to move a heavy steel generator across a flat concrete floor. Arrange the following methods in order from the HIGHEST amount of frictional resistance to the LOWEST amount of frictional resistance.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from highest to lowest resistance is: dragging directly on dry concrete, sliding with industrial lubricant, and placing on steel rollers.

Dry sliding friction creates the most resistance due to direct, rough surface-to-surface contact. Lubricating the surface reduces this resistance by creating a fluid film between the objects, lowering the friction coefficient. However, rolling friction (using rollers) is the most efficient method and creates the absolute least resistance, as it prevents the surfaces from scraping against each other entirely.

Step-by-Step Solution

1

Identify the primary type of friction acting in each of the three moving methods.

Dragging directly involves dry sliding friction; using lubricant involves fluid or mixed friction; using steel rollers involves rolling friction.

Recognizing the physical mechanism at the contact surface is the first step in comparing resistance levels.

2

Compare the relative magnitudes of these different types of friction.

Dry sliding friction provides the greatest resistance due to interlocking surface irregularities. Lubrication reduces this contact, lowering resistance. Rolling friction provides the least resistance as sliding is eliminated.

Fundamental mechanical principles state that, for a given load, dry kinetic friction is generally greater than fluid friction, which in turn is greater than rolling friction.

3

Order the methods from highest frictional resistance to lowest.

Highest is dry dragging, middle is lubricated sliding, lowest is steel rollers.

This matches the sequence requirements specified in the question stem.

Key Concept

Types and relative magnitudes of mechanical friction

Estimated Time:45s

Question 1796Question →

Arrange the following inclined planes in order from the LEAST ideal mechanical advantage (IMA) to the GREATEST ideal mechanical advantage.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from least to greatest mechanical advantage is: the 10-foot ramp (IMA=2), the 12-foot ramp (IMA=4), the 15-foot ramp (IMA=5), and the 16-foot ramp (IMA=8).

The ideal mechanical advantage (IMA) of an inclined plane is calculated by dividing the length of the slope by its vertical height. A longer slope relative to its height yields a higher mechanical advantage, meaning less effort force is required. Ordering the ramps by their calculated IMA values gives 2 (least), 4, 5, and 8 (greatest).

Step-by-Step Solution

1

Recall the formula for the ideal mechanical advantage (IMA) of an inclined plane.

\text{IMA} = \frac{\text{Length of Incline}}{\text{Vertical Height}}

The mechanical advantage quantifies how much the inclined plane multiplies the input force or reduces the required effort.

2

Calculate the IMA for each given ramp.

10-foot ramp:

10 \div 5 = 2

. 12-foot ramp:

12 \div 3 = 4

. 16-foot ramp:

16 \div 2 = 8

. 15-foot ramp:

15 \div 3 = 5

.

Calculating the individual values allows for direct comparison.

3

Order the calculated values from least to greatest.

The values in ascending order are 2, 4, 5, and 8.

The question specifically asks for the arrangement starting from the lowest mechanical advantage to the highest.

Key Concept

The ideal mechanical advantage of a ramp is determined by the ratio of its length to its vertical height.

Question 1797Question →

An industrial liquid cooling system normally relies on a mechanical pump for forced convection. An engineer is modifying the system to include a fail-safe thermosiphon loop that relies entirely on natural convection if the pump breaks down. Based on the principles of fluid dynamics and thermal energy transfer, which of the following design configurations is required for this fail-safe to work, and what mechanism drives it?

The radiator must be mounted physically higher than the heat source, allowing the heated fluid to expand, decrease in density, and rise into the cooling fins.

The radiator must be mounted physically lower than the heat source, allowing the heated fluid to thermally contract, increase in density, and sink downward.

The radiator must be bolted flush against the heat source to maximize the direct transfer of thermal energy through the static fluid and metal casing.

The system must use a fluid with a minimal specific heat capacity so that it absorbs and releases thermal energy at a rapid rate without requiring circulation.

Show answer & explanation

Answer: The radiator must be mounted physically higher than the heat source, allowing the heated fluid to expand, decrease in density, and rise into the cooling fins.

Answer

The radiator must be mounted physically higher than the heat source, allowing the heated fluid to expand, decrease in density, and rise into the cooling fins.

The correct answer accurately identifies that a natural convection loop (thermosiphon) requires the heat sink to be elevated above the heat source. When the fluid at the heat source warms up, thermal expansion decreases its density, making it buoyant. This hotter, lighter fluid naturally rises into the elevated radiator. As it cools in the radiator, its density increases, causing it to sink back down to the heat source, establishing a continuous, self-sustaining flow without a pump.

Step-by-Step Solution

1

Analyze the difference between forced and natural convection.

Forced convection uses a pump; natural convection relies solely on buoyancy forces caused by density differences in the fluid.

Understanding the driving force of the fail-safe system is required to determine the necessary physical layout.

2

Determine how heat affects the density of the cooling fluid.

As the fluid absorbs heat from the engine block, its molecules spread out (thermal expansion), which decreases its density and causes it to become buoyant.

Identifying the density change dictates the direction the hot fluid will naturally move (upwards).

3

Evaluate the placement of the radiator (heat sink) based on fluid movement.

Because hot fluid naturally rises and cold fluid naturally sinks, the radiator must be placed above the heat source to allow the rising hot fluid to enter it, cool down, become denser, and sink back down to complete the loop.

A continuous circulation loop cannot form if the radiator is placed below the heat source, as the hot fluid would remain trapped at the top.

