Force, Mass, and Motion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 4

Question 61Question →

A military transport truck with a mass of $8,000 \text{ kg}$ is towing a loaded artillery trailer with a mass of $4,000 \text{ kg}$ along a level, straight road. The truck's engine generates a total forward driving force of $36,000 \text{ N}$ . During motion, the truck experiences a resistive drag force of $8,000 \text{ N}$ , and the trailer experiences its own resistive drag force of $4,000 \text{ N}$ . Assuming the tow bar connecting them is perfectly rigid and horizontal, what is the tension force in the tow bar?

6,000 \text{ N}

12,000 \text{ N}

40,000 \text{ N}

8,000 \text{ N}

Show answer & explanation

Answer: $12,000 \text{ N}$

Answer

The tension force in the tow bar is

12,000 \text{ N}

.

To find the tension, you must analyze the forces. First, calculate the acceleration of the entire system. The total mass is

12,000 \text{ kg}

. The net force on the system is the driving force minus both drag forces:

36,000 \text{ N} - (8,000 \text{ N} + 4,000 \text{ N}) = 24,000 \text{ N}

. Using

a = F_{net}/m

, the system's acceleration is

24,000 \text{ N} / 12,000 \text{ kg} = 2.0 \text{ m/s}^2

. Next, isolate the trailer to find the tension. The net force required to accelerate just the trailer is

4,000 \text{ kg} \times 2.0 \text{ m/s}^2 = 8,000 \text{ N}

. The tension must provide this net force PLUS overcome the trailer's

4,000 \text{ N}

drag. Therefore, Tension = Net Force + Drag =

8,000 \text{ N} + 4,000 \text{ N} = 12,000 \text{ N}

.

Step-by-Step Solution

1

Calculate the total mass and the net forward force for the entire two-vehicle system.

Total mass =

12,000 \text{ kg}

. Net force =

36,000 \text{ N} - (8,000 \text{ N} + 4,000 \text{ N}) = 24,000 \text{ N}

.

Newton's Second Law must first be applied to the system as a whole to determine their shared acceleration.

2

Calculate the acceleration of the system using Newton's Second Law (

a = F_{net}/m

).

a = 24,000 \text{ N} / 12,000 \text{ kg} = 2.0 \text{ m/s}^2

.

Because the tow bar is rigid, the truck and trailer accelerate at the exact same rate.

3

Isolate the trailer as a free body and apply Newton's Second Law to find the tension (

T

) in the tow bar.

The net force on the trailer is

m \times a = 4,000 \text{ kg} \times 2.0 \text{ m/s}^2 = 8,000 \text{ N}

. Since

F_{net} = T - F_{drag}

, we get

8,000 \text{ N} = T - 4,000 \text{ N}

, which means

T = 12,000 \text{ N}

.

The tension in the tow bar must provide enough force to both overcome the trailer's drag and accelerate its mass.

Key Concept

Newton's Second Law applied to Multi-Body Systems

Question 62Question →

A mining crew extracts a dense mineral boulder. In their vessel's main processing bay, where artificial gravity is maintained at $10 \text{ m/s}^2$ , a spring scale indicates the boulder has a weight of $1500 \text{ N}$ . The boulder is then transported to a storage facility on a small moon where the local gravitational acceleration is $2 \text{ m/s}^2$ . What are the mass and weight of the boulder at the lunar storage facility?

Mass:

30 \text{ kg}

, Weight:

300 \text{ N}

Mass:

150 \text{ kg}

, Weight:

1500 \text{ N}

Mass:

150 \text{ kg}

, Weight:

300 \text{ N}

Mass:

1500 \text{ kg}

, Weight:

300 \text{ N}

Show answer & explanation

Answer: Mass: $150 \text{ kg}$ , Weight: $300 \text{ N}$

Answer

The mass is

150 \text{ kg}

and the weight is

300 \text{ N}

.

The correct answer accurately calculates the initial mass as

150 \text{ kg}

using the weight on the vessel (

1500 \text{ N} / 10 \text{ m/s}^2

). Because mass is an invariant property, it remains

150 \text{ kg}

on the moon. The new weight is then found by multiplying this mass by the moon's local gravity (

150 \text{ kg} \times 2 \text{ m/s}^2 = 300 \text{ N}

).

