All practice questions

5215 questions

Question 2001Question →

An automotive engineer is redesigning a vehicle's disc brake system to optimize heat dissipation. In the new design, the surface area of the brake pads is exactly doubled. However, the hydraulic system is calibrated to apply the exact same total normal force (clamping force) against the spinning rotor as the original design. Assuming the brake pad material and rotor material remain identical, how will the new design theoretically affect the kinetic frictional force generated during braking?

Show answer & explanation

Answer: The kinetic frictional force will remain unchanged, because it depends on the normal force and materials, not the contact area.

Answer

The kinetic frictional force will remain unchanged, because it depends on the normal force and materials, not the contact area.
According to the standard model of dry friction (Coulomb friction), the kinetic frictional force between two solid surfaces is directly proportional to the normal force pressing them together and the materials involved (the coefficient of friction), but it is completely independent of the apparent area of contact. Since the normal force and materials are unchanged, the friction remains the same.

Step-by-Step Solution

1
Identify the factors that determine kinetic frictional force.
Kinetic friction (FkF_k) is determined by the formula Fk=μkFNF_k = \mu_k F_N, where μk\mu_k is the coefficient of kinetic friction and FNF_N is the normal force.
Establishing the mathematical relationship is necessary to see which variables affect the outcome.
2
Evaluate the changes made in the new design.
The surface area doubled, but the normal force (clamping force) and the materials (which determine μk\mu_k) remained exactly the same.
To apply the friction formula, we must know if the variables within it have changed.
3
Determine the effect on the total frictional force.
Because neither the normal force nor the coefficient of friction changed, the calculated frictional force remains identical, proving it is independent of surface area.
This confirms the theoretical principle of dry friction.

Key Concept

Friction and Contact Area Independence
Question 2002Question →

A double-walled cryogenic storage vessel uses a vacuum gap between its inner and outer steel walls to keep the contents cold. While the vacuum effectively stops conduction and convection, thermal energy can still cross the empty space. Which of the following surface treatments on the walls facing the vacuum gap would most effectively reduce this remaining heat transfer?

Show answer & explanation

Answer: Applying a highly polished, reflective metallic finish

Answer

Applying a highly polished, reflective metallic finish
In a vacuum, the only possible method of heat transfer is thermal radiation (electromagnetic waves). A highly polished, reflective surface acts like a mirror for infrared radiation, bouncing the heat waves back and preventing them from being absorbed into the inner wall of the vessel.

Step-by-Step Solution

1
Identify the remaining mode of heat transfer across the vacuum.
Thermal radiation is the only mode of heat transfer that can travel through empty space (a vacuum), as it relies on electromagnetic waves rather than a physical medium.
Conduction and convection require matter (solids, liquids, or gases) to transfer heat.
2
Determine how to minimize thermal radiation.
Radiation is minimized when surfaces have low emissivity and high reflectivity.
Highly polished, light-colored, or shiny metallic surfaces reflect infrared waves instead of absorbing or radiating them.

Key Concept

Heat Transfer: Radiation
Estimated Time:1m 0s
Question 2003Question →

Match each wheel and axle configuration to its resulting Ideal Mechanical Advantage (IMA).

Click a left item, then click its matching right item

Items

Effort is applied to a wheel with a 10 cm10 \text{ cm} radius to turn an axle with a 2 cm2 \text{ cm} radius.
Effort is applied to a wheel with a 12 cm12 \text{ cm} radius to turn an axle with a 3 cm3 \text{ cm} radius.
Effort is applied to an axle with a 4 cm4 \text{ cm} radius to turn a wheel with an 8 cm8 \text{ cm} radius.
Effort is applied to an axle with a 2 cm2 \text{ cm} radius to turn a wheel with a 10 cm10 \text{ cm} radius.

Matches

Show answer & explanation

Answer

Match each configuration by correctly dividing the effort radius by the load radius.
The correct matches are found by calculating the ratio of the input (effort) distance to the output (load) distance. For a wheel and axle, this is equivalent to Effort RadiusLoad Radius\frac{\text{Effort Radius}}{\text{Load Radius}}. When the effort is on the wheel, the IMA is greater than 1. When the effort is on the axle, the IMA is less than 1.