Key Concept

Natural convection is driven by buoyancy forces resulting from the thermal expansion and decreased density of heated fluids.

Question 1798Question →

In a typical domestic water boiler, the heating element is installed near the bottom of the tank rather than the top. Which of the following best explains the reason for this placement?

To transfer heat upward through the fluid primarily by direct physical conduction from molecule to molecule.

To allow the heated water to expand, become less dense, and rise, creating a natural convection current.

To cause the heated water to contract and become denser, allowing it to efficiently collect heat at the bottom.

To compress the liquid water at the bottom of the tank so it can absorb thermal energy more rapidly.

Show answer & explanation

Answer: To allow the heated water to expand, become less dense, and rise, creating a natural convection current.

Answer

To allow the heated water to expand, become less dense, and rise, creating a natural convection current.

When water at the bottom of a tank is heated, it undergoes thermal expansion and its density decreases. The warmer, less dense water naturally rises due to buoyancy, while the cooler, denser water from the top sinks to take its place near the heating element. This creates a continuous, self-sustaining circulation called a natural convection current, which efficiently heats the entire volume of fluid.

Step-by-Step Solution

1

Identify what happens to the fluid immediately surrounding a heat source.

The water at the bottom of the tank absorbs heat from the heating element.

Heat transfer begins with the interaction between the heat source and the adjacent fluid.

2

Apply the principle of thermal expansion.

As the water warms, it expands, which causes its density to decrease relative to the surrounding cooler water.

Temperature and fluid density are inversely related due to thermal expansion.

3

Determine the resulting fluid movement caused by buoyancy.

The warmer, less dense water rises to the top of the tank, displacing cooler, denser water that sinks to the bottom to be heated.

This continuous circulation pattern, driven by density differences, is known as a natural convection current.

Key Concept

Natural Convection

Estimated Time:45s

Question 1799Question →

An arresting gear system is used to stop a $12,000 \text{ kg}$ aircraft landing on a flight deck. The aircraft touches down with a velocity of $144 \text{ km/h}$ and is brought to a complete stop in $2.0 \text{ seconds}$ by the arresting wire. Assuming a constant deceleration, what is the magnitude of the average net braking force applied to the aircraft?

600 \text{ N}

864,000 \text{ N}

240,000 \text{ N}

2,352,000 \text{ N}

Show answer & explanation

Answer: $240,000 \text{ N}$

Answer

The correct magnitude of the net braking force is

240,000 \text{ N}

.

The correct answer accurately calculates the force by first converting the velocity from km/h to m/s (

144 \text{ km/h} \times \frac{1000 \text{ m}}{3600 \text{ s}} = 40 \text{ m/s}

). It then finds the magnitude of acceleration (

a = \frac{\Delta v}{t} = \frac{40 \text{ m/s}}{2.0 \text{ s}} = 20 \text{ m/s}^2

) and applies Newton's Second Law (

F = m \times a = 12,000 \text{ kg} \times 20 \text{ m/s}^2 = 240,000 \text{ N}

).

Step-by-Step Solution

1

Convert the initial velocity from km/h to m/s.

144 \text{ km/h} \times \left(\frac{1000 \text{ m}}{3600 \text{ s}}\right) = 40 \text{ m/s}

Standard SI units (meters and seconds) are required to correctly calculate force in Newtons.

2

Calculate the magnitude of acceleration (deceleration) using the change in velocity over time.

a = \frac{40 \text{ m/s}}{2.0 \text{ s}} = 20 \text{ m/s}^2

Acceleration is defined as the rate of change of velocity.

3

Apply Newton's Second Law to find the average net braking force.

F = 12,000 \text{ kg} \times 20 \text{ m/s}^2 = 240,000 \text{ N}

Newton's Second Law states that force equals mass times acceleration (

F = ma

).

Key Concept

Newton's Second Law (F=ma) and Kinematics

Question 1800Question →

A mechanic uses a hydraulic floor jack to lift the front axle of a delivery truck. The jack's output piston has a cross-sectional area of $25 \text{ in}^2$ and must support a load of $5,000 \text{ lbs}$ . If the input piston has a cross-sectional area of $0.5 \text{ in}^2$ , what is the minimum input force the mechanic must apply to lift the truck? (Assume a frictionless, ideal system)

100 \text{ lbs}

200 \text{ lbs}

10,000 \text{ lbs}

250,000 \text{ lbs}

Show answer & explanation

Answer: $100 \text{ lbs}$

Answer

100 \text{ lbs}

In a closed hydraulic system, pressure is uniform. The pressure created by the load on the output piston is its force divided by its area (

5,000 / 25 = 200 \text{ psi}

). To produce this same pressure at the input piston, you multiply the pressure by the input piston's area (

200 \times 0.5

), which equals an input force of

100 \text{ lbs}

.

Step-by-Step Solution

1

Calculate the fluid pressure required at the output piston using the formula P = F/A.

5,000 \text{ lbs} / 25 \text{ in}^2 = 200 \text{ psi}

Pascal's Principle states that pressure applied to a confined fluid is transmitted equally in all directions.

2

Apply the calculated pressure to the input piston to find the required input force using F = P × A.

200 \text{ psi} \times 0.5 \text{ in}^2 = 100 \text{ lbs}

The input piston must generate the identical system pressure to balance and lift the load.

Key Concept

Pascal's Principle (Hydraulic Mechanical Advantage)

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