Force, Mass, and Motion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 7

Question 121Question →

A motorized winch is pulling a supply pallet across a rough concrete loading dock. The winch applies a constant horizontal pulling force of $1,500 \text{ N}$ . The kinetic friction between the pallet and the dock is $300 \text{ N}$ . If the pallet accelerates at $1.5 \text{ m/s}^2$ , what is the mass of the pallet?

80 \text{ kg}

800 \text{ kg}

1,000 \text{ kg}

1,800 \text{ kg}

Show answer & explanation

Answer: $800 \text{ kg}$

Answer

The correct mass of the pallet is

800 \text{ kg}

.

The correct answer is found by first determining the net force acting on the pallet. Subtracting the

300 \text{ N}

friction from the

1,500 \text{ N}

applied pulling force yields a net force of

1,200 \text{ N}

. Using Newton's Second Law (

F = ma

), dividing the net force by the acceleration (

1.5 \text{ m/s}^2

) gives a mass of

800 \text{ kg}

.

Step-by-Step Solution

1

Calculate the net force acting on the pallet by subtracting the friction force from the applied pulling force.

F_{net} = 1,500 \text{ N} - 300 \text{ N} = 1,200 \text{ N}

Newton's Second Law requires the total net force acting on the object, so all opposing forces must be accounted for.

2

Use Newton's Second Law (

F = ma

) to solve for the mass.

m = \frac{F_{net}}{a} = \frac{1,200 \text{ N}}{1.5 \text{ m/s}^2} = 800 \text{ kg}

Mass is equal to the net force divided by the resulting acceleration.

Key Concept

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

Question 122Question →

An automotive engineer is analyzing the physics of a racecar driving along a flat, circular test track. Match each observed physical phenomenon during the turn with its correct mechanical explanation.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The turning force is an inward centripetal force provided by friction. The outward sensation is caused by inertia. Losing friction results in a tangential straight-line path, and doubling the speed quadruples the required centripetal force.

Each matching pair accurately connects real-world driving observations with Newton's laws of motion. Circular paths require inward centripetal forces. Physical sensations of being pushed outward are simply inertia. Loss of that inward force results in a straight, tangential trajectory, and the mathematical relationship of

F = \frac{mv^2}{r}

dictates that doubling speed requires four times the inward force.

Step-by-Step Solution

1

Identify the primary force enabling circular motion.

The car requires a net inward force, known as centripetal force, which is supplied by road friction.

Without a force pulling the object toward the center of the curve, circular motion is impossible.

2

Analyze the physical cause of the driver's outward sensation.

The sensation is determined to be the result of inertia, not a real physical outward force.

Newton's First Law states objects resist changes in direction. The body tries to go straight while the car door pushes inward.

3

Determine the path of the vehicle if the centripetal force drops to zero (hitting ice).

The path becomes a straight line tangent to the exact point on the curve where friction was lost.

When the inward force ceases, the vehicle instantly resumes straight-line motion.

4

Calculate the proportional change in force if velocity is doubled.

Using

F = \frac{mv^2}{r}

, inserting

2v

yields

(2v)^2 = 4v^2

, meaning the required force is 4 times greater.

Centripetal force scales with the square of the velocity.

Key Concept

Centripetal Force, Inertia, and Tangential Velocity in Circular Motion

Question 123Question →

An automated loading mechanism pushes a $40 \text{ kg}$ projectile along a horizontal guide rail into a weapon system. The mechanism applies a constant forward force of $700 \text{ N}$ . If the sliding friction in the guide rail opposes the motion with a force of $100 \text{ N}$ , what is the acceleration of the projectile?

Show answer & explanation

Answer: 15

Answer

15

The correct acceleration is found by first determining the net force acting on the projectile. Subtracting the

100 \text{ N}

of friction from the

700 \text{ N}

applied force yields a net force of

600 \text{ N}

. According to Newton's Second Law (

F = ma

), dividing this net force by the

40 \text{ kg}

mass results in an acceleration of

15 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the net horizontal force acting on the projectile.

700 \text{ N} - 100 \text{ N} = 600 \text{ N}

The net force is the vector sum of all forces; friction directly opposes the forward applied force.

2

Use Newton's Second Law to set up the equation for acceleration.

a = \frac{F_{\text{net}}}{m}

Acceleration equals the net force divided by the mass of the object.

3

Substitute the known values into the equation.

a = \frac{600}{40} = 15 \text{ m/s}^2

Dividing the computed net force by the given mass provides the exact acceleration.