Step-by-Step Solution

1
Identify the effort radius and the load radius for each given configuration.
You determine whether the force is applied to the wheel (larger radius) or the axle (smaller radius).
The location of the applied force dictates which radius is the numerator in the IMA formula.
2
Apply the Ideal Mechanical Advantage formula: IMA=Effort RadiusLoad Radius\text{IMA} = \frac{\text{Effort Radius}}{\text{Load Radius}}.
Calculations yield 55, 44, 0.50.5, and 0.20.2 for the respective configurations.
This formula provides the theoretical multiplication of force for a wheel and axle mechanism.

Key Concept

Ideal Mechanical Advantage of a Wheel and Axle
Estimated Time:45s
Question 2004Question →

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.

Drag items to arrange them in the correct order

Show answer & explanation

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

1
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.
2
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.
3
Identify the actual compression action.
The piston moves up to decrease the internal volume.
Decreasing the volume of the sealed gas increases its pressure.
4
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 2005Question →

A mechanic checks a heavy-duty engine's coolant temperature gauge, which displays a reading of 35∘C35^\circ\text{C}. What is this temperature reading in degrees Fahrenheit?

Show answer & explanation

Answer: 95

Answer

95
The correct answer is derived by multiplying the given Celsius value by 9/5 to adjust for the difference in degree size, and then adding 32 to account for the difference in the freezing point baselines of the two scales.

Step-by-Step Solution

1
Identify the proper conversion formula.
F=95C+32F = \frac{9}{5}C + 32
This is the mathematical relationship used to convert temperatures from the Celsius scale to the Fahrenheit scale.
2
Substitute the given Celsius value into the formula.
F=95(35)+32F = \frac{9}{5}(35) + 32
The gauge reading is exactly 35∘C35^\circ\text{C}.
3
Calculate the proportional factor.
63+3263 + 32
Dividing 35 by 5 yields 7, and multiplying 7 by 9 yields 63.
4
Add the baseline offset to find the final temperature.
95
The Fahrenheit scale offset is 32 degrees above the freezing point equivalent.

Key Concept

Celsius to Fahrenheit Conversion
Question 2006Question →

A canoeist pulls a paddle backward through the water to propel the canoe. According to Newton's Third Law of Motion, which specific force directly causes the canoe and paddler to move forward?

Show answer & explanation

Answer: The water pushing forward against the paddle

Answer

The water pushing forward against the paddle
According to Newton's Third Law, every action has an equal and opposite reaction. The action is the paddle pushing backward on the water. Therefore, the reaction is the water pushing forward on the paddle, which drives the canoe forward.

Step-by-Step Solution

1
Identify the action force described in the scenario.
The paddle pushes backward against the water.
Newton's Third Law requires identifying the initial interacting bodies and the direction of the applied force.
2
Apply Newton's Third Law to find the reaction force.
The water pushes forward against the paddle.
Forces always occur in equal and opposite pairs acting on different bodies. If the action is backward on the water, the reaction must be forward on the paddle.

Key Concept

Action and reaction forces occur in equal and opposite pairs between two interacting bodies.
Question 2007Question →

During a runway clearing operation, an armored recovery vehicle pushes a disabled transport truck horizontally across the tarmac. The truck has a weight of 80,000 N80,000 \text{ N}. The recovery vehicle applies a forward force of 30,000 N30,000 \text{ N}, while the truck's damaged axles create a constant rolling resistance of 10,000 N10,000 \text{ N}. Assuming the acceleration due to gravity is 10 m/s210 \text{ m/s}^2, what is the forward acceleration of the disabled truck?

Show answer & explanation

Answer: 2.5 m/s22.5 \text{ m/s}^2

Answer

The disabled truck will have a forward acceleration of 2.5 m/s22.5 \text{ m/s}^2.
The correct acceleration is found by first converting the truck's weight to its mass, determining the net force by subtracting the rolling resistance from the applied force, and then dividing that net force by the mass.