Step-by-Step Solution

1

Calculate the mass of the boulder using its initial weight and the artificial gravity in the processing bay.

m = \frac{W_1}{g_1} = \frac{1500 \text{ N}}{10 \text{ m/s}^2} = 150 \text{ kg}

.

Mass is an intrinsic property that must be determined first to calculate weight in other environments.

2

Determine the mass of the boulder at the lunar storage facility.

The mass remains

150 \text{ kg}

.

Mass is an invariant measure of the amount of matter and does not change with location or local gravity.

3

Calculate the new weight of the boulder using the local gravitational acceleration on the small moon.

W_2 = m \times g_2 = 150 \text{ kg} \times 2 \text{ m/s}^2 = 300 \text{ N}

.

Weight is the gravitational force acting on an object, which depends on the local acceleration due to gravity.

Key Concept

Mass is an intrinsic, invariant property representing the amount of matter, whereas weight is the location-dependent gravitational force acting upon that mass.

Question 63Question →

During a manufacturing process, a pneumatic pusher applies a constant net horizontal force of $300 \text{ N}$ to slide a steel component across a frictionless track. If the component accelerates at $15 \text{ m/s}^2$ , what is the mass of the steel component?

20 \text{ kg}

30 \text{ kg}

315 \text{ kg}

4,500 \text{ kg}

Show answer & explanation

Answer: $20 \text{ kg}$

Answer

20 \text{ kg}

According to Newton's Second Law of Motion, the net force on an object is equal to its mass times its acceleration (

F = ma

). To find the mass when both force and acceleration are known, the formula must be rearranged to divide the net force by the acceleration (

m = \frac{F}{a}

). Dividing the given

300 \text{ N}

by

15 \text{ m/s}^2

yields a mass of

20 \text{ kg}

.

Step-by-Step Solution

1

Identify the given variables provided in the scenario.

Force (

F

) =

300 \text{ N}

, Acceleration (

a

) =

15 \text{ m/s}^2

.

Establishing the known physical quantities is required before selecting and applying the correct formula.

2

State Newton's Second Law of Motion and rearrange it algebraically to solve for mass.

The formula

F = ma

becomes

m = \frac{F}{a}

.

The question asks for the mass of the component, so the standard equation must be isolated for the variable

m

.

3

Substitute the known values into the rearranged equation and calculate the final result.

m = \frac{300}{15} = 20 \text{ kg}

.

Provides the final mass of the steel component based on the applied force and resulting acceleration.

Key Concept

Newton's Second Law (

F=ma

)

Question 64Question →

A mechanic is servicing a high-speed gearbox and must choose a lubricant. If a heavy, thick grease is used instead of a lightweight oil, the gearbox will require more mechanical power to maintain its high rotational speeds. What is the primary cause of this increased resistance?

The greater viscosity of the thick grease creates higher fluid friction against the moving gears.

The layer of grease increases the total surface area of the gears, which directly multiplies the kinetic friction.

The thick grease adds extra mass to the assembly, and this added weight is what strongly resists the rotational motion.

The thick grease absorbs all reaction forces between the gear teeth, neutralizing the inertia of the system.

Show answer & explanation

Answer: The greater viscosity of the thick grease creates higher fluid friction against the moving gears.

Answer

The greater viscosity of the thick grease creates higher fluid friction against the moving gears.

Thick grease has a high viscosity, meaning it strongly resists flow and deformation. When gears rotate at high speeds through this thick substance, they must continuously shear and displace the grease. This creates substantial fluid friction (drag), which opposes the motion of the gears and requires the system to draw more mechanical power to maintain its speed.

Step-by-Step Solution

1

Identify the type of resistance introduced when machine parts move through a liquid or semi-solid substance.

The resistance is fluid friction, also known as drag or viscous resistance.

Because the gears are completely coated by a lubricant, they must continuously push the fluid out of the way as they spin.

2

Compare the physical properties of a lightweight oil and a thick grease.

Thick grease has a much higher viscosity than lightweight oil.

Viscosity is the measure of a fluid's internal resistance to flow and deformation.

3

Determine how this viscosity affects high-speed mechanical operation.

Higher viscosity results in greater fluid friction against the fast-moving gears, requiring more energy from the motor to maintain speed.

Moving through a thicker, more resistant substance requires more force than moving through a thinner one.

