Newton's Second Law (F=ma) Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A military recovery vehicle is using a winch to pull a disabled transport truck out of deep mud on a level surface. The disabled truck has a weight of $50,000 \text{ N}$ . The mud exerts a constant resistive drag force of $12,000 \text{ N}$ against the truck's motion. If the winch must accelerate the truck horizontally at a rate of $0.5 \text{ m/s}^2$ , how much tension force must the winch cable provide? (Assume gravitational acceleration $g = 10 \text{ m/s}^2$ )

22,000 \text{ N}

37,000 \text{ N}

14,500 \text{ N}

2,500 \text{ N}

Show answer & explanation

Answer: $14,500 \text{ N}$

Answer

The winch cable must provide

14,500 \text{ N}

of tension force.

The correct answer is found by first converting the truck's weight (

50,000 \text{ N}

) to its mass (

5,000 \text{ kg}

) using

g = 10 \text{ m/s}^2

. Next, the net force required to accelerate this mass at

0.5 \text{ m/s}^2

is calculated as

2,500 \text{ N}

using

F = ma

. Finally, because the mud exerts a

12,000 \text{ N}

opposing drag, the winch must pull with enough force to overcome the drag and still provide the

2,500 \text{ N}

net force. Therefore, the total required tension is

12,000 \text{ N} + 2,500 \text{ N} = 14,500 \text{ N}

.

Step-by-Step Solution

1

Determine the mass of the disabled truck from its given weight.

m = \frac{W}{g} = \frac{50,000 \text{ N}}{10 \text{ m/s}^2} = 5,000 \text{ kg}

Newton's second law (

F = ma

) requires mass, not weight.

2

Calculate the required net force to achieve the target acceleration.

F_{\text{net}} = ma = 5,000 \text{ kg} \times 0.5 \text{ m/s}^2 = 2,500 \text{ N}

This is the net force that must remain after all opposing forces are overcome.

3

Set up the force balance equation for the horizontal direction.

F_{\text{net}} = T_{\text{winch}} - F_{\text{drag}}

The net force is the vector sum of the applied tension pulling forward and the drag force resisting backward.

4

Solve the equation for the required winch tension (

T_{\text{winch}}

).

2,500 \text{ N} = T_{\text{winch}} - 12,000 \text{ N} \implies T_{\text{winch}} = 14,500 \text{ N}

Adding the drag force to the required net force gives the total applied force.

Key Concept

Newton's Second Law applied to multi-force systems.

Question 2Question →

Match each mechanical operational scenario to its resulting acceleration using Newton's Second Law ( $F = ma$ ).

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings are determined by dividing the net force by the mass for each scenario: the aerospace capsule accelerates at

3.0 \text{ m/s}^2

, the forklift accelerates at

1.5 \text{ m/s}^2

, the bridge section accelerates at

0.5 \text{ m/s}^2

, and the submarine ballast accelerates at

4.0 \text{ m/s}^2

.

Newton's Second Law dictates that acceleration is directly proportional to net force and inversely proportional to mass (

a = F/m

). By dividing the net force by the mass in each of the four scenarios, the correct acceleration values are directly calculated and paired.

Step-by-Step Solution

1

Identify the known variables provided in each scenario.

Each scenario provides the net force (

F

) in Newtons and the object's mass (

m

) in kilograms.

Newton's Second Law requires both net force and mass to determine an object's resulting acceleration.

2

Rearrange Newton's Second Law (

F = ma

) to solve for the missing variable.

The formula becomes

a = F/m

.

Because the right items represent acceleration, the equation must be isolated for acceleration (

a

) before computing.

3

Calculate the specific acceleration for each mass and force pairing.

Capsule:

3,600 / 1,200 = 3.0 \text{ m/s}^2

. Forklift:

2,250 / 1,500 = 1.5 \text{ m/s}^2

. Bridge section:

1,250 / 2,500 = 0.5 \text{ m/s}^2

. Ballast:

16,000 / 4,000 = 4.0 \text{ m/s}^2

.

Dividing the specific force by the given mass maps each scenario to exactly one value in the right column.