Step-by-Step Solution

1
Calculate the mass of the truck from its weight.
m=80,000 N10 m/s2=8,000 kgm = \frac{80,000 \text{ N}}{10 \text{ m/s}^2} = 8,000 \text{ kg}
Newton's Second Law requires mass, not weight, to calculate acceleration.
2
Determine the net force acting on the truck.
Fnet=30,000 N−10,000 N=20,000 NF_{net} = 30,000 \text{ N} - 10,000 \text{ N} = 20,000 \text{ N}
The rolling resistance directly opposes the applied forward force, so it must be subtracted.
3
Calculate the acceleration using Newton's Second Law (F=maF = ma).
a=Fnetm=20,000 N8,000 kg=2.5 m/s2a = \frac{F_{net}}{m} = \frac{20,000 \text{ N}}{8,000 \text{ kg}} = 2.5 \text{ m/s}^2
Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Applying Newton's Second Law (F=maF=ma) in multi-force scenarios requiring weight-to-mass conversion.
Question 2008Question →

An underwater research drone is deployed in a freshwater lake. It records a hydrostatic pressure reading at a depth of 10 meters. The drone then descends vertically and records a second pressure reading at a depth of 40 meters. Assuming the water density is uniform, how does the second pressure reading compare to the first?

Show answer & explanation

Answer: The second reading is four times as large as the first reading.

Answer

The second reading is four times as large as the first reading.
Hydrostatic pressure is calculated using the equation P=ρghP = \rho g h. Because the density of the water (ρ\rho) and the acceleration due to gravity (gg) remain constant in this scenario, the pressure (PP) is directly proportional to the depth (hh). When the drone descends from 10 meters to 40 meters, the depth increases by a factor of 4. Therefore, the hydrostatic pressure also increases by exactly a factor of 4.

Step-by-Step Solution

1
Identify the mathematical formula for hydrostatic pressure.
P=ρghP = \rho g h, where PP is pressure, ρ\rho is density, gg is gravity, and hh is depth.
This formula establishes the mathematical relationship between fluid pressure and depth.
2
Determine the proportional relationship between the two recorded depths.
The second depth (40 meters) is exactly four times the first depth (10 meters).
Calculating the ratio of the depths allows for a direct comparison of the resulting pressures.
3
Apply the depth ratio to the pressure formula.
Since density and gravity are constant, increasing hh by a factor of 4 increases PP by a factor of 4.
Hydrostatic pressure is directly proportional to fluid depth.

Key Concept

Hydrostatic pressure is directly proportional to the depth of the fluid.
Question 2009Question →

When fastening a rigid steel bracket to a softer aluminum base, a wide, flat metal washer is typically placed beneath the bolt head and nut. Which of the following best describes the primary mechanical function of this flat washer?

Show answer & explanation

Answer: It distributes the compressive clamping force over a larger surface area to prevent crushing the softer material.

Answer

It distributes the compressive clamping force over a larger surface area to prevent crushing the softer material.
The correct answer accurately identifies that a flat washer increases the bearing area under the fastener. Because mechanical pressure is equal to force divided by area (P=FAP = \frac{F}{A}), increasing the contact area reduces the localized compressive stress on the softer material, preventing the bolt head from sinking into or crushing it.

Step-by-Step Solution

1
Analyze the forces acting on a joint when a bolt is tightened.
Tightening the bolt creates tension within the bolt shaft and downward compressive force against the clamped materials.
Understanding the primary stresses in a bolted joint is necessary to evaluate component functions.
2
Evaluate the material properties given in the scenario.
Aluminum is softer than steel and has a lower compressive yield strength, making it vulnerable to high localized pressure.
Identifying the weak point in the assembly explains why additional hardware is needed.
3
Apply the mechanical relationship between force, area, and pressure (P=FAP = \frac{F}{A}).
The flat washer has a much larger diameter than the bolt head. By spreading the same clamping force over this larger area, the overall pressure is significantly reduced.
This calculation proves that a larger surface area prevents the compressive stress from exceeding the aluminum's yield strength.