Key Concept

Fluid Friction and Viscosity

Question 65Question →

An automated logistics drone is transporting a sealed supply crate. On Earth, where the gravitational acceleration is considered to be $10 \text{ m/s}^2$ , the crate has a measured weight of $1400 \text{ N}$ . The crate is then delivered to a controlled low-gravity research habitat where the local gravitational acceleration is maintained at $3.5 \text{ m/s}^2$ .

What is the weight of the crate inside the low-gravity habitat in Newtons?

Show answer & explanation

Answer: 490

Answer

490

To find the new weight, first determine the crate's mass, which does not change. Dividing the Earth weight (

1400 \text{ N}

) by Earth's gravity (

10 \text{ m/s}^2

) gives a mass of

140 \text{ kg}

. Then, multiply this invariant mass by the habitat's gravity (

3.5 \text{ m/s}^2

) to find the new weight:

140 \text{ kg} \times 3.5 \text{ m/s}^2 = 490 \text{ N}

.

Step-by-Step Solution

1

Calculate the mass of the crate on Earth.

m = \frac{1400 \text{ N}}{10 \text{ m/s}^2} = 140 \text{ kg}

Mass is an intrinsic property of the object that remains constant regardless of location.

2

Calculate the weight of the crate in the low-gravity habitat.

W = 140 \text{ kg} \times 3.5 \text{ m/s}^2 = 490 \text{ N}

Weight is the force exerted by gravity on a mass, which changes depending on the local gravitational acceleration.

Key Concept

Mass is invariant, while weight depends on the local gravitational field.

Question 66Question →

When a massive steel cargo ship collides with a small wooden fishing boat, the impact force exerted by the cargo ship on the wooden boat is significantly greater in magnitude than the reaction force exerted by the wooden boat on the cargo ship, due to the ship's vastly greater mass and momentum.

True

False

Show answer & explanation

Answer: False

Answer

The statement is false.

The statement is false because Newton's Third Law mandates that forces between two interacting objects are always exactly equal in magnitude and opposite in direction, irrespective of their differing masses or momentums.

Step-by-Step Solution

1

Analyze the interacting bodies and the nature of the forces described in the scenario.

The two bodies are a massive cargo ship and a small wooden boat experiencing a collision, which constitutes an interacting force pair.

Identifying the system and the interaction is necessary to apply the correct physical laws.

2

Apply Newton's Third Law to the interaction.

The law states that force pairs between two interacting objects are always equal in magnitude and opposite in direction (

F_{ship} = -F_{boat}

).

This fundamental law dictates how forces operate between any two interacting bodies, regardless of their physical properties.

3

Evaluate the role of mass and momentum mentioned in the statement.

While the ship has significantly greater mass and momentum, these factors determine the resulting acceleration (

a = \frac{F}{m}

) and subsequent damage, not the magnitude of the interacting force pair itself.

It is critical to distinguish between the contact force itself and the effects (acceleration, deformation) of that force.

Key Concept

Newton's Third Law of Motion (Equal and Opposite Reaction)

Question 67Question →

At an Earth-based testing facility (where $g = 10 \text{ m/s}^2$ ), a suspended spring scale reads $750 \text{ N}$ when a communications satellite module is attached to it. The module is later transported to a planetary outpost where the local gravitational acceleration is $4 \text{ m/s}^2$ . Which of the following correctly identifies the module's mass and its new weight at the outpost?

Mass =

75 \text{ kg}

, Weight =

300 \text{ N}

Mass =

75 \text{ kg}

, Weight =

750 \text{ N}

Mass =

750 \text{ kg}

, Weight =

3000 \text{ N}

Mass =

300 \text{ N}

, Weight =

75 \text{ kg}

Show answer & explanation

Answer: Mass = $75 \text{ kg}$ , Weight = $300 \text{ N}$

Answer

Mass =

75 \text{ kg}

, Weight =

300 \text{ N}

The correct answer accurately separates the concepts of mass and weight. First, the mass is found by dividing the Earth weight by Earth's gravity (

750 \text{ N} / 10 \text{ m/s}^2 = 75 \text{ kg}

). Because mass never changes regardless of location, it stays

75 \text{ kg}

. The new weight is then found by multiplying this constant mass by the outpost's gravity (

75 \text{ kg} \times 4 \text{ m/s}^2 = 300 \text{ N}

).

Step-by-Step Solution

1

Calculate the module's mass using its weight on Earth.

m = \frac{W}{g} = \frac{750 \text{ N}}{10 \text{ m/s}^2} = 75 \text{ kg}

.

Weight is the product of mass and gravitational acceleration (

W = mg

). Rearranging this formula allows us to find the intrinsic mass.

2

Determine the module's mass at the planetary outpost.

The mass remains

75 \text{ kg}

.

Mass is a measure of the amount of matter in an object. It is an invariant property that does not change when moved to a different gravitational field.

3

Calculate the module's new weight at the planetary outpost.

W_{new} = m \times g_{outpost} = 75 \text{ kg} \times 4 \text{ m/s}^2 = 300 \text{ N}

.

Weight is a force that depends on the local gravitational pull. The new weight must be calculated using the outpost's specific gravitational acceleration.

Key Concept

Mass is an invariant property representing the amount of matter (measured in kilograms), whereas weight is the gravitational force acting on that mass (measured in Newtons) and varies depending on the local gravitational field.

Question 68Question →

A tower crane is lowering a massive concrete beam to the ground. For a brief period, the beam descends at a constant, steady velocity. According to Newton's First Law, what must be true about the primary forces acting on the beam during this steady descent?

The upward tension in the cable exactly equals the downward weight of the beam, resulting in zero net force.

The downward weight of the beam must exceed the upward tension in order to overcome the beam's inertia and maintain its downward motion.

The upward tension in the cable must be exactly equal to the beam's mass to prevent it from accelerating.

The net downward force acting on the beam is proportional to its steady downward velocity.

Show answer & explanation

Answer: The upward tension in the cable exactly equals the downward weight of the beam, resulting in zero net force.

Answer

The upward tension in the cable exactly equals the downward weight of the beam, resulting in zero net force.

According to Newton's First Law, an object in motion will maintain a constant velocity as long as the net external force acting on it is zero. Since the beam descends at a steady, unchanging speed, its acceleration is zero. Therefore, the upward force (cable tension) and the downward force (beam's weight) must be perfectly equal and balanced.

Step-by-Step Solution

1

Identify the object's state of motion described in the scenario.

The concrete beam is moving at a constant, steady velocity.

Determining the state of motion (constant velocity vs. accelerating) is the first step in applying Newton's Laws.

2

Apply Newton's First Law of motion to the object's state.

Because the velocity is constant, the acceleration is zero. Therefore, the net external force acting on the beam must be zero.

Newton's First Law dictates that an object maintains a constant velocity if and only if the forces acting upon it are balanced (net force is zero).

3

Evaluate the specific forces acting on the beam.

The primary forces are the downward force of gravity (weight) and the upward force from the cable (tension). To achieve a net force of zero, these opposing forces must be exactly equal in magnitude.

For vertical forces to cancel out and produce a zero net force, the upward pulls must perfectly equal the downward pulls.

Key Concept

Objects moving in a straight line at a constant velocity have zero acceleration and therefore experience a net force of zero, meaning all opposing forces perfectly balance each other.

Question 69Question →

A compact utility tractor applies a constant net forward force of $1,200 \text{ N}$ to push a stalled passenger vehicle on a level, paved road. If the vehicle accelerates at a rate of $1.5 \text{ m/s}^2$ , what is the mass of the vehicle?

Show answer & explanation

Answer: 800

Answer

800 kg

According to Newton's Second Law (

F=ma

), the mass of an object is equal to the net force acting upon it divided by its acceleration. By dividing the applied net force of

1,200 \text{ N}

by the acceleration of

1.5 \text{ m/s}^2

, we determine the mass of the vehicle is

800 \text{ kg}

.

Step-by-Step Solution

1

Identify the known variables provided in the problem.

Net Force (

F

) =

1,200 \text{ N}

, Acceleration (

a

) =

1.5 \text{ m/s}^2

.

Extracting the given information is the first step to determine which physics formula to apply.

2

State the formula for Newton's Second Law of Motion.

F = ma

This formula establishes the mathematical relationship between net force, mass, and acceleration.

3

Rearrange the formula to solve for the unknown variable, mass (

m

).

m = \frac{F}{a}

To find the mass, it must be isolated algebraically on one side of the equation.

4

Substitute the known values into the rearranged formula and compute the result.

m = \frac{1,200}{1.5} = 800

Executing the division calculation provides the final mass in kilograms.