Key Concept

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

Question 124Question →

A mechanical centrifuge features a horizontal rotating arm with a heavy sample container secured at the outer end. During high-speed operation, the retaining bracket holding the container abruptly breaks, eliminating the inward force. According to the principles of circular motion and inertia, which of the following best describes the immediate trajectory of the sample container?

It will fly directly outward along the radius, straight away from the center of the centrifuge.

It will snap inward toward the center hub as an equal and opposite reaction to the break.

It will travel in a straight line tangent to the circular path at the exact point of the break.

It will continue to curve but accelerate, because removing the restraining force inversely increases its acceleration.

Show answer & explanation

Answer: It will travel in a straight line tangent to the circular path at the exact point of the break.

Answer

The sample container will travel in a straight line tangent to the circular path.

The correct answer accurately describes the tangent path. When the inward centripetal force provided by the bracket is suddenly removed, there is no longer a net force acting on the container to pull it into a circular path. Due to inertia (Newton's First Law), the container will continue moving in a straight line at its current instantaneous velocity. Because the velocity vector is always tangent to the circular path at any given moment, the object will fly off in a straight, tangent line.

Step-by-Step Solution

1

Identify the forces acting on the container before the break.

The bracket provides an inward centripetal force that constantly changes the container's direction, keeping it in a circular path.

Understanding the source of the circular motion.

2

Analyze the state of the system immediately after the bracket breaks.

The inward centripetal force drops to zero. No other horizontal forces are acting on the container.

Determining the net force acting on the object at the moment of release.

3

Apply Newton's First Law of Motion (Inertia).

Without a net external force, the container will continue moving in a straight line at its current instantaneous velocity, which is tangent to the circle.

Predicting the trajectory based on the principle of inertia.

Key Concept

Tangential Velocity and Inertia in Circular Motion

Question 125Question →

According to Newton's Third Law of Motion, every action has an equal and opposite reaction acting on different bodies. Match each described mechanical action force in the left column with its precise corresponding reaction force in the right column.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches pair the specific interacting bodies in each scenario by reversing the direction of the force and swapping the subject and object.

In every mechanical interaction, forces occur in equal and opposite pairs. To correctly identify the reaction force, you must isolate the exact two interacting bodies and simply reverse both the direction of the force and their roles. If Body A pushes Body B forward, the precise reaction is Body B pushing Body A backward.

Step-by-Step Solution

1

Identify the two distinct interacting objects in the given action force.

The subject (the pusher) and the object (the pushed) are isolated for each scenario.

Newton's Third Law requires that action-reaction pairs act on two different, specific interacting bodies.

2

Reverse the roles of the two interacting objects.

The object being pushed becomes the new subject exerting the reaction force.

The reaction force must be exerted by the receiving body back onto the originating body.

3

Invert the direction of the applied force.

A backward action becomes a forward reaction; a downward action becomes an upward reaction.

Reaction forces are always exactly opposite in direction to their corresponding action forces.

Key Concept

Newton's Third Law states that force pairs consist of the exact same two interacting bodies, with the roles of the 'pusher' and 'pushed' swapped, and the direction of the force inverted.

Estimated Time:1m 30s

Question 126Question →

Determine if the following statement is true or false: When a vehicle travels along a flat, circular track at a constant speed, a real outward force known as centrifugal force actively pushes the vehicle away from the center of the turn.

True

False

Show answer & explanation

Answer: False

Answer

False

The sensation of being pushed outward is due to the vehicle's inertia (its tendency to travel in a straight line), not an actual outward force. The only real applied force acting in the radial direction is the inward centripetal force, which is supplied by the friction between the tires and the road.

Step-by-Step Solution

1

Analyze the forces acting on the vehicle during circular motion.

Identify that the real forces acting on the vehicle are gravity (downward), normal force (upward), and friction (inward toward the center).

To distinguish between real, applied physical forces and apparent forces.

2

Evaluate the concept of centrifugal force.

Determine that the outward 'push' felt by passengers is not a real force, but rather the result of the vehicle's inertia resisting the inward change in direction.

To address the common misconception stated in the problem.

Key Concept

The difference between real centripetal force and apparent centrifugal force due to inertia.

Question 127Question →

An artillery cannon fires a heavy projectile horizontally across a testing ground. As expanding gases force the projectile rapidly forward out of the barrel, the entire cannon assembly recoils backward. Which of the following statements correctly describes the relationship between the forces acting on the projectile and the cannon?