Key Concept

Load Distribution and Surface Pressure in Bolted Joints
Question 2010Question →

When a heavy-duty brake rotor becomes intensely hot during a steep descent, it transfers a portion of its thermal energy to the surrounding wheel components via thermal radiation, which requires neither direct physical contact nor moving air currents to function.

Show answer & explanation

Answer: True

Answer

True
The statement accurately defines the fundamental nature of thermal radiation in a mechanical context. A glowing brake rotor emits infrared electromagnetic waves that travel across the air gap and get absorbed by nearby wheel components, heating them without any need for solid contact or air circulation.

Step-by-Step Solution

1
Identify the modes of heat transfer mentioned or implied in the mechanical scenario.
The scenario describes heat moving from a hot brake rotor to surrounding components across an air gap without direct contact or moving air currents.
Differentiating between conduction, convection, and radiation is necessary to evaluate the physical claim.
2
Recall the fundamental mechanism of thermal radiation.
Thermal radiation is the transfer of heat energy through electromagnetic waves, typically infrared.
To verify if radiation matches the conditions described in the stem.
3
Evaluate the statement's claim about radiation's physical requirements.
Because it relies on electromagnetic waves, radiation indeed transfers heat without needing direct physical contact (conduction) or moving fluids (convection).
To confirm the factual accuracy of the entire statement.

Key Concept

Thermal radiation transfers heat via electromagnetic waves and does not require a physical medium or direct contact.
Estimated Time:45s
Question 2011Question →

A heavy steel transport barge leaves the salty water of an ocean bay and enters a freshwater river. The total weight of the barge and its cargo remains exactly the same. Given that saltwater has a significantly higher density than freshwater, how will the depth that the barge sinks into the water (its draft) change, and why?

Show answer & explanation

Answer: It will sink deeper into the water, because it must displace a larger volume of the less-dense freshwater to equal its own weight.

Answer

The barge will sink deeper into the water because it must displace a larger volume of the less-dense freshwater to equal its own weight.
According to Archimedes' principle, a floating object displaces a weight of fluid equal to its own true weight. Because the barge's weight is constant, it must displace the exact same *weight* of water in both locations to stay afloat. Since freshwater is less dense (weighs less per unit of volume) than saltwater, a larger physical *volume* of freshwater must be displaced to equal the barge's massive weight. To displace more volume, the barge must sink deeper into the water, increasing its draft.

Step-by-Step Solution

1
Identify the conditions for a floating object.
A floating object is in equilibrium, meaning the upward buoyant force (FbF_b) must exactly equal the object's downward true weight (WW).
This is the fundamental principle of flotation derived from Archimedes' principle.
2
Relate the buoyant force to fluid density and displaced volume.
Buoyant force equals the weight of the displaced fluid, expressed as Fb=ρ×V×gF_b = \rho \times V \times g, where ρ\rho is fluid density, VV is displaced volume, and gg is gravity.
This formula shows how fluid properties generate the upward force.
3
Apply the relationship to the barge moving from saltwater to freshwater.
Since FbF_b must remain constant (because the barge's weight is constant), and the fluid density (ρ\rho) decreases in freshwater, the displaced volume (VV) must increase to compensate.
Displacing a larger volume of water means the hull of the barge must sink deeper (increasing its draft).

Key Concept

Buoyancy and floating equilibrium (Archimedes' Principle)
Estimated Time:1m 0s
Question 2012Question →

A motorized telescope mount uses a compound gear system to adjust its viewing angle. The driving gear, Gear W, has 24 teeth and rotates counter-clockwise at 400 RPM400\text{ RPM}. Gear W meshes directly with Gear X, which has 96 teeth. Gear X and Gear Y are rigidly mounted on the same intermediate shaft. Gear Y has 30 teeth and meshes with the final output gear, Gear Z, which has 120 teeth. What is the rotational speed and direction of Gear Z?