Key Concept

Solving for acceleration using Newton's Second Law (

a = F/m

)

Question 3Question →

An autonomous warehouse transport vehicle with a mass of $2,000 \text{ kg}$ experiences a constant frictional resistance of $2,000 \text{ N}$ while moving across a level concrete floor. When its electric motors produce a forward thrust of $6,000 \text{ N}$ , the vehicle accelerates at a steady rate. If the motors are commanded to double their forward thrust to $12,000 \text{ N}$ while the frictional resistance remains unchanged, what is the vehicle's new acceleration?

4.0 \text{ m/s}^2

5.0 \text{ m/s}^2

6.0 \text{ m/s}^2

0.5 \text{ m/s}^2

Show answer & explanation

Answer: $5.0 \text{ m/s}^2$

Answer

The new acceleration is

5.0 \text{ m/s}^2

.

According to Newton's Second Law, acceleration is determined by the net force acting on an object (

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

). The net force is the forward thrust minus the friction. With a new thrust of

12,000 \text{ N}

and a constant friction of

2,000 \text{ N}

, the net force is

10,000 \text{ N}

. Dividing this by the mass of

2,000 \text{ kg}

yields an acceleration of

5.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the forces acting on the vehicle in the new scenario.

Forward thrust (

F_{thrust}

) =

12,000 \text{ N}

. Frictional resistance (

F_{friction}

) =

2,000 \text{ N}

.

Newton's Second Law requires the net force, which is the sum of all opposing forces.

2

Calculate the new net force.

F_{net} = 12,000 \text{ N} - 2,000 \text{ N} = 10,000 \text{ N}

.

The net force is the actual force available to accelerate the mass.

3

Apply Newton's Second Law (

F = ma

) to find the new acceleration.

a = \frac{F_{net}}{m} = \frac{10,000 \text{ N}}{2,000 \text{ kg}} = 5.0 \text{ m/s}^2

.

Acceleration is equal to the net force divided by the mass.

Key Concept

Acceleration is directly proportional to the net force, not just the applied force. To find acceleration, all opposing forces must be subtracted from the applied force before dividing by mass.

Question 4Question →

A twin-engine military cargo aircraft with a total mass of $80,000 \text{ kg}$ is accelerating down a runway for takeoff. Each of the two engines generates $140,000 \text{ N}$ of forward thrust. If the combined forces of rolling friction and aerodynamic drag opposing the aircraft's motion amount to $80,000 \text{ N}$ , what is the forward acceleration of the aircraft in $\text{m/s}^2$ ?

Show answer & explanation

Answer: 2.5

Answer

The forward acceleration of the aircraft is 2.5 m/s².

To accurately determine the acceleration, one must first find the net force acting on the aircraft. The total forward thrust is the sum of both engines (

140,000 \text{ N} \times 2 = 280,000 \text{ N}

). Subtracting the opposing forces of friction and drag (

80,000 \text{ N}

) yields a net forward force of

200,000 \text{ N}

. Dividing this net force by the aircraft's mass of

80,000 \text{ kg}

gives a forward acceleration of

2.5 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the total forward thrust applied to the aircraft.

2 \times 140,000 \text{ N} = 280,000 \text{ N}

The aircraft has two engines, and the problem provides the thrust generated by each individual engine.

2

Calculate the net force (

F_{net}

) acting on the aircraft.

F_{net} = 280,000 \text{ N} - 80,000 \text{ N} = 200,000 \text{ N}

Net force is the vector sum of all forces. The opposing forces (drag and friction) must be subtracted from the forward thrust.

3

Apply Newton's Second Law to calculate the acceleration.

a = \frac{200,000 \text{ N}}{80,000 \text{ kg}} = 2.5 \text{ m/s}^2

According to Newton's Second Law, acceleration equals the net force divided by the mass (

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

).

Key Concept

Newton's Second Law of Motion (

F_{net} = ma

)

Question 5Question →

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

600 \text{ N}

864,000 \text{ N}

240,000 \text{ N}

2,352,000 \text{ N}

Show answer & explanation

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

Answer

The correct magnitude of the net braking force is

240,000 \text{ N}

.

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

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

). It then finds the magnitude of acceleration (

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

) and applies Newton's Second Law (

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

).

Step-by-Step Solution

1

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

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

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

2

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

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

Acceleration is defined as the rate of change of velocity.

3

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

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

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

F = ma

).

Key Concept

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

Question 6Question →

A naval torpedo with a mass of $1,200 \text{ kg}$ is fired from a submarine. If the propulsion system generates a constant net forward force of $6,000 \text{ N}$ , what is the forward acceleration of the torpedo?

0.2 \text{ m/s}^2

0.5 \text{ m/s}^2

5.0 \text{ m/s}^2

50.0 \text{ m/s}^2

Show answer & explanation

Answer: $5.0 \text{ m/s}^2$

Answer

The correct answer is

5.0 \text{ m/s}^2

.

According to Newton's Second Law (

F = ma

), acceleration is calculated by dividing the net force by the mass. Dividing

6,000 \text{ N}

by

1,200 \text{ kg}

yields

5.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

Mass (

m

) =

1,200 \text{ kg}

, Net Force (

F

) =

6,000 \text{ N}

.

Extracting the known variables is necessary to apply the correct physics formula.

2

Apply Newton's Second Law of Motion.

The formula is

F = ma

. Rearranging to solve for acceleration gives

a = \frac{F}{m}

.

Newton's Second Law relates force, mass, and acceleration.

3

Substitute the values into the formula and solve.

a = \frac{6000}{1200} = 5.0 \text{ m/s}^2

.

Dividing the net force by the mass computes the resulting acceleration.

Key Concept

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (

F = ma

).

Question 7Question →

Match each physical scenario with the magnitude of its resulting acceleration. Apply Newton's Second Law of Motion ( $F=ma$ ) and ensure you calculate the net force for each situation.

Click a left item, then click its matching right item

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Answer

The correct matches are: Transport vehicle maps to 2.0 m/s², Hovercraft maps to 3.0 m/s², Hoisted payload maps to 6.0 m/s², and Descending elevator maps to 4.0 m/s².

Each correct match is derived by first identifying all acting forces on the object, determining the net force (

F_{net}

), and then dividing by the mass (

a = F_{net}/m

). For horizontal motion, opposing forces (friction, drag) are subtracted from applied thrust. For vertical motion, the object's weight (

mg

) must be calculated and subtracted from the cable tension.

Step-by-Step Solution

1

Calculate the acceleration for the transport vehicle.

Net force = 12,000 N - 2,000 N - 2,000 N = 8,000 N. Acceleration = 8,000 N / 4,000 kg = 2.0 m/s².

Forces acting in the opposite direction of motion (drag and friction) must be subtracted from the forward thrust.

2

Calculate the acceleration for the hovercraft.

Net force = (2 * 3,000 N) - 1,500 N = 4,500 N. Acceleration = 4,500 N / 1,500 kg = 3.0 m/s².

The total thrust from both propellers must be combined before subtracting the opposing water current.

3

Calculate the acceleration for the hoisted payload.

Weight = 500 kg * 10 m/s² = 5,000 N. Net upward force = 8,000 N - 5,000 N = 3,000 N. Acceleration = 3,000 N / 500 kg = 6.0 m/s².

In vertical motion, the downward force of gravity (weight) must be calculated and subtracted from the upward tension to find the net force.

4

Calculate the acceleration for the descending elevator.

Weight = 800 kg * 10 m/s² = 8,000 N. Net downward force = 8,000 N - 4,800 N = 3,200 N. Acceleration = 3,200 N / 800 kg = 4.0 m/s².

Because the elevator descends, the downward gravitational force exceeds the upward tension. Net force is weight minus tension.

Key Concept

Newton's Second Law of Motion (

F_{net} = ma

)

Question 8Question →

Using Newton's Second Law ( $F = ma$ ), match each mechanical scenario with its correct missing value (force, mass, or acceleration).

Click a left item, then click its matching right item

Show answer & explanation

Answer

The matches are calculated by rearranging

F = ma

to solve for the missing variable, factoring in net force where applicable, and applying direct proportionality.

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

F = ma

). By determining the net force and algebraically rearranging the formula, or by applying proportional reasoning rules, each scenario can be correctly matched to its missing value.

Step-by-Step Solution

1

Calculate the net force where opposing forces are present.

Subtract friction from the applied force to find the true net force acting on the object.

Newton's Second Law only applies to the net force, not just the applied force.

2

Apply Newton's Second Law (

F = ma

) or its rearranged forms.

Use

F = ma

for force,

m = \frac{F}{a}

for mass, and

a = \frac{F}{m}

for acceleration.

These equations isolate the missing variable for the first three scenarios.

3

Apply proportional reasoning for the final scenario.

Recognize that tripling the force triples the acceleration.

Since

a = \frac{F}{m}

, acceleration and force are directly proportional when mass is constant.

Key Concept

Newton's Second Law

Estimated Time:1m 30s

Question 9Question →

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 10Question →

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 11Question →

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 12Question →

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 13Question →

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 14Question →

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

Question 15Question →

A deck winch on a naval vessel applies a constant net horizontal force of $4,500 \text{ N}$ to drag a heavy supply pallet across a level deck. If the pallet has a mass of $1,500 \text{ kg}$ , what is the acceleration of the pallet?

Show answer & explanation

Answer: 3

Answer

The correct answer is 3.

By applying Newton's Second Law (

F = ma

) and rearranging for acceleration (

a = \frac{F}{m}

), we divide the net force of

4,500 \text{ N}

by the mass of

1,500 \text{ kg}

to find an acceleration of

3 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given information

Force (

F

) =

4,500 \text{ N}

, Mass (

m

) =

1,500 \text{ kg}

Extracting the known variables is the first step in solving a physics calculation problem.

2

Select the appropriate formula

F = ma

Newton's Second Law relates force, mass, and acceleration.

3

Rearrange the formula to solve for acceleration

a = \frac{F}{m}

We need to isolate the unknown variable, acceleration (

a

).

4

Substitute the values and calculate

a = \frac{4500}{1500} = 3 \text{ m/s}^2

Plugging in the given numbers yields the final numerical answer.

Key Concept

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (

F = ma

).

Question 16Question →

A combat engineer squad is using a motorized winch to pull a $2,500 \text{ kg}$ concrete barrier horizontally across rough ground to construct a defensive position. The winch applies a constant tension of $12,000 \text{ N}$ to the towing cable. If the friction between the barrier and the ground opposes the motion with a force of $7,000 \text{ N}$ , what is the acceleration of the barrier?

0.5 \text{ m/s}^2

2.0 \text{ m/s}^2

4.8 \text{ m/s}^2

0.2 \text{ m/s}^2

Show answer & explanation

Answer: $2.0 \text{ m/s}^2$

Answer

2.0 \text{ m/s}^2

The correct answer is found by first calculating the net force, which is the applied tension minus the opposing friction (

12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

). Then, using Newton's Second Law (

a = \frac{F}{m}

), the net force is divided by the mass of the barrier (

\frac{5,000 \text{ N}}{2,500 \text{ kg}}

) to yield an acceleration of

2.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify the applied force and the opposing force acting on the barrier.

Applied Force =

12,000 \text{ N}

, Opposing Friction =

7,000 \text{ N}

.

To find the net force, all horizontal forces acting on the object must be accounted for.

2

Calculate the net force (

F_{net}

) acting on the concrete barrier.

F_{net} = 12,000 \text{ N} - 7,000 \text{ N} = 5,000 \text{ N}

.

Net force is the vector sum of all forces; opposite forces are subtracted.

3

Apply Newton's Second Law (

F = ma

) to find the acceleration.

a = \frac{F_{net}}{m} = \frac{5,000 \text{ N}}{2,500 \text{ kg}} = 2.0 \text{ m/s}^2

.

Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

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

Question 17Question →

An automated cargo tug applies a forward thrust of $24,000 \text{ N}$ to a $1,000 \text{ kg}$ supply sled. If the ground surface creates a constant opposing frictional force of $4,000 \text{ N}$ , what is the resulting acceleration of the sled?

20 \text{ m/s}^2

24 \text{ m/s}^2

2 \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

The sled experiences a forward thrust of

24,000 \text{ N}

and a backward frictional force of

4,000 \text{ N}

, resulting in a net force of

20,000 \text{ N}

. Using Newton's Second Law (

F = ma

), dividing the net force (

20,000 \text{ N}

) by the mass (

1,000 \text{ kg}

) gives an acceleration of

20 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the net force acting on the sled.

F_{\text{net}} = 24,000 \text{ N} - 4,000 \text{ N} = 20,000 \text{ N}

Acceleration is determined by the net force, which is the applied force minus any opposing forces like friction.

2

Apply Newton's Second Law (

F = ma

) to find the acceleration.

a = \frac{F_{\text{net}}}{m} = \frac{20,000 \text{ N}}{1,000 \text{ kg}} = 20 \text{ m/s}^2

Rearranging the formula to solve for acceleration gives

a = \frac{F}{m}

.

Key Concept

Newton's Second Law (

F = ma

)

Estimated Time:45s

Question 18Question →

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

3.75 \text{ m/s}^2

0.4 \text{ m/s}^2

2.5 \text{ m/s}^2

0.25 \text{ m/s}^2

Show answer & explanation

Answer: $2.5 \text{ m/s}^2$

Answer

The disabled truck will have a forward acceleration of

2.5 \text{ m/s}^2

.

The correct acceleration is found by first converting the truck's weight to its mass, determining the net force by subtracting the rolling resistance from the applied force, and then dividing that net force by the mass.

Step-by-Step Solution

1

Calculate the mass of the truck from its weight.

m = \frac{80,000 \text{ N}}{10 \text{ m/s}^2} = 8,000 \text{ kg}

Newton's Second Law requires mass, not weight, to calculate acceleration.

2

Determine the net force acting on the truck.

F_{net} = 30,000 \text{ N} - 10,000 \text{ N} = 20,000 \text{ N}

The rolling resistance directly opposes the applied forward force, so it must be subtracted.

3

Calculate the acceleration using Newton's Second Law (

F = ma

).

a = \frac{F_{net}}{m} = \frac{20,000 \text{ N}}{8,000 \text{ kg}} = 2.5 \text{ m/s}^2

Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Applying Newton's Second Law (

F=ma

) in multi-force scenarios requiring weight-to-mass conversion.

Question 19Question →

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

Show answer & explanation

Answer: 24

Answer

24

To find the acceleration, we first determine the net force acting on the torpedo. The forward propulsive force is

45,000 \text{ N}

, but water resistance pushes back with

9,000 \text{ N}

. Subtracting the opposing force gives a net force of

36,000 \text{ N}

. Using Newton's Second Law (

F = ma

), we rearrange the formula to solve for acceleration (

a = \frac{F}{m}

). Dividing the net force (

36,000 \text{ N}

) by the mass (

1,500 \text{ kg}

) results in an acceleration of

24 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the net force (

F_{net}

) acting on the torpedo.

F_{net} = 45,000 \text{ N} - 9,000 \text{ N} = 36,000 \text{ N}

The torpedo experiences forces in opposite directions, so the drag force must be subtracted from the forward thrust to find the total effective force.

2

Calculate the acceleration (

a

) using Newton's Second Law.

a = \frac{F_{net}}{m} = \frac{36,000 \text{ N}}{1,500 \text{ kg}} = 24 \text{ m/s}^2

Newton's Second Law states that acceleration equals the net force divided by the mass.

Key Concept

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

Question 20Question →

A military hovercraft with a mass of $6,000 \text{ kg}$ is transporting equipment across a frozen lake. The hovercraft's thrusters generate a forward force of $27,000 \text{ N}$ , while air resistance and surface friction create a combined opposing force of $9,000 \text{ N}$ . What is the forward acceleration of the hovercraft?

3.0 \text{ m/s}^2

4.5 \text{ m/s}^2

0.3 \text{ m/s}^2

0.33 \text{ m/s}^2

Show answer & explanation

Answer: $3.0 \text{ m/s}^2$

Answer

The correct forward acceleration of the hovercraft is

3.0 \text{ m/s}^2

.

The correct answer accurately determines the net force by subtracting the opposing friction (

9,000 \text{ N}

) from the applied thrust (

27,000 \text{ N}

) to get

18,000 \text{ N}

. Dividing this net force by the mass (

6,000 \text{ kg}

) yields an acceleration of

3.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the net forward force acting on the hovercraft.

F_{net} = 27,000 \text{ N} - 9,000 \text{ N} = 18,000 \text{ N}

Acceleration is determined by the net force, which is the sum of all forces acting on the object. The opposing force must be subtracted from the forward thrust.

2

Set up Newton's Second Law equation.

F_{net} = m \times a

This formula relates net force, mass, and acceleration.

3

Rearrange the equation to solve for acceleration and substitute the known values.

a = \frac{18,000 \text{ N}}{6,000 \text{ kg}} = 3.0 \text{ m/s}^2

Dividing the net force by the mass gives the resulting acceleration.

Key Concept

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass (

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

).

Newton's Second Law (F=ma)

Answer

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