The backward force on the cannon is significantly smaller than the forward force on the projectile because the cannon has a larger mass.

The cannon recoils backward because its heavy downward weight acts horizontally to counterbalance the projectile's momentum.

The force accelerating the projectile forward is exactly equal in magnitude to the reaction force pushing the cannon backward.

The backward recoil is caused entirely by the projectile's resting inertia resisting the sudden forward acceleration.

Show answer & explanation

Answer: The force accelerating the projectile forward is exactly equal in magnitude to the reaction force pushing the cannon backward.

Answer

The force acting on the projectile and the reaction force acting on the cannon are exactly equal in magnitude.

Newton's Third Law dictates that all forces exist in pairs. During the firing sequence, the forward action force applied to the projectile generates a simultaneous, equal, and opposite backward reaction force on the cannon. The cannon moves backward much slower only because of its massive size, not because it experiences less force.

Step-by-Step Solution

1

Identify the interacting physical bodies in the system.

The expanding explosive gases interact simultaneously with both the projectile and the cannon barrel.

Newton's Third Law applies to the mutual interaction forces between interacting objects.

2

Apply the principle of action and reaction to the interacting bodies.

The action force pushes the projectile forward, and a simultaneous reaction force pushes the cannon backward.

Forces always occur in equal and opposite pairs.

3

Evaluate the relationship between force, mass, and the resulting motion.

The forces are perfectly identical in magnitude. The cannon accelerates much less than the projectile only because it has significantly more mass.

Newton's Second Law (

F=ma

) dictates that the same magnitude of force applied to a larger mass results in a smaller acceleration, which often creates the illusion of unequal forces.

Key Concept

Newton's Third Law (Action/Reaction)

Question 128Question →

A mechanical centrifugal clutch connects a small engine to a drive shaft. As the engine's rotational speed increases, internal weighted shoes slide outward against spring tension until they press firmly against the outer drum, engaging the drive. According to the principles of circular motion, which of the following best explains the physical cause of the shoes moving outward?

The inertia of the shoes causes them to naturally tend toward a straight-line path, and at higher speeds, the springs fail to provide enough inward centripetal force to keep them at a small radius.

An outward centripetal force is generated by the engine's rotation, which actively overcomes the springs and pushes the weighted shoes away from the center.

The turning shaft generates an equal and opposite reaction force that acts outward on the shoes, driving them into the drum.

The high velocity of the spinning shoes creates a high static pressure zone at the center of the clutch, pushing the shoes outward.

Show answer & explanation

Answer: The inertia of the shoes causes them to naturally tend toward a straight-line path, and at higher speeds, the springs fail to provide enough inward centripetal force to keep them at a small radius.

Answer

The inertia of the shoes causes them to naturally tend toward a straight-line path, and at higher speeds, the springs fail to provide enough inward centripetal force to keep them at a small radius.

By Newton's First Law, the rotating shoes have mass and velocity, meaning they naturally tend to travel in a straight, tangential path (inertia). To stay in a tight circular path around the shaft, they require a continuous inward pull, known as centripetal force, which is provided by the springs. As the engine speeds up, the inward force required to maintain that small radius increases significantly. When that required force exceeds the tension the springs can provide, the shoes travel outward along their inertial path until the outer drum stops them.

Step-by-Step Solution

1

Identify the forces acting on the rotating shoes.

The only actual radial force applied to the shoes is the tension from the springs, which pulls them inward toward the center shaft.

Understanding the free-body diagram prevents the assumption of fictional outward forces.

2

Apply Newton's First Law (Inertia) to the moving shoes.

Because the shoes have mass and velocity, they want to travel in a straight, tangential line due to inertia.

Circular motion requires a constant inward force to continuously pull the object out of its natural straight-line path.

3

Evaluate the relationship between rotational speed and required force.

As speed increases, a much larger inward force (

F = mv^2/r

) is required to keep the shoes in a tight circle. When the speed exceeds what the spring tension can counteract, the shoes follow their inertial path outward until they hit the drum.

This explains the mechanical engagement of the clutch without inventing an outward pushing force.

Key Concept

Inertia and Centripetal Force

Question 129Question →

Evaluate the accuracy of the following claim: During a head-on collision between a heavy commercial transport truck and a lightweight passenger car, the impact force that the truck exerts on the car is greater in magnitude than the force that the car exerts on the truck.

True

False

Show answer & explanation

Answer: False

Answer

The claim is false. The forces exerted by the two vehicles upon each other are identical in magnitude.

The statement is false because Newton's Third Law of Motion dictates that any two interacting bodies exert equal and opposite forces upon one another. Even though the truck possesses a much larger mass, the actual force of impact it applies to the car is exactly the same magnitude as the force the car applies to the truck.

Step-by-Step Solution

1

Identify the two interacting objects and the physical law governing their interaction.

The objects are the heavy truck and the lightweight car. The mutual interaction is governed by Newton's Third Law of Motion (action and reaction).

Determining the correct physical principle is necessary to evaluate the relationship between the forces during the collision.

2

Apply Newton's Third Law to the collision scenario.

The law states that for every action force, there is an equal and opposite reaction force. Therefore, the force the truck exerts on the car must be identical in magnitude to the force the car exerts on the truck.

This direct application of the law disproves the claim made in the question stem.

3

Differentiate between the applied force and the resulting acceleration to avoid common misconceptions.

While the impact forces are exactly equal, the car experiences a significantly greater acceleration (and consequently more structural damage) because its mass is much smaller (

a = \frac{F}{m}

).

Clarifying why the car suffers more damage confirms that the unequal effects are due to mass differences under Newton's Second Law, not unequal forces.

Key Concept

Newton's Third Law states that all forces exist in pairs, and whenever two objects interact, they exert forces upon each other that are equal in magnitude and opposite in direction.

Alternative Method

You can logically verify this by considering Newton's Second Law combined with the Third Law. The perfectly equal forces cause different accelerations inversely proportional to the masses (

a = \frac{F}{m}

). The car's massive acceleration often misleads observers into incorrectly assuming the force applied to it was larger.

Estimated Time:45s

Question 130Question →

A motorized boat is accelerating forward across a body of water. According to Newton's Third Law of Motion, which specific force is the reaction force that directly propels the boat forward?

The force of the water pushing forward against the propeller blades

The force of the propeller blades pushing backward against the water

The internal rotational force generated by the boat's engine

The forward momentum of the boat overcoming the water's resting resistance

Show answer & explanation

Answer: The force of the water pushing forward against the propeller blades

Answer

The force of the water pushing forward against the propeller blades directly propels the boat.

According to Newton's Third Law, forces always come in pairs. When the boat's propeller pushes water backward (action), the water simultaneously exerts an equal and opposite force forward on the propeller (reaction). Because the propeller is attached to the boat, this reaction force is what propels the entire vessel forward.

Step-by-Step Solution

1

Identify the interacting bodies in the mechanical system.

The two primary interacting bodies are the boat's propeller and the surrounding water.

Newton's Third Law requires identifying the two distinct bodies exerting forces on each other.

2

Determine the action force created by the boat's mechanism.

The turning propeller exerts a force backward against the water.

To move forward, a marine propulsion system must push fluid in the opposite direction.

3

Apply Newton's Third Law to find the equal and opposite reaction force.

If the propeller pushes the water backward, the water must push the propeller forward with an equal magnitude of force.

Forces always occur in simultaneous pairs acting on different objects.

4

Isolate the force that acts specifically on the boat.

The forward force from the water acting on the propeller blades is what accelerates the boat forward.

An object's acceleration is determined only by the external forces acting upon it, not the forces it exerts on other things.

Key Concept

Newton's Third Law requires that for every action force, there is a simultaneous reaction force equal in magnitude and opposite in direction, acting on two different bodies.

Question 131Question →

Two warehouse workers are sitting on identical, frictionless wheeled carts facing each other. Worker X and his cart have a combined mass of $120 \text{ kg}$ , while Worker Y and his cart have a combined mass of $60 \text{ kg}$ . Worker X pushes against Worker Y's cart with a steady force of $240 \text{ N}$ . Which of the following best describes the forces and resulting accelerations experienced by both workers during the push?

Both workers experience an equal force of

240 \text{ N}

in opposite directions, but Worker Y accelerates twice as fast as Worker X.

Worker Y experiences a

240 \text{ N}

force, while Worker X experiences a

120 \text{ N}

reaction force due to the difference in their masses.

Worker X remains stationary during the push because his significantly greater inertia resists any backward reaction force.

Both workers experience an equal force of

240 \text{ N}

, but Worker X accelerates twice as fast because greater mass leads to greater acceleration.

Show answer & explanation

Answer: Both workers experience an equal force of $240 \text{ N}$ in opposite directions, but Worker Y accelerates twice as fast as Worker X.

Answer

Both workers experience an equal force of

240 \text{ N}

in opposite directions, but Worker Y accelerates twice as fast as Worker X.

The correct answer accurately combines Newton's Third and Second Laws. By the Third Law, the action force of

240 \text{ N}

exerted by Worker X creates an equal and opposite reaction force of

240 \text{ N}

on Worker X. By the Second Law (

F = ma

), acceleration is inversely proportional to mass. Since Worker Y has half the mass (

60 \text{ kg}

) of Worker X (

120 \text{ kg}

), the same

240 \text{ N}

force will cause Worker Y to accelerate exactly twice as fast.

Step-by-Step Solution

1

Determine the force acting on both workers using Newton's Third Law.

Both Worker X and Worker Y experience a

240 \text{ N}

force in opposite directions.

Newton's Third Law states that for every action, there is an equal and opposite reaction. The push of

240 \text{ N}

generates a reaction force of exactly

240 \text{ N}

on the person pushing.

2

Calculate the acceleration of Worker X using Newton's Second Law (

a = \frac{F}{m}

).

Acceleration of Worker X =

\frac{240 \text{ N}}{120 \text{ kg}} = 2 \text{ m/s}^2

.

Acceleration depends on the net force applied and the total mass of the object.

3

Calculate the acceleration of Worker Y using Newton's Second Law (

a = \frac{F}{m}

).

Acceleration of Worker Y =

\frac{240 \text{ N}}{60 \text{ kg}} = 4 \text{ m/s}^2

.

Worker Y has the same magnitude of force applied but half the mass, resulting in a different acceleration.

4

Compare the accelerations of the two workers.

Worker Y (

4 \text{ m/s}^2

) accelerates exactly twice as fast as Worker X (

2 \text{ m/s}^2

).

The inversely proportional relationship between mass and acceleration means the object with half the mass achieves twice the acceleration under an identical force.

Key Concept

Interaction of Newton's Third Law (Force Pairs) and Second Law (

F = ma

)

Question 132Question →

An industrial electromagnet attracts a piece of scrap steel. The magnet pulls the steel forward, and the steel pulls the magnet backward with an equal and opposite force. Because these two forces are equal in magnitude and opposite in direction, they cancel each other out, preventing the steel from accelerating.

True

False

Show answer & explanation

Answer: False

Answer

The statement is False.

The forces in an action-reaction pair never cancel each other out because they act on completely different objects. The net force determining the acceleration of the scrap steel depends only on the magnetic pull acting directly on the steel, completely independent of the reaction force the steel exerts back on the magnet.

Step-by-Step Solution

1

Identify the two forces described in the scenario.

Force 1 is the magnet pulling on the steel. Force 2 is the steel pulling on the magnet.

Mapping the specific forces is required to apply Newton's Laws of Motion correctly.

2

Determine which object receives each force.

The first force acts exclusively on the scrap steel, while the second force acts exclusively on the electromagnet.

Net force calculations must be done for a single object at a time.

3

Evaluate whether the forces can cancel each other out.

Because the forces are applied to completely different objects, they do not cancel each other.

Forces can only cancel out and result in zero net force if they are acting in opposite directions on the exact same body.

Key Concept

Action and reaction force pairs act on completely different objects, so they never cancel each other out when determining the net force on a single object.

Estimated Time:45s

Question 133Question →

According to Newton's Third Law of Motion, forces always exist in action-reaction pairs acting between interacting objects. For each mechanical action described below, identify its exact corresponding reaction force.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Match each action force with the reaction force that reverses the roles of the exact same two interacting bodies and points in the opposite direction.

Newton's Third Law dictates that forces always come in pairs. If Object A exerts a force on Object B, then Object B simultaneously exerts a force of equal magnitude in the exact opposite direction on Object A. The correct matches precisely swap the interacting bodies and reverse the direction of the applied force for each mechanical scenario.

Step-by-Step Solution

1

Identify the two specific interacting objects (Object A and Object B) in each action scenario.

The interacting pairs are: Rotors and Air; Gun mechanism and Nail; Treads and Dirt; Spring and Axle.

Newton's Third Law force pairs strictly occur between the two specific bodies that are interacting.

2

Determine the direction of the initial action force applied by Object A onto Object B.

Rotors push down; Gun pushes forward; Treads push backward; Spring pushes down.

The corresponding reaction force must be exactly opposite in direction.

3

Identify the statement that correctly reverses the interacting objects (Object B acting on Object A) and reverses the direction.

Air pushes rotors up; Nail pushes gun backward; Dirt pushes treads forward; Axle pushes spring up.

This guarantees an equal and opposite force acting on the counterpart body, completely fulfilling the action-reaction criteria.

Key Concept

Newton's Third Law (Action/Reaction force pairs)

Question 134Question →

A $75 \text{ kg}$ mechanic stands on a slick, oil-covered garage floor with negligible friction. The mechanic pushes forward horizontally against a stationary $150 \text{ kg}$ tool cabinet with a constant force of $200 \text{ N}$ . Which of the following statements correctly describes the forces involved in this interaction?

The cabinet exerts a

100 \text{ N}

backward force on the mechanic, reflecting the ratio of their masses.

The mechanic experiences a backward reaction force only if the

200 \text{ N}

push fails to overcome the cabinet's inertia.

The cabinet experiences a

200 \text{ N}

forward force, and the mechanic experiences a

200 \text{ N}

backward force simultaneously.

The

200 \text{ N}

action force and the

200 \text{ N}

reaction force both act on the cabinet, preventing it from accelerating rapidly.

Show answer & explanation

Answer: The cabinet experiences a $200 \text{ N}$ forward force, and the mechanic experiences a $200 \text{ N}$ backward force simultaneously.

Answer

The statement accurately describing the interaction is that the cabinet experiences a

200 \text{ N}

forward force, and the mechanic simultaneously experiences a

200 \text{ N}

backward force.

According to Newton's Third Law, any force exerted by one object on another is accompanied by an equal and opposite force exerted back by the second object on the first. Because the mechanic pushes the cabinet with

200 \text{ N}

forward, the cabinet simultaneously pushes the mechanic with

200 \text{ N}

backward. The differing masses do not alter the force magnitudes, though they result in different accelerations.

Step-by-Step Solution

1

Identify the interacting bodies in the given scenario.

The two interacting bodies are the mechanic and the tool cabinet.

Newton's Third Law applies to the forces exerted between two interacting objects.

2

Determine the magnitude and direction of the action force.

The mechanic exerts a forward force of

200 \text{ N}

on the tool cabinet.

This is the initial action provided in the problem description.

3

Apply Newton's Third Law to find the reaction force.

The tool cabinet must exert an equal and opposite reaction force of

200 \text{ N}

backward on the mechanic.

Forces always exist in equal and opposite pairs acting on different objects, regardless of their respective masses or whether they accelerate.

Key Concept

Newton's Third Law of Motion states that when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Question 135Question →

When an $80 \text{ kg}$ railway worker pushes horizontally against a stationary $4,000 \text{ kg}$ railcar, the railcar exerts a backward reaction force on the worker that is greater than the worker's forward pushing force, due to the railcar's significantly larger mass.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because action and reaction forces in a mechanical interaction are always exactly equal in magnitude, even when there is an extreme discrepancy between the masses of the two interacting objects.

Step-by-Step Solution

1

Identify the two interacting bodies and the nature of the interaction.

The worker applies a forward pushing force (action) on the railcar, and the railcar applies a backward contact force (reaction) on the worker.

Forces always occur in pairs resulting from mutual interactions between two objects.

2

Evaluate the magnitude of the forces using Newton's Third Law of Motion.

The force exerted by the worker is exactly equal in magnitude to the force exerted by the railcar.

Newton's Third Law states that for every action, there is an equal and opposite reaction, regardless of differences in size, mass, or acceleration.

3

Determine if the railcar's larger mass increases its reaction force.

The mass difference does not change the force equality; it only means the railcar will experience significantly less acceleration from the same force compared to the worker.

Force equality is universally true in action-reaction pairs;

F=ma

dictates acceleration, not the initial interaction force.

Key Concept

Newton's Third Law (Action/Reaction)

Estimated Time:45s

Question 136Question →

During a space mission in zero gravity, a compressed spring mechanism is used to separate a $10 \text{ kg}$ research probe from a $500 \text{ kg}$ main spacecraft. When the spring releases and pushes the two objects apart, which of the following statements correctly describes the interaction between them?

The main spacecraft exerts a larger force on the probe due to its greater inertia, overpowering the probe's reaction force.

The main spacecraft experiences a greater acceleration because its significantly larger mass amplifies the force applied by the spring.

Both objects experience the exact same magnitude of force, but the lighter probe undergoes a much greater acceleration.

The forces exerted on each object are equal and opposite, meaning they cancel each other out and prevent any initial acceleration.

Show answer & explanation

Answer: Both objects experience the exact same magnitude of force, but the lighter probe undergoes a much greater acceleration.

Answer

Both objects experience the exact same magnitude of force, but the lighter probe undergoes a much greater acceleration.

According to Newton's Third Law, the force exerted on the probe is exactly equal in magnitude and opposite in direction to the force exerted on the spacecraft. However, because the probe has a much smaller mass, Newton's Second Law (

a=F/m

) dictates that it will experience a proportionally larger acceleration.

Step-by-Step Solution

1

Analyze the forces acting on each object during the separation.

The spring applies an equal and opposite force to both the probe and the spacecraft.

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction.

2

Determine how each object's mass affects its resulting acceleration.

The

10 \text{ kg}

probe will accelerate much faster than the

500 \text{ kg}

spacecraft.

Newton's Second Law (

F=ma

) shows that acceleration is inversely proportional to mass when the force is constant (

a=F/m

).

Key Concept

Newton's Third Law (Action/Reaction)

Question 137Question →

Determine the acceleration for each of the military transport operations described below. Sequence the operations from the lowest rate of acceleration to the highest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from lowest to highest acceleration is: Naval destroyer, Armored personnel carrier, Transport plane, and Rescue helicopter.

By systematically calculating the acceleration for each scenario using the formula

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

, we can determine their respective values and order them properly. The naval destroyer evaluates to

0.5 \text{ m/s}^2

, the armored personnel carrier evaluates to

2.0 \text{ m/s}^2

, the transport plane evaluates to

4.0 \text{ m/s}^2

, and the rescue helicopter evaluates to

5.0 \text{ m/s}^2

. Placing these in ascending order yields the correct sequence.

Step-by-Step Solution

1

Calculate the acceleration of the naval destroyer.

a = \frac{15 - 5}{20} = 0.5 \text{ m/s}^2

Using the formula

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

2

Calculate the acceleration of the armored personnel carrier.

a = \frac{22 - 10}{6} = 2.0 \text{ m/s}^2

Using the formula

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

3

Calculate the acceleration of the transport plane.

a = \frac{60 - 0}{15} = 4.0 \text{ m/s}^2

Using the formula

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

, remembering that 'from rest' means an initial velocity of

0 \text{ m/s}

4

Calculate the acceleration of the rescue helicopter.

a = \frac{45 - 0}{9} = 5.0 \text{ m/s}^2

Using the formula

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

, remembering that 'from rest' means an initial velocity of

0 \text{ m/s}

5

Sequence the vehicles by their calculated acceleration values from lowest to highest.

0.5 < 2.0 < 4.0 < 5.0

To satisfy the condition of ordering from lowest rate to highest rate.

Key Concept

Acceleration is the rate of change of velocity over time, calculated using the formula

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

.

Question 138Question →

A coastal patrol boat is cruising at an initial velocity of $5.0 \text{ m/s}$ . The captain orders the engines to increase power, causing the boat to accelerate at a constant rate of $0.2 \text{ m/s}^2$ for exactly $1.5 \text{ minutes}$ .

What is the final velocity of the boat in $\text{m/s}$ ?

Show answer & explanation

Answer: 23

Answer

23.0

The correct answer is derived by first converting the time from minutes to seconds (

1.5 \text{ min} = 90 \text{ s}

), calculating the total change in velocity (

0.2 \times 90 = 18.0 \text{ m/s}

), and then adding that change to the initial cruising velocity (

5.0 + 18.0 = 23.0 \text{ m/s}

).

Step-by-Step Solution

1

Extract and convert the time variable into seconds.

t = 1.5 \text{ minutes} \times 60 \text{ seconds/minute} = 90 \text{ seconds}

Acceleration is given in meters per second squared (

\text{m/s}^2

), so time must be in seconds to ensure unit consistency.

2

Calculate the total change in velocity during the acceleration phase.

\Delta v = a \times t = 0.2 \text{ m/s}^2 \times 90 \text{ s} = 18.0 \text{ m/s}

The change in velocity is the product of the constant acceleration and the duration of that acceleration.

3

Add the change in velocity to the initial velocity.

v_f = v_i + \Delta v = 5.0 \text{ m/s} + 18.0 \text{ m/s} = 23.0 \text{ m/s}

The final velocity is the starting velocity plus the amount the velocity increased.

Key Concept

Applying the constant acceleration formula (

v_f = v_i + at

) with necessary unit conversions.

Estimated Time:1m 0s

Question 139Question →

A maglev transit pod enters a straight acceleration zone with an initial velocity of $20 \text{ m/s}$ . The pod's linear induction motors apply a constant acceleration of $5 \text{ m/s}^2$ for exactly $0.1 \text{ minutes}$ . What is the pod's final velocity at the end of this time period?

20.5 \text{ m/s}

30 \text{ m/s}

50 \text{ m/s}

70 \text{ m/s}

Show answer & explanation

Answer: $50 \text{ m/s}$

Answer

The correct answer is

50 \text{ m/s}

.

The final velocity is found by first converting the given time to standard units (

0.1 \text{ minutes} = 6 \text{ seconds}

). Next, determine the total velocity gained by multiplying acceleration by time (

5 \text{ m/s}^2 \times 6 \text{ s} = 30 \text{ m/s}

). Finally, add this gained velocity to the initial velocity of

20 \text{ m/s}

to get a final velocity of

50 \text{ m/s}

.

Step-by-Step Solution

1

Convert the given time from minutes to seconds.

0.1 \text{ minutes} \times 60 \text{ seconds/minute} = 6 \text{ seconds}

Acceleration is given in

\text{m/s}^2

, so time must be in seconds to match units.

2

Calculate the total change in velocity (

\Delta v

) during the acceleration period.

\Delta v = a \times t = 5 \text{ m/s}^2 \times 6 \text{ s} = 30 \text{ m/s}

This determines how much speed the pod gained.

3

Add the change in velocity to the initial velocity to find the final velocity.

v_f = v_i + \Delta v = 20 \text{ m/s} + 30 \text{ m/s} = 50 \text{ m/s}

The final velocity is the starting velocity plus whatever velocity was gained.

Key Concept

Applying kinematic equations for constant acceleration (

v_f = v_i + at

) with required unit conversions.

Question 140Question →

Calculate the acceleration for each of the following pieces of equipment. Arrange the scenarios in order from the greatest acceleration to the least acceleration.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from greatest to least acceleration is: Emergency response boat (

2.5 \text{ m/s}^2

), Heavy towing winch (

1.5 \text{ m/s}^2

), Runway snowplow (

1.2 \text{ m/s}^2

), and Construction crane (

0.5 \text{ m/s}^2

).

To determine the correct order, we must calculate the magnitude of acceleration for each scenario using the formula

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

. The boat has the highest acceleration (

2.5 \text{ m/s}^2

), followed by the winch (

1.5 \text{ m/s}^2

), the snowplow (

1.2 \text{ m/s}^2

), and finally the crane (

0.5 \text{ m/s}^2

). Arranging them from greatest to least yields this precise sequence.

Step-by-Step Solution

1

Calculate the acceleration of the emergency response boat.

The boat accelerates at

2.5 \text{ m/s}^2

.

Using the formula

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

, we get

a = \frac{25.0 - 5.0}{8.0} = 2.5 \text{ m/s}^2

.

2

Calculate the acceleration of the heavy towing winch.

The winch accelerates at

1.5 \text{ m/s}^2

.

Using the formula

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

, we get

a = \frac{4.0 - 1.0}{2.0} = 1.5 \text{ m/s}^2

.

3

Calculate the acceleration of the runway snowplow.

The snowplow accelerates at

1.2 \text{ m/s}^2

.

From a complete stop,

v_i = 0

.

a = \frac{12.0 - 0}{10.0} = 1.2 \text{ m/s}^2

.

4

Calculate the acceleration of the construction crane.

The crane accelerates at

0.5 \text{ m/s}^2

.

From rest,

v_i = 0

.

a = \frac{3.0 - 0}{6.0} = 0.5 \text{ m/s}^2

.

5

Order the calculated acceleration values from greatest to least.

Boat (

2.5

) > Winch (

1.5

) > Snowplow (

1.2

) > Crane (

0.5

).

The prompt requires arranging the scenarios in descending order based on their calculated magnitudes of acceleration.

Key Concept

Acceleration is defined as the rate at which an object changes its velocity over a specific interval of time.

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