Show answer & explanation

Answer: 25 RPM25\text{ RPM}, counter-clockwise

Answer

The final output gear, Gear Z, rotates at 25 RPM25\text{ RPM} in the counter-clockwise direction.
In a compound gear system, the overall speed ratio is determined by analyzing each meshing pair. The first pair (W to X) reduces the speed from 400 RPM400\text{ RPM} to 100 RPM100\text{ RPM} (400×24/96400 \times 24/96) and reverses the direction from counter-clockwise to clockwise. Since Gear Y shares a shaft with Gear X, it also rotates at 100 RPM100\text{ RPM} clockwise. The second meshing pair (Y to Z) further reduces the speed from 100 RPM100\text{ RPM} to 25 RPM25\text{ RPM} (100×30/120100 \times 30/120) and reverses the direction again, making the final output counter-clockwise.

Step-by-Step Solution

1
Calculate the rotational speed and direction of Gear X.
Speed of Gear X is 100 RPM100\text{ RPM}, rotating clockwise.
Gear X is driven by Gear W. The speed ratio is 24/96=1/424/96 = 1/4. 400 RPM×(1/4)=100 RPM400\text{ RPM} \times (1/4) = 100\text{ RPM}. Meshing gears rotate in opposite directions, so Gear X rotates clockwise.
2
Determine the speed and direction of Gear Y.
Speed of Gear Y is 100 RPM100\text{ RPM}, rotating clockwise.
Gear Y is rigidly mounted on the same shaft as Gear X, meaning they share the exact same rotational speed and direction.
3
Calculate the rotational speed and direction of Gear Z.
Speed of Gear Z is 25 RPM25\text{ RPM}, rotating counter-clockwise.
Gear Z is driven by Gear Y. The speed ratio is 30/120=1/430/120 = 1/4. 100 RPM×(1/4)=25 RPM100\text{ RPM} \times (1/4) = 25\text{ RPM}. Meshing gears rotate in opposite directions, so Gear Z rotates counter-clockwise.

Key Concept

Compound Gear Trains and Rotational Direction
Question 2013Question →

A technician uses a T-handle socket wrench to tighten a nut. The wide horizontal T-handle functions as the wheel, and the narrow vertical shaft functions as the axle. If the technician turns the T-handle clockwise, what is the direction of the shaft's rotation, and how does the output force at the shaft compare to the effort force applied to the handle?

Show answer & explanation

Answer: The shaft rotates clockwise, and the output force is greater than the effort force.

Answer

The shaft rotates clockwise, and the output force is greater than the effort force.
A wheel and axle mechanism consists of two parts that rotate together on the same axis. Therefore, if the wheel (T-handle) is turned clockwise, the axle (shaft) also turns clockwise. Because the input effort is applied to the larger radius of the handle, the mechanism multiplies the force, resulting in a greater output force at the smaller radius of the axle.

Step-by-Step Solution

1
Determine the direction of rotation for the axle (shaft).
The shaft rotates clockwise, the same as the handle.
In a wheel and axle mechanism, both components are rigidly attached to the same axis and rotate as a single solid unit.
2
Evaluate the force relationship between the input and output.
The output force at the shaft is greater than the effort force applied to the handle.
Applying effort to the component with the larger diameter (the wheel/handle) to drive the component with the smaller diameter (the axle/shaft) creates a mechanical advantage greater than 1, which multiplies the force.

Key Concept

Wheel and Axle Rotational Direction and Mechanical Advantage
Question 2014Question →

An engineering team is evaluating the efficiency and safety of a newly designed transport vehicle. Match each mechanical situation observed during testing to the primary type of frictional resistance dominating that situation.

Click a left item, then click its matching right item

Items

Tires resting on a steep, sloped ramp without slipping.
The vehicle's aerodynamic body pushing through high-speed winds.
Locked wheels skidding across a wet asphalt surface during an emergency stop.
Cylindrical bearings allowing the axles to turn with minimal effort.

Matches

Show answer & explanation

Answer

Tires resting without slipping match with static friction. The aerodynamic body pushing through winds matches with fluid friction. Locked wheels skidding match with kinetic friction. Cylindrical bearings match with rolling friction.
Each mechanical situation directly illustrates one of the four primary types of friction: static (no relative motion), kinetic (continuous sliding), rolling (rotating elements), and fluid (resistance through a gas or liquid).