Key Concept

Newton's Second Law of Motion (F=ma)

Question 70Question →

A $2,000 \text{ kg}$ pickup truck is coasting along a level road at a velocity of $15 \text{ m/s}$ . What is the magnitude of the truck's momentum?

Show answer & explanation

Answer: 30000

Answer

30000

Momentum is directly proportional to both mass and velocity. By multiplying the

2,000 \text{ kg}

mass by the

15 \text{ m/s}

velocity, we determine the total momentum is

30,000 \text{ kg} \cdot \text{m/s}

.

Step-by-Step Solution

1

Identify the known variables from the text.

Mass (

m

) is

2,000 \text{ kg}

and velocity (

v

) is

15 \text{ m/s}

.

Momentum calculation requires both the mass and the velocity of the object.

2

Apply the formula for momentum.

p = m \times v

The linear momentum of an object is defined as the product of its mass and its velocity.

3

Calculate the final value.

p = 2,000 \times 15 = 30,000

Multiplying the mass by the velocity yields the total magnitude of momentum.

Key Concept

Momentum is the product of an object's mass and its velocity (

p = mv

).

Question 71Question →

Based on Newton's First Law (Inertia), match each physical scenario on the left with the correct description of its resulting motion or force balance on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The elevator scenario pairs with passengers continuing downward; the turning vehicle pairs with objects moving in a straight path (appearing to move right); the stationary block pairs with remaining stationary due to no unbalanced forces; and the skydiver pairs with balanced forces resulting in zero net force.

Each pairing correctly applies the principle of inertia to a specific physical system. Newton's First Law explains both why moving objects resist stopping or turning (the elevator and vehicle scenarios) and why objects maintain their current state when forces are balanced (the stationary block and the constant-velocity skydiver).

Step-by-Step Solution

1

Analyze the descending elevator scenario.

Matches with passengers feeling pushed downward.

Newton's First Law states objects in motion stay in motion. The elevator stops, but the passengers' inertia carries them downward momentarily.

2

Analyze the vehicle turning left.

Matches with unsecured objects sliding to the right.

Objects tend to travel in a straight line. As the car turns left underneath them, their straight-line inertia makes them move right relative to the car.

3

Analyze the stationary block on a frictionless table.

Matches with remaining completely stationary.

An object at rest stays at rest unless acted upon by an external force, regardless of the lack of friction.

4

Analyze the skydiver at terminal velocity.

Matches with downward gravity balanced by upward air resistance.

Terminal velocity is a constant speed. A constant speed in a straight line means acceleration is zero, requiring a net force of zero.

Key Concept

Newton's First Law dictates that an object's state of motion (either at rest or moving at a constant velocity) will not change unless an unbalanced external force acts upon it. This resistance to change is known as inertia.

Question 72Question →

An aviation mechanic pushes a loaded tool cart across a level hangar floor. If the mechanic applies a net forward force of $120 \text{ N}$ and the cart accelerates at $2 \text{ m/s}^2$ , what is the mass of the cart?

60 \text{ kg}

240 \text{ kg}

12 \text{ kg}

120 \text{ kg}

Show answer & explanation

Answer: $60 \text{ kg}$

Answer

The mass of the tool cart is

60 \text{ kg}

.

According to Newton's Second Law (

F = ma

), mass is equal to net force divided by acceleration. Dividing

120 \text{ N}

by

2 \text{ m/s}^2

results in

60 \text{ kg}

.

Step-by-Step Solution

1

Identify the given variables from the scenario.

Net force (

F

) =

120 \text{ N}

, Acceleration (

a

) =

2 \text{ m/s}^2

.

These are the known values required to solve for the missing variable.

2

Apply Newton's Second Law of Motion.

The formula is

F = ma

.

This law defines the physical relationship between net force, mass, and acceleration.

3

Rearrange the formula to solve for mass (

m

).

m = \frac{F}{a}

To find the unknown mass, it must be isolated on one side of the equation.

4

Substitute the values and calculate the final result.

m = \frac{120}{2} = 60 \text{ kg}

Performing the division yields the actual mass of the object.

Key Concept

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

F = ma

), meaning an object's mass can be calculated by dividing the net force by its acceleration.

Question 73Question →

A $4,000 \text{ kg}$ empty railcar is rolling along a straight, level track at a velocity of $6 \text{ m/s}$ . It collides and automatically couples with a stationary loaded railcar that has a mass of $8,000 \text{ kg}$ . Assuming no external friction is acting on the railcars, what is the final velocity of the two coupled railcars immediately after the impact?

2 \text{ m/s}

3 \text{ m/s}

6 \text{ m/s}

19.6 \text{ m/s}

Show answer & explanation

Answer: $2 \text{ m/s}$

Answer

The final velocity is

2 \text{ m/s}

.

By the law of conservation of momentum, the total momentum before the collision equals the total momentum after. The initial momentum is

4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

. After the railcars couple, the new total mass is

12,000 \text{ kg}

. Dividing the total momentum by the total mass gives a final velocity of

2 \text{ m/s}

.

Step-by-Step Solution

1

Calculate the total initial momentum of the system.

p_{initial} = 4,000 \text{ kg} \times 6 \text{ m/s} = 24,000 \text{ kg}\cdot\text{m/s}

Because momentum is conserved in the collision, finding the total momentum before impact is required.

2

Determine the total mass of the coupled railcars.

m_{total} = 4,000 \text{ kg} + 8,000 \text{ kg} = 12,000 \text{ kg}

In an inelastic collision where objects couple together, they move as a single combined mass after impact.

3

Calculate the final velocity using the conserved momentum and total mass.

v_{final} = \frac{24,000 \text{ kg}\cdot\text{m/s}}{12,000 \text{ kg}} = 2 \text{ m/s}

Dividing the total conserved momentum by the new total mass isolates the final velocity of the combined system.

Key Concept

Conservation of Momentum in Inelastic Collisions

Question 74Question →

An engineering team is analyzing how different mechanical interactions affect the control and efficiency of an off-road vehicle. Match each vehicle component or scenario to the specific type of frictional resistance it primarily demonstrates.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: stationary tires demonstrate Static Friction; brake pads demonstrate Kinetic Friction; ball bearings demonstrate Rolling Friction; and moving through mud demonstrates Fluid Friction.

Each mechanical scenario perfectly isolates one of the four primary types of friction. Stationary objects resisting motion rely on static friction. Surfaces sliding past one another generate kinetic friction. Round objects moving over a surface experience rolling friction. Objects moving through a liquid or gas encounter fluid friction.

Step-by-Step Solution

1

Analyze the tire scenario

The tires are stationary relative to the rock surface.

Identifying that there is no relative motion points to static friction.

2

Analyze the brake pad scenario

The pads rub directly against the moving steel rotors.

Solid surfaces sliding against each other exhibit kinetic (sliding) friction.

3

Analyze the ball bearing scenario

The bearings roll along their inner and outer races.

Objects rolling over a surface experience rolling friction, which is much lower than sliding friction.

4

Analyze the mud scenario

The vehicle body pushes through a semi-liquid medium.

Moving through liquids or gases involves fluid (viscous) friction.

Key Concept

Types of Frictional Resistance in Mechanics

Question 75Question →

Two detached shipping crates, Crate X ( $200\text{ kg}$ ) and Crate Y ( $800\text{ kg}$ ), are gliding freely across a perfectly level, frictionless warehouse floor. Both crates are traveling in a straight line at a constant velocity of $3\text{ m/s}$ . Which of the following statements is correct regarding their inertia and motion?

Crate Y has four times the inertia of Crate X, meaning it requires four times as much opposing force to stop in the same amount of time.

Crate Y has greater inertia primarily because its larger weight creates a stronger downward force against the floor.

The crates remain in constant motion because their forward action forces are balanced by equal and opposite reaction forces.

If an identical braking force is applied to both crates, Crate Y will decelerate to a stop more rapidly than Crate X.

Show answer & explanation

Answer: Crate Y has four times the inertia of Crate X, meaning it requires four times as much opposing force to stop in the same amount of time.

Answer

Crate Y has four times the inertia of Crate X, meaning it requires four times as much opposing force to stop in the same amount of time.

The correct answer accurately identifies that inertia is entirely a function of mass. Because Crate Y's mass is four times greater than Crate X's mass, its inertia is proportionally larger. As a direct consequence, stopping Crate Y in the identical amount of time as Crate X requires four times the applied opposing force.

Step-by-Step Solution

1

Identify the relevant physics principle governing objects moving at a constant velocity without friction.

Newton's First Law (inertia) applies, indicating that an object's resistance to any change in its motion is entirely dependent on its mass.

The crates are coasting on a frictionless surface with no external driving forces, meaning their behavior is purely a function of inertia.

2

Evaluate and compare the physical properties of the two crates.

Crate Y (

800\text{ kg}

) possesses exactly four times the mass of Crate X (

200\text{ kg}

).

Comparing their mass establishes their relative inertia, as mass is the only measure of inertia.

3

Determine how this difference in inertia affects the external forces required to alter their state of motion.

Because Crate Y has four times the inertia, it takes four times the braking force to achieve the same rate of deceleration as Crate X.

Newton's Second Law (

F = ma

) demonstrates that applied force must scale proportionately with mass to produce the identical acceleration or deceleration.

Key Concept

Inertia is an intrinsic property of matter that depends exclusively on mass, representing an object's natural resistance to any change in its velocity.

Question 76Question →

In the context of Newton's Third Law of Motion, every action force has a specific, equal, and opposite reaction force acting on a different body. Match each described action force on the left with its exact corresponding reaction force on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings strictly follow the A-on-B / B-on-A rule, where the reaction force is always the exact same type of force exerted in the opposite direction by the receiving object back onto the originating object.

According to Newton's Third Law, forces always come in pairs. If body A exerts a force on body B, then body B simultaneously exerts an equal and opposite force on body A. The correct matches precisely swap the 'exerter' and the 'receiver' of the force while maintaining the identical fundamental type of force (gravitational, magnetic, aerodynamic, or mechanical).

Step-by-Step Solution

1

Analyze the action force to identify the two interacting bodies (Object A and Object B).

For example, in the skydiver scenario, Object A is the Earth and Object B is the skydiver.

Newton's Third Law strictly dictates that action and reaction forces must occur between two interacting objects.

2

Identify the type and direction of the force exerted by Object A on Object B.

The Earth exerts a downward gravitational force on the skydiver.

You must know the exact nature of the action force to find its true paired reaction.

3

Reverse the roles of the objects and the direction of the force to find the reaction.

The reaction must be Object B (the skydiver) exerting an upward gravitational force on Object A (the Earth).

Reaction forces are always equal in magnitude, opposite in direction, of the same type, and act on the opposing body.

4

Repeat this reversal process for all given scenarios and select the matching right-side items.

Helicopter on air pairs with air on helicopter; Magnet on steel pairs with steel on magnet; Nozzle on water pairs with water on nozzle.

This guarantees an accurate mapping of all Newton's Third Law pairs without falling for common distractors like balancing forces.

Key Concept

Newton's Third Law (Action/Reaction Pairs)

Question 77Question →

Match each mechanical scenario to its corresponding missing value (net force, mass, or acceleration) using Newton's Second Law ( $F = ma$ ).

Click a left item, then click its matching right item

Show answer & explanation

Answer

Match the scenarios by calculating the missing variable:

10 \text{ kg}

at

3 \text{ m/s}^2

matches

30 \text{ N}

;

100 \text{ N}

at

5 \text{ m/s}^2

matches

20 \text{ kg}

;

25 \text{ kg}

at

50 \text{ N}

matches

2 \text{ m/s}^2

;

200 \text{ kg}

at

4 \text{ m/s}^2

matches

800 \text{ N}

.

The correct matches are found by identifying the two known variables in Newton's Second Law (

F = ma

) for each scenario and algebraically solving for the third unknown variable.

Step-by-Step Solution

1

Calculate the net force for the gear assembly.

F = 10 \text{ kg} \times 3 \text{ m/s}^2 = 30 \text{ N}

Applying the direct formula

F = ma

to find the required force.

2

Calculate the mass of the mechanism.

m = \frac{100 \text{ N}}{5 \text{ m/s}^2} = 20 \text{ kg}

Rearranging the formula to

m = \frac{F}{a}

to solve for mass.

3

Calculate the acceleration of the engine block.

a = \frac{50 \text{ N}}{25 \text{ kg}} = 2 \text{ m/s}^2

Rearranging the formula to

a = \frac{F}{m}

to solve for acceleration.

4

Calculate the net force for the payload.

F = 200 \text{ kg} \times 4 \text{ m/s}^2 = 800 \text{ N}

Applying the direct formula

F = ma

to find the required force.

Key Concept

Newton's Second Law (

F = ma

)

Question 78Question →

In a mechanical system where a solid weight is swung in a horizontal circle on a tether, match each observed physical action or effect with the correct physics terminology.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match the inward pull to centripetal force, the release direction to tangential path, the resistance to turning to inertia, and the outward sensation to the centrifugal effect.

In circular motion, the tether provides an inward centripetal force. Inertia is the mass's resistance to turning, causing the centrifugal effect (outward sensation). If the tether breaks, this inertia carries the mass in a straight tangential path.

Step-by-Step Solution

1

Analyze the inward pulling force described in the first scenario.

Matches with 'Centripetal force'.

By definition, the net inward force keeping an object in circular motion is the centripetal force.

2

Determine the path of the object if the tether breaks.

Matches with 'Tangential path'.

Newton's First Law states an object will move in a straight line if no net force acts upon it, making its path tangent to the circle.

3

Identify the property causing resistance to turning.

Matches with 'Inertia'.

Inertia is the fundamental resistance of mass to any change in its state of motion.

4

Identify the term for the apparent outward push.

Matches with 'Centrifugal effect'.

The sensation of being thrown outward is a perceived effect in a rotating frame, known as the centrifugal effect.

Key Concept

Circular Motion and Centripetal Force

Question 79Question →

A rubber drive belt is slipping on a steel motor pulley because there is insufficient frictional resistance between the two surfaces. Which of the following adjustments will most effectively increase the frictional force to prevent the belt from slipping?

Using a narrower belt to decrease the contact area

Increasing the tension on the drive belt

Replacing the pulley with a heavier one of the same size

Applying a sudden rotational force to use the pulley's inertia

Show answer & explanation

Answer: Increasing the tension on the drive belt

Answer

Increasing the tension on the drive belt

The correct adjustment increases the belt's tension. Friction depends on two main factors: the materials involved (coefficient of friction) and how hard they are pressed together (normal force). In a mechanical drive system, increasing the belt tension pulls the belt tighter around the pulley, directly increasing the normal force pressing inward. This higher normal force generates a proportionally higher static friction, giving the belt better grip to prevent slipping.

Step-by-Step Solution

1

Identify the formula and components of mechanical friction.

The maximum static frictional force is determined by the equation

F_f = \mu F_N

, where

\mu

is the coefficient of friction and

F_N

is the normal force.

Understanding the mathematical relationship reveals which physical variables can be manipulated to change the friction.

2

Determine how normal force is generated in a belt and pulley system.

The normal force (the force pressing the belt perpendicularly into the face of the pulley) is generated by the tension pulling on the ends of the belt.

To increase

F_N

(and thereby increase

F_f

), we must increase the force that squeezes the two components together.

3

Evaluate the given modifications.

Increasing the tension directly increases the normal force. Changing the surface area or pulley mass does not affect the normal force between the mating surfaces.

This confirms that tightening the belt is the mechanically correct method to stop slipping.

Key Concept

Frictional force is directly proportional to the normal force pressing two surfaces together, and in a belt-drive system, this normal force is created by belt tension.

Estimated Time:1m 0s

Question 80Question →

A warehouse automated sorting system applies a constant net horizontal force of $200 \text{ N}$ to a package with a mass of $50 \text{ kg}$ . What is the resulting acceleration of the package?

4 \text{ m/s}^2

0.25 \text{ m/s}^2

40 \text{ m/s}^2

10,000 \text{ m/s}^2

Show answer & explanation

Answer: $4 \text{ m/s}^2$

Answer

The resulting acceleration of the package is

4 \text{ m/s}^2

.

According to Newton's Second Law (

F = ma

), acceleration is calculated by dividing the applied net force by the object's mass. Dividing

200 \text{ N}

by

50 \text{ kg}

correctly results in

4 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the known variables provided in the problem.

Net Force (

F

) =

200 \text{ N}

; Mass (

m

) =

50 \text{ kg}

.

Correctly identifying the givens ensures the proper values are placed into the physics formula.

2

State Newton's Second Law of Motion and rearrange it to solve for acceleration.

The formula

F = ma

becomes

a = \frac{F}{m}

.

The question asks for the resulting acceleration, so the formula must isolate

a

.

3

Substitute the known values into the rearranged formula and calculate the result.

a = \frac{200}{50} = 4 \text{ m/s}^2

.

Executing the division yields the final acceleration value in standard metric units.

Key Concept

Newton's Second Law (

F = ma

) demonstrates that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Estimated Time:30s

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