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

Question 1Question →

In a vacuum chamber where there is no air resistance, a 10-pound iron ball and a 1-pound wooden block are dropped simultaneously from exactly the same height. Which of the following statements correctly describes their fall?

The wooden block will hit the ground first because it requires less force to accelerate.

The iron ball will hit the ground first because it has a greater mass.

Both objects will accelerate at the same rate and hit the ground at the exact same time.

The iron ball will hit the ground first because it experiences a stronger downward pull from gravity.

Show answer & explanation

Answer: Both objects will accelerate at the same rate and hit the ground at the exact same time.

Answer

Both objects will accelerate at the same rate and hit the ground at the exact same time.

In the absence of air resistance, the only force acting on the objects is gravity. Gravity provides a constant acceleration to all objects, independent of their mass. Therefore, both the heavy iron ball and the light wooden block will fall at exactly the same rate and hit the ground simultaneously.

Step-by-Step Solution

1

Identify the environment and conditions.

The objects are dropped in a vacuum chamber, meaning there is no air resistance.

Air resistance is the primary factor that causes objects of different shapes and masses to fall at different rates in everyday situations.

2

Apply the principles of free fall gravity.

Gravity causes all objects to accelerate downwards at a constant rate, regardless of their mass.

The acceleration due to gravity is independent of an object's mass. Although a heavier object has a greater gravitational force acting on it, it also has more inertia, so the resulting acceleration is identical.

Key Concept

In a vacuum, the acceleration due to gravity is constant for all objects, meaning they will fall at the same rate regardless of their mass.

Estimated Time:30s

Question 2Question →

Match each physical scenario with the correct principle of Newton's First Law (Inertia) that it best demonstrates.

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Answer

The passenger in a braking car matches maintaining forward velocity in a decelerating frame; the freight train matches high mass causing high inertia; the deep space wrench matches dynamic equilibrium with no net forces; the tablecloth trick matches a stationary object's resistance to acceleration.

Each scenario isolates a distinct application of inertia: inertia of motion relative to a slowing frame (passenger), the mass-dependency of inertia (freight train), motion in the complete absence of external forces (space wrench), and inertia of rest against brief frictional forces (tablecloth).

Step-by-Step Solution

1

Analyze the passenger braking scenario to determine the state of motion.

The passenger is moving at a constant speed, and the vehicle frame slows down, causing apparent forward motion.

Identifying the reference frame is crucial to understanding why the passenger appears to lurch forward.

2

Evaluate the freight train scenario in relation to the object's physical properties.

The key variable is the train's massive weight and mass, which makes it extremely difficult to stop.

This establishes the direct relationship between mass and the magnitude of inertia.

3

Determine the net forces acting on the wrench in deep space.

There are zero net external forces acting on the wrench, resulting in constant velocity.

This applies Newton's First Law in a purely frictionless, zero-gravity environment.

4

Analyze the initial state and forces in the tablecloth scenario.

The dishes are at rest, and the rapid pull minimizes the time friction can act to move them.

This demonstrates inertia of rest and the role of force duration.

Key Concept

Newton's First Law dictates that an object's state of motion (or rest) remains unchanged unless acted upon by a net external force, with the object's mass serving as the measure of its resistance to such changes (inertia).

Question 3Question →

Match each practical mechanical scenario or design observation to the fundamental principle of friction and resistance that best explains it.

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Answer

The locked wheels scenario pairs with area independence; the bearing replacement pairs with the advantage of rolling resistance over sliding; the accelerating crate pairs with the static friction threshold being overcome by kinetic friction; and the submersible's power demand pairs with the non-linear scaling of fluid drag.

Each scenario perfectly illustrates a unique property of friction: area independence for kinetic sliding, the mechanical advantage of rolling over sliding, the maximum threshold of static resistance transitioning to kinetic, and the velocity-dependent nature of fluid drag.

Step-by-Step Solution

1

Analyze the tire width scenario.

Identify that changing tire width alters contact area but not vehicle weight or normal force.

The kinetic friction formula (

F_k = \mu_k N

) shows that resistance depends strictly on normal force and material coefficient, not surface area.

2

Analyze the bearing replacement scenario.

Recognize the mechanical shift from a journal (sliding) bearing to a ball (rolling) bearing.

Rolling friction coefficients are fundamentally much smaller than sliding kinetic friction coefficients, significantly reducing heat and energy loss.

3

Analyze the sliding crate scenario.

Identify the transition state from stationary to moving.

Static friction resists movement up to a maximum limit (

F_{s(max)} = \mu_s N

). Once this is broken, the typically lower kinetic friction takes over, resulting in a sudden net force that causes acceleration.

4

Analyze the submersible speed scenario.

Identify that motion occurs through a fluid medium (water).

Unlike dry kinetic friction which is relatively constant across speeds, fluid drag increases with the square of the velocity, requiring exponentially more power at higher speeds.

Key Concept

Principles of Static, Kinetic, Rolling, and Fluid Friction

Question 4Question →

Based on Newton's First Law of motion, how does an unbelted passenger's body tend to react relative to a vehicle in various situations? Pair each specific vehicle maneuver with the passenger's corresponding initial directional tendency.

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Answer

Braking pairs with sliding forward; accelerating pairs with pressing backward; turning left pairs with leaning right; and steady cruising pairs with no directional change.

Each pair correctly applies the concept of inertia. A passenger's body will always resist changes in the vehicle's speed or direction, maintaining its current state of motion or rest until an unbalanced force acts upon it.

Step-by-Step Solution

1

Analyze the sudden braking scenario.

The passenger's body tends to slide or lean forward.

Due to inertia, an object in motion tends to stay in motion. The car slows, but the passenger's body wants to continue at its original speed.

2

Analyze the rapid acceleration scenario.

The passenger's body is pressed backward into the seat.

An object at rest tends to stay at rest. As the car shoots forward, the passenger's mass resists the forward motion, causing them to lag behind.

3

Analyze the sharp left turn scenario.

The passenger's body tends to slide or lean to the right.

Objects in motion tend to move in a straight line. The car curves left, but the body attempts to travel straight, appearing to move right relative to the vehicle's interior.

4

Analyze the steady cruising scenario.

The passenger's body experiences no change in perceived direction.

With a constant velocity and no change in direction, the net force is zero, and the body remains in equilibrium with the car.

Key Concept

Newton's First Law (Inertia)

Question 5Question →

An engineer simultaneously launches a $1\text{ kg}$ testing sphere and a $5\text{ kg}$ testing sphere vertically upward with the exact same initial velocity. At the precise instant they reach their maximum heights (apexes), which of the following statements accurately describes their vertical accelerations? (Assume $g = 9.8\text{ m/s}^2$ and ignore air resistance).

The

5\text{ kg}

sphere experiences a greater downward acceleration because its heavier weight exerts a stronger pull.

Both spheres experience a downward acceleration of

0\text{ m/s}^2

because they are momentarily stationary.

The

1\text{ kg}

sphere experiences a greater downward acceleration because its smaller mass provides less inertia against gravity.

Both spheres experience a constant downward acceleration of

9.8\text{ m/s}^2

.

Show answer & explanation

Answer: Both spheres experience a constant downward acceleration of $9.8\text{ m/s}^2$ .

Answer

Both spheres experience a constant downward acceleration of

9.8\text{ m/s}^2

.

In the absence of air resistance, the acceleration due to gravity (

g

) is constant for all objects, regardless of their mass. When an object reaches its highest point, its velocity is momentarily zero, but the gravitational force continues to pull on it without interruption, causing a constant downward acceleration of

9.8\text{ m/s}^2

.

Step-by-Step Solution

1

Analyze the forces acting on the spheres at the apex.

Gravity is the only force acting on both spheres, meaning they are in a continuous state of free fall.

Because air resistance is ignored, gravitational pull is the sole factor determining acceleration throughout the entire flight.

2

Determine the effect of mass on gravitational acceleration.

The acceleration due to gravity is independent of an object's mass.

Although a heavier object experiences a greater gravitational force (weight), it also has proportionally more inertia (mass). These factors cancel out (

a = F/m

), resulting in the same constant acceleration of

9.8\text{ m/s}^2

for both spheres.

3

Evaluate the effect of momentary zero velocity on acceleration.

Acceleration remains

9.8\text{ m/s}^2

downward even when vertical velocity is momentarily

0\text{ m/s}

.

Acceleration is the rate of change of velocity. Gravity continuously changes the upward velocity to a downward velocity, passing through zero without the acceleration itself ever dropping to zero.

Key Concept

Constant Gravitational Acceleration in Free Fall

Question 6Question →

A mechanic swings a $2 \text{ lb}$ hammer, striking a $100 \text{ lb}$ stationary steel anvil. During the brief fraction of a second of contact, the hammer rapidly decelerates to a stop while the anvil remains practically motionless. Which of the following statements correctly compares the interaction forces between the hammer and the anvil during the exact moment of impact?

The force the hammer exerts on the anvil is exactly equal in magnitude to the force the anvil exerts on the hammer.

The anvil exerts a greater force on the hammer because the hammer undergoes a much larger change in acceleration during the impact.

The hammer exerts a greater force on the anvil because the heavy mass and inertia of the anvil prevent it from generating an equal reaction force.

The forces would only be equal if both objects had the same mass; otherwise, the object with greater mass exerts the dominant force.

Show answer & explanation

Answer: The force the hammer exerts on the anvil is exactly equal in magnitude to the force the anvil exerts on the hammer.

Answer

The force the hammer exerts on the anvil is exactly equal in magnitude to the force the anvil exerts on the hammer.

According to Newton's Third Law of Motion, forces always occur in equal and opposite pairs. When the hammer strikes the anvil, the interaction consists of the hammer pushing on the anvil and the anvil pushing on the hammer. These two forces are simultaneously created and are always perfectly equal in magnitude, regardless of the fact that the anvil is

50

times heavier than the hammer or that the hammer is rapidly decelerating. The difference in their observed movement is due to their differing masses (Newton's Second Law), not a difference in the force applied.

Step-by-Step Solution

1

Identify the two interacting bodies in the mechanical system.

The interacting bodies are the

2 \text{ lb}

hammer and the

100 \text{ lb}

anvil.

Newton's Third Law always applies to the mutual interaction between exactly two distinct objects.

2

Apply Newton's Third Law to the specific moment of impact.

The force of the hammer on the anvil (

F_{H \to A}

) must equal the negative force of the anvil on the hammer (

-F_{A \to H}

).

For every action force, there is an equal and opposite reaction force, regardless of mass or velocity.

3

Differentiate between the interaction force and the resulting acceleration.

Both objects experience the exact same magnitude of force, but the hammer decelerates rapidly because it has a much smaller mass.

Newton's Second Law (

F = ma

) explains the differing accelerations, while Newton's Third Law dictates the equal forces.

Key Concept

Action and reaction forces between two interacting bodies are always perfectly equal in magnitude and opposite in direction, entirely independent of the objects' masses or rates of acceleration.

Estimated Time:1m 30s

Question 7Question →

Based on Newton's First Law of Motion (Inertia), how does each object behave in its respective environment? Match each physical scenario on the left with the correct description of its resulting motion or behavior on the right.

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Answer

The satellite matches with maintaining a constant trajectory (no net force); the astronaut matches with shifting right relative to the cabin (inertia of direction); the water droplet matches with flying off in a straight tangent line (removal of centripetal force); and the granite block matches with exhibiting extreme resistance to motion (high mass means high inertia).

Each correct pairing directly applies Newton's First Law (Inertia) to distinct physical environments. Objects free of external forces (the satellite) travel at constant velocity. Objects in accelerating reference frames (the turning spacecraft) appear to move opposite the acceleration because they maintain their straight-line inertia. Objects released from circular paths (the droplet) travel straight tangentially. Finally, massive objects (the granite block) inherently resist acceleration due to their large mass, which is completely independent of surface friction.

Step-by-Step Solution

1

Analyze the deep-space satellite scenario.

It experiences zero net external forces (no gravity, no drag).

According to the First Law, an object with no net force acting upon it will maintain a constant velocity (speed and direction) indefinitely.

2

Analyze the astronaut in the turning spacecraft.

The spacecraft accelerates to the left, but no lateral force acts directly on the unbelted astronaut.

The astronaut's inertia keeps them moving in their original straight line, making them appear to 'fall' toward the right wall of the turning ship.

3

Analyze the detaching water droplet.

The physical connection providing inward (centripetal) force is broken.

Without a net force pulling it into a curve, the droplet obeys inertia and continues in a straight line tangent to its path.

4

Analyze the stationary granite block on a frictionless surface.

Friction is zero, but the object's mass is extremely high.

Mass is the physical measure of inertia; greater mass means greater intrinsic resistance to acceleration, regardless of friction.

Key Concept

Inertia is the inherent tendency of an object to resist changes to its state of motion or rest. This resistance is directly proportional to the object's mass and dictates that an object will maintain a constant velocity unless acted upon by a net external force.

Question 8Question →

According to Newton's Third Law of Motion, mechanical forces always occur in equal and opposite action-reaction pairs acting on different objects. Match each described action force in the left column to its corresponding reaction force in the right column.

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Answer

The correct matches pair the action force on the second object with an equal and opposite reaction force acting back on the first object. Worker's boots pair with the concrete floor's forward friction. The hammer head pairs with the nail's upward contact force. The locomotive wheel pairs with the track's forward force. The electromagnet pairs with the iron block's downward magnetic pull.

According to Newton's Third Law, for every action force there is an equal and opposite reaction force. These forces must act on two different, interacting bodies. By identifying the two bodies in the action (e.g., boots pushing on the floor), the exact reaction is simply the reverse physical interaction (the floor pushing on the boots).

Step-by-Step Solution

1

Identify the two interacting objects in each action force description.

The identified pairs are: boots/floor, hammer/nail, wheel/track, and electromagnet/block.

Newton's Third Law states that forces only exist in pairs between exactly two interacting bodies.

2

Determine the direction of the original action force.

The action directions are backward (boots), downward (hammer), backward (wheel), and upward (magnet).

The reaction force must be in the exact opposite direction of the action force.

3

Locate the corresponding reaction force that acts on the first object in the opposite direction.

Boots receive a forward force; the hammer receives an upward force; the wheel receives a forward force; the magnet receives a downward force.

Reaction forces act on the source object, opposite to the action force's direction.

Key Concept

Newton's Third Law of Motion (Action and Reaction Forces)

Estimated Time:1m 30s

Question 9Question →

A tugboat is pushing a heavy cargo barge steadily forward through a shipping channel. The bow of the tugboat is in direct contact with the stern of the barge, exerting a constant forward pushing force of $10,000 \text{ N}$ on the barge. According to Newton's Third Law of Motion, which of the following accurately describes the reaction force in this specific mechanical interaction?

The barge exerts a

10,000 \text{ N}

backward pushing force directly against the bow of the tugboat.

The barge exerts a backward force greater than

10,000 \text{ N}

on the tugboat because the barge has a significantly larger mass.

The surrounding water exerts a

10,000 \text{ N}

backward fluid drag force on the barge to maintain a constant speed.

The barge generates an internal resistance of

10,000 \text{ N}

that cancels out the tugboat's applied force within the same body.

Show answer & explanation

Answer: The barge exerts a $10,000 \text{ N}$ backward pushing force directly against the bow of the tugboat.

Answer

The barge exerts a

10,000 \text{ N}

backward pushing force directly against the bow of the tugboat.

The correct answer accurately applies the principle that interacting objects exert equal and opposite forces on each other. If the tugboat pushes the barge forward with a specific force, the barge simultaneously pushes the tugboat backward with the exact same amount of force.

Step-by-Step Solution

1

Identify the primary action force and the two interacting bodies described in the scenario.

The action force is the tugboat pushing forward on the barge with

10,000 \text{ N}

. The two interacting bodies are the tugboat and the barge.

Newton's Third Law applies specifically to a pair of interacting objects.

2

Determine the magnitude and direction of the reaction force.

The reaction force must be exactly equal in magnitude (

10,000 \text{ N}

) and exactly opposite in direction (backward).

According to the law of action and reaction, forces always occur in equal and opposite pairs.

3

Identify which body the reaction force acts upon.

Since the tugboat acts on the barge, the barge must act back on the tugboat.

Action and reaction forces act on different bodies, never on the same body.

Key Concept

Newton's Third Law states that forces occur in simultaneous pairs acting on different objects with equal magnitude and opposite direction.

Estimated Time:1m 0s

Question 10Question →

A fighter jet is launched from an aircraft carrier's catapult system. The jet accelerates from rest to a takeoff speed of $180 \text{ km/h}$ in exactly $2.5 \text{ seconds}$ . Assuming the acceleration is constant, what is the magnitude of the jet's average acceleration in $\text{m/s}^2$ ?

72 \text{ m/s}^2

125 \text{ m/s}^2

20 \text{ m/s}^2

0.05 \text{ m/s}^2

Show answer & explanation

Answer: $20 \text{ m/s}^2$

Answer

20 \text{ m/s}^2

Acceleration is the rate of change of velocity over time. To solve this problem, the final velocity must first be converted from kilometers per hour to standard SI units (meters per second). Multiplying

180 \text{ km/h}

by

\frac{1000}{3600}

gives

50 \text{ m/s}

. Since the jet starts from rest, the change in velocity is

50 \text{ m/s}

. Dividing this change by the total time of

2.5 \text{ seconds}

yields an average acceleration of

20 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given variables and the target unit.

Initial velocity

v_i = 0

, final velocity

v_f = 180 \text{ km/h}

, time

t = 2.5 \text{ s}

. Target unit is

\text{m/s}^2

.

Establishing knowns and units is required to select the correct formula and conversions.

2

Convert the final velocity from

\text{km/h}

to

\text{m/s}

.

180 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 50 \text{ m/s}

.

Standard kinematics formulas require consistent SI units (meters and seconds) before calculating acceleration.

3

Apply the average acceleration formula.

a = \frac{\Delta v}{t} = \frac{50 \text{ m/s} - 0 \text{ m/s}}{2.5 \text{ s}}

.

Acceleration is defined as the rate of change of velocity over time.

4

Calculate the final magnitude.

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

.

Dividing

50

by

2.5

yields the constant acceleration rate.

Key Concept

Calculating average acceleration utilizing consistent unit conversions.

Question 11Question →

According to the principle of action and reaction, interacting objects apply forces to one another. Pair the following initial mechanical forces with their direct reaction forces.

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Answer

The correct pairings directly flip the interacting objects and reverse the direction of the force. The jet engine pushing gas backward matches with gas pushing the engine forward. The swimmer pushing the wall backward matches with the wall pushing the swimmer forward. The blades pushing air downward matches with air pushing the blades upward. The hose pushing water forward matches with water pushing the hose backward.

Each correct match demonstrates Newton's Third Law by identifying the exact same two interacting bodies from the action statement, reversing their roles as the object applying the force and the object receiving the force, and reversing the physical direction of that force.

Step-by-Step Solution

1

Identify the two interacting objects in each initial force description.

In the jet engine scenario, the objects are the engine and the exhaust gases. In the swimmer scenario, they are the feet and the wall. In the helicopter scenario, they are the blades and the air. In the fire hose scenario, they are the hose and the water.

Newton's Third Law always involves two distinct objects interacting with one another.

2

Identify the physical direction of the applied initial force.

The initial forces are directed backward (gas), backward (wall), downward (air), and forward (water).

Reaction forces act in the exact opposite direction of the initial action force.

3

Formulate the reaction force by swapping the objects and reversing the direction.

The correct reactions are: gas pushing engine forward, wall pushing feet forward, air pushing blades upward, and water pushing hose backward.

If the first object exerts a force on the second object, the second object must exert an equal and opposite force on the first object.

Key Concept

For every action force, there is a simultaneous reaction force that is equal in magnitude, opposite in direction, and acts on a different object.

Estimated Time:1m 0s

Question 12Question →

A spacecraft hovers above a moon with no atmosphere. An astronaut drops a $5\text{ kg}$ tool from rest and observes that it takes exactly $4\text{ seconds}$ to fall $32\text{ meters}$ to the surface. Later, the astronaut drops a $10\text{ kg}$ piece of equipment from the exact same height. What is the weight of the $10\text{ kg}$ equipment on this moon, and how long will it take to reach the surface?

Weight is

40\text{ N}

; fall time is

4\text{ s}

Weight is

10\text{ kg}

; fall time is

4\text{ s}

Weight is

100\text{ N}

; fall time is

4\text{ s}

Weight is

40\text{ N}

; fall time is

2\text{ s}

Show answer & explanation

Answer: Weight is $40\text{ N}$ ; fall time is $4\text{ s}$

Answer

The weight of the equipment is

40\text{ N}

, and it will take

4\text{ s}

to fall.

The correct answer accurately calculates the moon's gravity as

4\text{ m/s}^2

using the first object's fall data. It then applies this gravity to find the second object's weight (

10\text{ kg} \times 4\text{ m/s}^2 = 40\text{ N}

) and correctly applies the principle that in a vacuum, mass does not affect fall time, resulting in the same

4\text{ s}

duration.

Step-by-Step Solution

1

Calculate the acceleration due to gravity on the moon using the kinematic equation

d = \frac{1}{2}at^2

.

32 = 0.5 \times a \times (4^2) \rightarrow 32 = 8a \rightarrow a = 4\text{ m/s}^2

.

The local acceleration must be known to determine the weight of the second object.

2

Determine the weight of the

10\text{ kg}

equipment on the moon.

W = m \times a = 10 \times 4 = 40\text{ N}

.

Weight is the force of gravity exerted on a mass in a specific gravitational field.

3

Determine the fall time for the

10\text{ kg}

equipment.

The fall time is

4\text{ s}

.

In a vacuum (no atmosphere), all objects accelerate downward at the exact same rate regardless of their mass.

Key Concept

Free fall kinematics and the distinction between mass and weight

Estimated Time:2m 0s

Question 13Question →

A $50\text{-kg}$ solid iron block and a $10\text{-kg}$ solid iron block are dropped simultaneously from a height of $100\text{ m}$ inside a large vacuum chamber. Which of the following statements correctly describes the acceleration of the two blocks as they fall?

Both blocks will experience an identical downward acceleration of approximately

9.8 \text{ m/s}^2

.

The

50\text{-kg}

block will accelerate five times faster than the

10\text{-kg}

block due to its greater mass.

Both blocks will experience an identical downward acceleration of approximately

9.8 \text{ km/h}^2

.

The

50\text{-kg}

block will accelerate at

490 \text{ m/s}^2

and the

10\text{-kg}

block at

98 \text{ m/s}^2

.

Show answer & explanation

Answer: Both blocks will experience an identical downward acceleration of approximately $9.8 \text{ m/s}^2$ .

Answer

Both blocks will experience an identical downward acceleration of approximately

9.8 \text{ m/s}^2

.

In the absence of air resistance, all objects near Earth's surface fall with the same constant acceleration due to gravity, which is roughly

9.8 \text{ m/s}^2

. Although the

50\text{-kg}

block experiences a stronger gravitational force (weight), it also has proportionally more inertia resisting motion. These two factors perfectly balance each other out, resulting in an identical rate of acceleration for both blocks.

Step-by-Step Solution

1

Identify the forces acting on the objects during their fall in the vacuum chamber.

The only force acting on both blocks is the gravitational pull of the Earth (their weight).

Because the chamber is a vacuum, air resistance is completely eliminated.

2

Apply Newton's Second Law of Motion (

F = ma

) to determine the rate of acceleration.

Acceleration (

a

) is equal to the force of gravity divided by the mass of the object (

a = \frac{F}{m}

).

This formula shows the relationship between the downward force, the object's inertia, and its resulting acceleration.

3

Calculate the theoretical acceleration for both masses.

Since the force of gravity (

F

) is equal to mass times gravitational acceleration (

F = m \times g

), the formula simplifies to

a = \frac{m \times g}{m}

, which means

a = g

.

The mass variable cancels itself out mathematically, proving that acceleration due to gravity is independent of an object's mass.

Key Concept

In a vacuum, all objects experience free fall at the exact same rate of gravitational acceleration, roughly

9.8 \text{ m/s}^2

, because their proportionally greater weight is perfectly offset by their proportionally greater inertia.

Question 14Question →

Arrange the following stages of a skydiver's descent from an aircraft to the ground in the correct chronological order.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence starts with initial downward acceleration, followed by increasing air resistance, reaching a constant terminal velocity, and finally parachute deployment to decelerate.

The sequence accurately describes the physical forces during an atmospheric free fall. Initially, gravity causes acceleration. As speed increases, so does opposing air resistance. Eventually, air resistance equals the gravitational force, resulting in a constant speed known as terminal velocity. Finally, deploying a parachute increases surface area, creating excess drag to rapidly decelerate the skydiver.

Step-by-Step Solution

1

Identify the initial state of the fall.

The skydiver steps out and accelerates downward.

At the start of the fall, speed is very low, so gravity is the dominant force causing an initial downward acceleration.

2

Determine what happens as the skydiver's downward speed increases.

Upward air resistance grows.

Air resistance (drag) increases proportionally as the speed of the falling object moving through the atmosphere increases.

3

Identify the state where the forces eventually balance.

Air resistance balances gravity, leading to a constant speed.

This state is known as terminal velocity. The net force becomes zero, meaning acceleration stops and the skydiver falls at a steady rate.

4

Identify the final stage required before safely reaching the ground.

The parachute is deployed to slow the fall.

Deploying the parachute vastly increases the surface area, which temporarily makes air resistance much greater than gravity, safely decelerating the descent.

Key Concept

Gravity, Air Resistance, and Terminal Velocity

Question 15Question →

A cargo aircraft accelerates from rest to a final velocity of $90 \text{ m/s}$ in exactly $3 \text{ minutes}$ . What is the average acceleration of the aircraft in $\text{m/s}^2$ ?

30 \text{ m/s}^2

2.0 \text{ m/s}^2

0.5 \text{ m/s}^2

270 \text{ m/s}^2

Show answer & explanation

Answer: $0.5 \text{ m/s}^2$

Answer

The average acceleration of the aircraft is

0.5 \text{ m/s}^2

.

The correct average acceleration is found by first converting the given time of 3 minutes into 180 seconds. Then, using the kinematic formula for acceleration (change in velocity divided by time), dividing the final velocity of

90 \text{ m/s}

by 180 seconds results in

0.5 \text{ m/s}^2

.

Step-by-Step Solution

1

Convert the time from minutes to seconds.

3 \text{ minutes} \times 60 \text{ seconds/minute} = 180 \text{ seconds}

.

Acceleration is requested in

\text{m/s}^2

, so the time variable must be in seconds.

2

Apply the formula for average acceleration:

a = \frac{v_f - v_i}{t}

.

a = \frac{90 \text{ m/s} - 0 \text{ m/s}}{180 \text{ s}}

.

This formula determines the rate of change of velocity over the given time period.

3

Calculate the final acceleration value.

a = 0.5 \text{ m/s}^2

.

Dividing

90

by

180

yields

0.5

.

Key Concept

Calculating average acceleration requiring unit conversion.

Question 16Question →

A specialized rover is designed to operate on both Earth (where gravitational acceleration is $10\text{ m/s}^2$ ) and an exoplanet (where gravitational acceleration is $15\text{ m/s}^2$ ). The rover carries a scientific payload that is measured to have a weight of $600\text{ N}$ on Earth. When the rover arrives on the exoplanet, it suspends the payload from a spring scale to verify its properties, and later pushes the payload horizontally across a frictionless ice field to accelerate it at $4\text{ m/s}^2$ . What will the spring scale read, and what horizontal force must the rover apply?

Spring scale:

900\text{ N}

; Horizontal force:

240\text{ N}

Spring scale:

900\text{ N}

; Horizontal force:

3600\text{ N}

Spring scale:

9000\text{ N}

; Horizontal force:

2400\text{ N}

Spring scale:

900\text{ N}

; Horizontal force:

15\text{ N}

Show answer & explanation

Answer: Spring scale: $900\text{ N}$ ; Horizontal force: $240\text{ N}$

Answer

Spring scale:

900\text{ N}

; Horizontal force:

240\text{ N}

The payload's mass is an invariant property, calculated from its Earth weight (

m = \frac{W}{g} = \frac{600}{10} = 60\text{ kg}

). On the exoplanet, the spring scale measures the local gravitational force (weight), which is mass times local gravity (

60 \times 15 = 900\text{ N}

). The horizontal force depends only on the invariant mass and the desired acceleration (

F = ma = 60 \times 4 = 240\text{ N}

).

Step-by-Step Solution

1

Determine the invariant mass of the payload using its Earth weight.

m = \frac{W_{\text{Earth}}}{g_{\text{Earth}}} = \frac{600\text{ N}}{10\text{ m/s}^2} = 60\text{ kg}

Mass is the amount of matter and remains constant regardless of location. It is required to determine both the new weight and the horizontal force.

2

Calculate the new weight on the exoplanet to find the spring scale reading.

W_{\text{exo}} = m \times g_{\text{exo}} = 60\text{ kg} \times 15\text{ m/s}^2 = 900\text{ N}

A spring scale measures the local force of gravity (weight), which depends on the local gravitational acceleration.

3

Calculate the required horizontal force using Newton's Second Law.

F = m \times a = 60\text{ kg} \times 4\text{ m/s}^2 = 240\text{ N}

Horizontal acceleration on a frictionless surface depends only on the object's mass (inertia) and the applied force, not on its weight.

Key Concept

Mass is an invariant property that determines inertia and relates to force (

F=ma

), while weight is a location-dependent gravitational force (

W=mg

) measured by spring scales.

Question 17Question →

Arrange the following stages of a skydiver's jump in chronological order, starting from the moment they step out of a hovering helicopter until just before they touch the ground.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence follows the progression of forces: maximum initial acceleration, decreasing acceleration as drag builds, first terminal velocity, rapid deceleration upon parachute deployment, and finally a second, slower terminal velocity.

A falling object initially accelerates under gravity alone. As its velocity increases, air resistance grows until it perfectly opposes gravity, resulting in a constant terminal velocity. Deploying a parachute drastically increases the surface area, creating a temporary net upward force that slows the fall until a new, slower terminal velocity is established for a safe landing.

Step-by-Step Solution

1

Analyze the initial phase of the jump.

Identify that at the moment of the jump, velocity is zero.

Without velocity, there is no air resistance. Gravity is the only force, causing maximum acceleration.

2

Evaluate the effect of increasing speed.

Determine that accelerating downwards causes air resistance to grow.

Air drag is proportional to velocity. As drag increases, it opposes gravity, reducing the net downward acceleration.

3

Identify the first equilibrium state.

Recognize that terminal velocity is reached when air resistance equals gravity.

When the net force is zero, Newton's first law dictates that acceleration stops and velocity becomes constant.

4

Assess the impact of parachute deployment.

Identify that the parachute causes a massive, sudden increase in air drag.

The drag force temporarily exceeds the gravitational force, creating an upward net force that rapidly slows the downward fall.

5

Determine the final state before landing.

Conclude that a new equilibrium is reached at a much slower speed.

As the skydiver slows down, the drag on the parachute decreases until it balances gravity once more.

Key Concept

The relationship between gravity, air resistance, and terminal velocity during free fall.

Question 18Question →

A skydiver jumps from a stationary hot air balloon. Arrange the following moments of the jump in order of the skydiver's acceleration, starting from the greatest downward acceleration and ending with the greatest upward acceleration.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence tracks the decreasing downward acceleration: immediately after jumping (maximum downward), followed by several seconds into the fall (reduced downward), then falling at terminal velocity (zero acceleration), and finally the moment the parachute inflates (strong upward acceleration).

The correct sequence tracks the net force acting on the skydiver. Initially, only gravity acts, causing maximum downward acceleration. As speed increases, upward air drag grows, reducing the net downward force and acceleration. At terminal velocity, drag equals weight, making net force and acceleration zero. When the parachute opens, drag vastly exceeds weight, creating a net upward force and thus an upward acceleration.

Step-by-Step Solution

1

Analyze the forces acting immediately after the jump.

Velocity is zero, so air drag is zero. The only force is gravity, resulting in the maximum downward acceleration of approximately 9.8 m/s².

Air drag depends on velocity. Without velocity, there is no drag to oppose gravity.

2

Evaluate the forces during the middle of the fall before terminal velocity.

As the skydiver speeds up, upward air drag increases. The net downward force becomes less than gravity, so downward acceleration is less than 9.8 m/s².

Net force equals weight minus air drag. As drag increases, net force decreases, reducing acceleration according to Newton's Second Law.

3

Identify the conditions at terminal velocity.

Upward air drag exactly equals downward weight. The net force is zero, meaning acceleration is exactly 0 m/s².

Terminal velocity is reached when opposing forces balance out completely, ending any change in speed.

4

Assess the moment the parachute inflates.

The huge surface area creates an upward air drag much greater than the downward weight. The net force points upward, creating a strong upward acceleration.

A net upward force is required to rapidly decrease the downward velocity to a safe landing speed.

Key Concept

The relationship between gravity, air resistance, and net acceleration during free fall through an atmosphere.

Question 19Question →

In mechanical engineering, understanding the dominant forces at contact interfaces is critical for system design. Match each practical mechanical scenario to the primary type of friction or resistance that governs its operation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The conveyor belt pairs with Static Friction; the skidding tire pairs with Kinetic (Sliding) Friction; the oil-supported crankshaft pairs with Viscous/Fluid Resistance; and the steel spheres pair with Rolling Resistance.

Each mechanical scenario operates under a distinct physical resistance mechanism. Static friction transfers torque when parts move together without slipping. Kinetic friction dominates during sliding events like skidding. Viscous resistance occurs when fluids separate moving parts, and rolling resistance occurs due to material deformation in rolling elements.

Step-by-Step Solution

1

Analyze the contact interface of the conveyor belt.

Identify that the belt does not slip against the drive pulley.

Since the surfaces are stationary relative to one another at the point of contact, the force transferring the torque is static friction.

2

Analyze the state of the skidding automotive tire.

Identify that the rubber is actively sliding across the asphalt.

Sliding motion between two dry solid surfaces is always characterized by kinetic (sliding) friction.

3

Analyze the hydrodynamic journal bearing supporting the crankshaft.

Identify that a pressurized oil film entirely separates the solid components.

Because there is no solid-to-solid contact, the resistance to rotation is purely the viscous drag of the fluid.

4

Analyze the spheres in the high-speed wheel hub.

Identify that the spheres roll along the raceway rather than sliding.

The continuous micro-deformation of the materials as they roll creates energy loss, which defines rolling resistance.

Key Concept

Identifying applied frictional forces in complex mechanical systems

Estimated Time:1m 30s

Question 20Question →

A stationary drone drops a $5\text{ kg}$ supply package from a high altitude. Ignoring air resistance and assuming the acceleration due to gravity is $10\text{ m/s}^2$ , what is the downward velocity of the package after it has been falling for exactly $4\text{ seconds}$ ?

80\text{ m/s}

50\text{ m/s}

40\text{ m/s}

8\text{ m/s}

Show answer & explanation

Answer: $40\text{ m/s}$

Answer

The downward velocity of the package is

40\text{ m/s}

.

In free fall without air resistance, velocity increases at a constant rate equal to gravitational acceleration, regardless of mass. Multiplying the acceleration (

10\text{ m/s}^2

) by the time (

4\text{ seconds}

) gives the correct velocity of

40\text{ m/s}

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

Initial velocity (

v_0

) =

0\text{ m/s}

, Acceleration (

g

) =

10\text{ m/s}^2

, Time (

t

) =

4\text{ s}

, Mass (

m

) =

5\text{ kg}

.

Extracting variables is the necessary first step to choosing the correct kinematic formula.

2

Select the correct formula to find the final velocity.

Use the formula

v = v_0 + gt

.

This formula relates velocity, acceleration, and time without needing the fall distance.

3

Substitute the values into the formula and solve.

v = 0 + (10 \times 4) = 40\text{ m/s}

.

Performing the calculation yields the final velocity. The mass of

5\text{ kg}

is irrelevant because all objects in free fall accelerate at the same rate in the absence of air resistance.

Key Concept

In free fall with no air resistance, the velocity of an object increases linearly with time (

v = gt

), completely independent of the object's mass.

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