Step-by-Step Solution

1
Analyze the sloped ramp scenario.
Identified no relative motion between the tires and the ramp.
Surfaces at rest relative to each other experience static friction.
2
Analyze the high-speed wind scenario.
Identified interaction between a solid moving body and a gas (air).
Gases and liquids behave as fluids, meaning aerodynamic drag is a form of fluid friction.
3
Analyze the emergency stop scenario.
Identified the tires locking and sliding continuously across the pavement.
Active sliding between two solid surfaces characterizes kinetic friction.
4
Analyze the axle bearing scenario.
Identified cylindrical elements rotating to facilitate movement.
The rotation of cylinders or spheres between surfaces is the defining characteristic of rolling friction.

Key Concept

Frictional Resistance Types and Applications
Question 2015Question →

A winch cable made of steel is subjected to heavy pulling forces. The cable can stretch slightly under this tension rather than snapping instantly. Which material property allows the steel to stretch and deform under pulling forces without breaking?

Show answer & explanation

Answer: Ductility

Answer

Ductility
Ductility is the specific mechanical property that allows a material to be drawn out or stretched under tension without fracturing. This makes it ideal for cables that must handle pulling forces safely.

Step-by-Step Solution

1
Identify the type of force acting on the cable.
The cable is subjected to heavy pulling forces, which is known as tension.
Understanding the force helps determine which material property is relevant.
2
Determine which material property describes stretching under tension.
Ductility is the property that allows a material to deform or stretch under tensile stress without breaking.
Matching the force (tension) and behavior (stretching) to the correct definition isolates the correct property.

Key Concept

Ductility and Tensile Stress
Estimated Time:45s
Question 2016Question →

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

Drag items to arrange them in the correct order

Show answer & explanation

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 (10,00010,000), bus (25,00025,000), car (30,00030,000), and truck (36,00036,000).

Step-by-Step Solution

1
Recall the formula for calculating momentum.
p=m×vp = m \times v
Momentum requires multiplying the mass of the object by its velocity.
2
Calculate the momentum for the motorcycle.
400 kg×25 m/s=10,000 kg⋅m/s400 \text{ kg} \times 25 \text{ m/s} = 10,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the first vehicle.
3
Calculate the momentum for the bus.
5,000 kg×5 m/s=25,000 kg⋅m/s5,000 \text{ kg} \times 5 \text{ m/s} = 25,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the second vehicle.
4
Calculate the momentum for the car.
1,500 kg×20 m/s=30,000 kg⋅m/s1,500 \text{ kg} \times 20 \text{ m/s} = 30,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the third vehicle.
5
Calculate the momentum for the truck.
3,000 kg×12 m/s=36,000 kg⋅m/s3,000 \text{ kg} \times 12 \text{ m/s} = 36,000 \text{ kg}\cdot\text{m/s}
This establishes the total momentum for the fourth vehicle.
6
Order the resulting values from lowest to highest.
10,000<25,000<30,000<36,00010,000 < 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 2017Question →

During a testing sequence, a heavy torpedo with a mass of 1,500 kg1,500 \text{ kg} is fired from a submarine tube. The launch mechanism applies a forward propulsive force of 45,000 N45,000 \text{ N}. If the water resistance creates a constant opposing drag force of 9,000 N9,000 \text{ N}, what is the initial acceleration of the torpedo?

Show answer & explanation

Answer: 24

Answer

24
To find the acceleration, we first determine the net force acting on the torpedo. The forward propulsive force is 45,000 N45,000 \text{ N}, but water resistance pushes back with 9,000 N9,000 \text{ N}. Subtracting the opposing force gives a net force of 36,000 N36,000 \text{ N}. Using Newton's Second Law (F=maF = ma), we rearrange the formula to solve for acceleration (a=Fma = \frac{F}{m}). Dividing the net force (36,000 N36,000 \text{ N}) by the mass (1,500 kg1,500 \text{ kg}) results in an acceleration of 24 m/s224 \text{ m/s}^2.

Step-by-Step Solution

1
Calculate the net force (FnetF_{net}) acting on the torpedo.
Fnet=45,000 N−9,000 N=36,000 NF_{net} = 45,000 \text{ N} - 9,000 \text{ N} = 36,000 \text{ N}
The torpedo experiences forces in opposite directions, so the drag force must be subtracted from the forward thrust to find the total effective force.
2
Calculate the acceleration (aa) using Newton's Second Law.
a=Fnetm=36,000 N1,500 kg=24 m/s2a = \frac{F_{net}}{m} = \frac{36,000 \text{ N}}{1,500 \text{ kg}} = 24 \text{ m/s}^2
Newton's Second Law states that acceleration equals the net force divided by the mass.

Key Concept

Newton's Second Law (F=ma) and Net Force
Question 2018Question →

During a hydro-engineering project, a completely sealed hollow steel sphere is used as an underwater sensor housing. The sphere has an external volume of 2.5 m32.5 \text{ m}^3 and a dry weight of 35,000 N35,000 \text{ N} in the air. When completely submerged in a testing pool where the water's weight density is 10,000 N/m310,000 \text{ N/m}^3, what is the net downward force (apparent weight) of the housing in Newtons?

Show answer & explanation

Answer: 10000

Answer

10000
The net downward force, or apparent weight, is found by subtracting the upward buoyant force from the object's true dry weight. Since the object displaces 2.5 m32.5 \text{ m}^3 of water with a weight density of 10,000 N/m310,000 \text{ N/m}^3, the buoyant force is 25,000 N25,000 \text{ N}. Subtracting this upward force from the 35,000 N35,000 \text{ N} downward dry weight leaves a net downward force of 10,000 N10,000 \text{ N}.

Step-by-Step Solution

1
Calculate the buoyant force acting on the submerged housing.
25,000 N
According to Archimedes' principle, the buoyant force equals the weight of the fluid displaced by the object's external volume (2.5 m3×10,000 N/m3=25,000 N2.5 \text{ m}^3 \times 10,000 \text{ N/m}^3 = 25,000 \text{ N}).
2
Calculate the apparent weight (net downward force).
10,000 N
The apparent weight is the actual weight in air minus the upward buoyant force (35,000 N−25,000 N=10,000 N35,000 \text{ N} - 25,000 \text{ N} = 10,000 \text{ N}).

Key Concept

Archimedes' Principle and Apparent Weight
Question 2019Question →

Wheel and axle mechanisms can be designed to multiply either force or speed. Match each real-world application of a wheel and axle to its correct mechanical description.

Click a left item, then click its matching right item

Items

Doorknob
Automobile drive wheels
Manual hand winch
Ceiling fan

Matches

Show answer & explanation

Answer

Doorknob matches the internal latch description; Automobile drive wheels match the engine and tire description; Manual hand winch matches the handle and cable drum description; Ceiling fan matches the motor and blades description.
Each mechanism uses the wheel and axle principle based on its specific need. The doorknob and hand winch are force multipliers because effort is applied to the larger wheel. The drive wheels and ceiling fan are speed multipliers because effort is applied to the smaller axle.

Step-by-Step Solution

1
Identify the mechanisms that act as force multipliers (input on the wheel).
The doorknob and manual hand winch both receive input force on the larger radius to produce a larger output force on the smaller radius.
Determining the location of the input force helps classify the mechanical advantage.
2
Identify the mechanisms that act as speed multipliers (input on the axle).
The automobile drive wheels and ceiling fan both receive input force on the smaller central radius to produce greater speed at the larger outer radius.
Speed multipliers take advantage of the larger circumference of the wheel covering more distance in the same amount of time.
3
Pair each specific device with its corresponding functional description.
The doorknob operates an internal latch; the drive wheels rotate the outer tire; the winch winds a cable around a drum; the ceiling fan spins blades.
Matching the physical components completes the logical pairing for each wheel and axle application.

Key Concept

Force Multipliers vs. Speed Multipliers in Wheel and Axle Systems
Question 2020Question →

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.

Drag items to arrange them in the correct order

Show answer & explanation

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

1
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.
2
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
PreviousPage 101 / 261Next
All practice questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin