Force, Mass, and Motion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 6

Question 101Question →

A logistics technician is tasked with repositioning a large, heavy equipment pod across a flat warehouse floor. Rank the following movement scenarios in order from the greatest magnitude of frictional resistance to the least magnitude of frictional resistance.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from greatest to least resistance is: breaking the pod loose from a standstill (static friction), sliding continuously on a dry floor (kinetic friction), sliding continuously on a greased floor (lubricated friction), and moving the pod on wheeled dollies (rolling friction).

In mechanical systems, friction types follow a general hierarchy of resistance. Static friction (starting motion) is the highest because surfaces settle and interlock. Kinetic friction (dry sliding) is lower than static but still high due to direct surface scraping. Introducing a lubricant reduces this direct contact, lowering resistance further. Finally, replacing sliding motion with rolling motion (using wheels) typically offers the lowest resistance because the contact point rolls over the surface rather than dragging across it.

Step-by-Step Solution

1

Evaluate the resistance when starting motion from a dead stop.

Identified as static friction.

Static friction must be overcome to initiate movement and is typically the strongest resistive force between two unlubricated solid surfaces.

2

Evaluate the resistance when sliding continuously on a dry surface.

Identified as dry kinetic (sliding) friction.

Kinetic friction opposes ongoing motion and is generally weaker than static friction for the same surfaces.

3

Evaluate the effect of adding grease to the sliding surfaces.

Identified as lubricated boundary or fluid friction.

Lubricants physically separate the solid surfaces, reducing direct contact and thus lowering the resistance compared to dry sliding.

4

Evaluate the resistance when wheels are introduced.

Identified as rolling friction.

Rolling friction involves rolling rather than dragging, which requires significantly less force to maintain motion than sliding.

5

Order the scenarios by the magnitude of frictional force from highest to lowest.

Static friction > Dry kinetic friction > Lubricated sliding friction > Rolling friction.

This sequence follows fundamental mechanical principles regarding types of resistance.

Key Concept

Types and Magnitudes of Mechanical Friction

Estimated Time:45s

Question 102Question →

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

The kinetic frictional force will double, because there is twice as much brake pad material in contact with the rotor.

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

The kinetic frictional force will be reduced by half, because the clamping force is spread out over a larger surface area.

The kinetic frictional force will increase, because the larger pads produce a stronger reaction force against the rotor's inertia.

Show answer & explanation

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

Answer

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

According to the standard model of dry friction (Coulomb friction), the kinetic frictional force between two solid surfaces is directly proportional to the normal force pressing them together and the materials involved (the coefficient of friction), but it is completely independent of the apparent area of contact. Since the normal force and materials are unchanged, the friction remains the same.

Step-by-Step Solution

1

Identify the factors that determine kinetic frictional force.

Kinetic friction (

F_k

) is determined by the formula

F_k = \mu_k F_N

, where

\mu_k

is the coefficient of kinetic friction and

F_N

is the normal force.

Establishing the mathematical relationship is necessary to see which variables affect the outcome.

2

Evaluate the changes made in the new design.

The surface area doubled, but the normal force (clamping force) and the materials (which determine

\mu_k

) remained exactly the same.

To apply the friction formula, we must know if the variables within it have changed.

3

Determine the effect on the total frictional force.

Because neither the normal force nor the coefficient of friction changed, the calculated frictional force remains identical, proving it is independent of surface area.

This confirms the theoretical principle of dry friction.

Key Concept

Friction and Contact Area Independence

Question 103Question →

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

The water pushing forward against the paddle

The forward inertia of the canoe resisting the backward pull

The backward force of the paddle being greater than the mass of the canoe

The reduced surface friction between the canoe hull and the water

Show answer & explanation

Answer: The water pushing forward against the paddle

Answer

The water pushing forward against the paddle

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

Step-by-Step Solution

1

Identify the action force described in the scenario.

The paddle pushes backward against the water.

Newton's Third Law requires identifying the initial interacting bodies and the direction of the applied force.

2

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

The water pushes forward against the paddle.

Forces always occur in equal and opposite pairs acting on different bodies. If the action is backward on the water, the reaction must be forward on the paddle.

Key Concept

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

Question 104Question →

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 105Question →

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

Click a left item, then click its matching right item

Show answer & explanation

Answer

Tires resting without slipping match with static friction. The aerodynamic body pushing through winds matches with fluid friction. Locked wheels skidding match with kinetic friction. Cylindrical bearings match with rolling friction.

Each mechanical situation directly illustrates one of the four primary types of friction: static (no relative motion), kinetic (continuous sliding), rolling (rotating elements), and fluid (resistance through a gas or liquid).

Step-by-Step Solution

1

Analyze the sloped ramp scenario.

Identified no relative motion between the tires and the ramp.

Surfaces at rest relative to each other experience static friction.

2

Analyze the high-speed wind scenario.

Identified interaction between a solid moving body and a gas (air).

Gases and liquids behave as fluids, meaning aerodynamic drag is a form of fluid friction.

3

Analyze the emergency stop scenario.

Identified the tires locking and sliding continuously across the pavement.

Active sliding between two solid surfaces characterizes kinetic friction.

4

Analyze the axle bearing scenario.

Identified cylindrical elements rotating to facilitate movement.

The rotation of cylinders or spheres between surfaces is the defining characteristic of rolling friction.

Key Concept

Frictional Resistance Types and Applications

Question 106Question →

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

Drag items to arrange them in the correct order

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Answer

The correct sequence from lowest to highest momentum is: motorcycle, bus, car, and finally the truck.

The correct sequence is found by multiplying each vehicle's mass by its velocity and then ordering the products from smallest to largest: motorcycle (

10,000

), bus (

25,000

), car (

30,000

), and truck (

36,000

).

Step-by-Step Solution

1

Recall the formula for calculating momentum.

p = m \times v

Momentum requires multiplying the mass of the object by its velocity.

2

Calculate the momentum for the motorcycle.

400 \text{ kg} \times 25 \text{ m/s} = 10,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the first vehicle.

3

Calculate the momentum for the bus.

5,000 \text{ kg} \times 5 \text{ m/s} = 25,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the second vehicle.

4

Calculate the momentum for the car.

1,500 \text{ kg} \times 20 \text{ m/s} = 30,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the third vehicle.

5

Calculate the momentum for the truck.

3,000 \text{ kg} \times 12 \text{ m/s} = 36,000 \text{ kg}\cdot\text{m/s}

This establishes the total momentum for the fourth vehicle.

6

Order the resulting values from lowest to highest.

10,000 < 25,000 < 30,000 < 36,000

The question requires arranging the vehicles in ascending order based on their momentum.

Key Concept

The total momentum of a moving object is directly proportional to both its mass and its velocity.

Estimated Time:1m 0s

Question 107Question →

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 108Question →

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}

).

Question 109Question →

A sledgehammer head with a weight of $19.6 \text{ N}$ on Earth strikes a metal spike with a downward velocity of $4 \text{ m/s}$ . The impact brings the hammer head to a complete stop in $20 \text{ ms}$ (milliseconds). What is the average impact force exerted on the spike? (Assume $g = 9.8 \text{ m/s}^2$ )

0.4 \text{ N}

3,920 \text{ N}

400 \text{ N}

0.16 \text{ N}

Show answer & explanation

Answer: $400 \text{ N}$

Answer

The correct answer is

400 \text{ N}

.

The force is found by first converting weight to mass (

19.6 / 9.8 = 2 \text{ kg}

) and time to seconds (

20 \text{ ms} = 0.02 \text{ s}

). The change in momentum is

2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

. Dividing this change by the impact duration (

0.02 \text{ s}

) gives an average impact force of

400 \text{ N}

.

Step-by-Step Solution

1

Calculate the mass of the sledgehammer head.

m = \frac{W}{g} = \frac{19.6 \text{ N}}{9.8 \text{ m/s}^2} = 2 \text{ kg}

Momentum equations require mass, not weight.

2

Convert the impact time to standard SI units (seconds).

t = 20 \text{ ms} = 0.02 \text{ s}

Standard units must be used to calculate force in Newtons.

3

Calculate the change in momentum (impulse).

\Delta p = m \times \Delta v = 2 \text{ kg} \times 4 \text{ m/s} = 8 \text{ kg} \cdot \text{m/s}

Impulse is equal to the change in momentum.

4

Calculate the average impact force.

F = \frac{\Delta p}{\Delta t} = \frac{8 \text{ kg} \cdot \text{m/s}}{0.02 \text{ s}} = 400 \text{ N}

Force is the rate of change of momentum.

Key Concept

Impulse and Momentum

Question 110Question →

Arrange the following vehicle scenarios in order from the lowest acceleration to the highest acceleration.

Drag items to arrange them in the correct order

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Answer

The correct sequence from lowest to highest acceleration is: the forklift (

0 \text{ m/s}^2

), the motorized cart (

2 \text{ m/s}^2

), the delivery van (

4 \text{ m/s}^2

), and the sports car (

5 \text{ m/s}^2

).

By applying the acceleration formula

a = \frac{\Delta v}{t}

to each scenario, we find the respective accelerations are

0 \text{ m/s}^2

,

2 \text{ m/s}^2

,

4 \text{ m/s}^2

, and

5 \text{ m/s}^2

. Placing them in ascending numeric order yields the correct sequence.

Step-by-Step Solution

1

Calculate the acceleration of the forklift.

a = 0 \text{ m/s}^2

Because the forklift maintains a constant speed in a straight line, its velocity does not change.

2

Calculate the acceleration of the motorized cart.

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

Using the formula

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

, we get

\frac{6 - 0}{3} = 2

.

3

Calculate the acceleration of the delivery van.

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

Using the formula

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

, we get

\frac{22 - 10}{3} = 4

.

4

Calculate the acceleration of the sports car.

a = 5 \text{ m/s}^2

Using the formula

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

, we get

\frac{15 - 0}{3} = 5

.

Key Concept

Acceleration is the rate at which an object changes its velocity, calculated by dividing the change in velocity by the elapsed time.

Estimated Time:1m 0s

Question 111Question →

Match each flight deck towing and movement scenario to its resulting acceleration using Newton's Second Law ( $F = ma$ ). Assume no friction unless stated.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches pair the aircraft with

0.8 \text{ m/s}^2

, the munitions cart with

4.0 \text{ m/s}^2

, the helicopter with

0.25 \text{ m/s}^2

, and the fuel pod with

1.2 \text{ m/s}^2

.

Each acceleration is determined by dividing the net force acting on the object by its mass. In scenarios where multiple forces act on the object, the net force must be found first by subtracting any resistance from the applied force.

Step-by-Step Solution

1

Calculate the acceleration for the aircraft.

Dividing the net force of

11,200 \text{ N}

by the mass of

14,000 \text{ kg}

yields

0.8 \text{ m/s}^2

.

Applying Newton's Second Law directly.

2

Calculate the acceleration for the munitions cart.

Dividing the net force of

12,800 \text{ N}

by the mass of

3,200 \text{ kg}

yields

4.0 \text{ m/s}^2

.

Applying Newton's Second Law directly.

3

Determine the net force and calculate the acceleration for the helicopter.

Subtract the

2,000 \text{ N}

resistance from the

6,000 \text{ N}

applied force to find a net force of

4,000 \text{ N}

. Dividing this by the

16,000 \text{ kg}

mass gives

0.25 \text{ m/s}^2

.

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

4

Calculate the acceleration for the fuel pod.

Dividing the net force of

4,800 \text{ N}

by the mass of

4,000 \text{ kg}

yields

1.2 \text{ m/s}^2

.

Applying Newton's Second Law directly.

Key Concept

Newton's Second Law (

F = ma

)

Estimated Time:1m 30s

Question 112Question →

A hydraulic press ram must reach a downward operating velocity of $0.8 \text{ m/s}$ starting from rest. If the hydraulic system is calibrated to accelerate the ram at a constant rate of $0.2 \text{ m/s}^2$ , how many seconds will it take for the ram to reach its target velocity?

0.16 \text{ s}

0.25 \text{ s}

4.0 \text{ s}

40.0 \text{ s}

Show answer & explanation

Answer: $4.0 \text{ s}$

Answer

It will take

4.0 \text{ s}

for the hydraulic press ram to reach the target velocity.

The time required to reach a specific velocity from rest is calculated by dividing the target velocity by the constant acceleration (

t = \frac{v}{a}

). Dividing

0.8 \text{ m/s}

by

0.2 \text{ m/s}^2

results exactly in

4.0 \text{ seconds}

.

Step-by-Step Solution

1

Identify the known kinematic variables from the scenario.

Initial velocity is

0 \text{ m/s}

, final velocity is

0.8 \text{ m/s}

, and acceleration is

0.2 \text{ m/s}^2

.

Organizing the known values determines which rate formula must be applied.

2

Rearrange the acceleration formula to solve for time.

The formula

a = \frac{\Delta v}{t}

becomes

t = \frac{\Delta v}{a}

.

To isolate the unknown variable (time) from the standard acceleration equation.

3

Calculate the final elapsed time.

0.8 \div 0.2 = 4.0 \text{ seconds}

.

Executing the division yields the time required to reach the target velocity.

Key Concept

Kinematic Rate Equations (Solving for Time)

Estimated Time:45s

Question 113Question →

A factory conveyor belt transports manufactured parts a distance of $45 \text{ meters}$ across the production floor in exactly $15 \text{ seconds}$ . What is the average speed of the conveyor belt in meters per second?

Show answer & explanation

Answer: 3

Answer

The average speed of the conveyor belt is

3 \text{ m/s}

.

The average speed is correctly calculated by dividing the total distance traveled (

45 \text{ meters}

) by the total time taken (

15 \text{ seconds}

), which equals

3 \text{ m/s}

.

Step-by-Step Solution

1

Identify the given values for distance and time.

Distance (

d

) =

45 \text{ meters}

, Time (

t

) =

15 \text{ seconds}

.

These variables are required to calculate average speed.

2

Apply the average speed formula.

v = \frac{d}{t} = \frac{45}{15}

.

Average speed is defined as the total distance traveled divided by the elapsed time.

3

Calculate the final speed.

v = 3

.

To find the numerical value of the speed in meters per second.

Key Concept

Average Speed

Question 114Question →

During a facility upgrade, an industrial overhead crane is lifting a large generator component vertically. The component has a mass of $2,500 \text{ kg}$ . The crane's hoist mechanism applies an upward tension force of $35,000 \text{ N}$ . Assuming the acceleration due to gravity is $10 \text{ m/s}^2$ , what is the upward acceleration of the generator component?

0.25 \text{ m/s}^2

4.0 \text{ m/s}^2

12.8 \text{ m/s}^2

14.0 \text{ m/s}^2

Show answer & explanation

Answer: $4.0 \text{ m/s}^2$

Answer

The upward acceleration of the generator component is

4.0 \text{ m/s}^2

.

To find the acceleration, we first determine the net force acting on the component. The crane pulls up with

35,000 \text{ N}

, but gravity pulls down with a force equal to the object's weight. The weight is the mass times gravity (

2,500 \text{ kg} \times 10 \text{ m/s}^2 = 25,000 \text{ N}

). The net upward force is the difference between these two opposing forces (

35,000 \text{ N} - 25,000 \text{ N} = 10,000 \text{ N}

). Finally, applying Newton's Second Law (

a = F_{net} / m

), we divide the net force by the mass (

10,000 \text{ N} / 2,500 \text{ kg}

) to find an acceleration of

4.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the downward weight force of the generator component.

Weight (

W

) =

m \times g

=

2,500 \text{ kg} \times 10 \text{ m/s}^2

=

25,000 \text{ N}

.

Gravity pulls down on the mass, creating an opposing force that must be overcome to lift the component.

2

Determine the net force acting on the component.

Net Force (

F_{net}

) = Upward Force - Downward Weight =

35,000 \text{ N} - 25,000 \text{ N}

=

10,000 \text{ N}

.

Newton's Second Law requires the total net force, taking all acting forces (tension and gravity) into account.

3

Calculate the acceleration using Newton's Second Law (

F = ma

).

Acceleration (

a

) =

F_{net} / m

=

10,000 \text{ N} / 2,500 \text{ kg}

=

4.0 \text{ m/s}^2

.

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

Key Concept

Newton's Second Law requires determining the net force by summing all forces acting on an object (including gravity) before dividing by mass to find acceleration.

Question 115Question →

A test sled has a weight of $2,940 \text{ N}$ (where $g = 9.8 \text{ m/s}^2$ ). During a braking test, a friction track applies a constant drag force of $588 \text{ N}$ . If it takes exactly $10 \text{ seconds}$ for the sled to come to a complete halt, what was its initial velocity?

1.96 \text{ m/s}

2 \text{ m/s}

19.6 \text{ m/s}

50 \text{ m/s}

Show answer & explanation

Answer: $19.6 \text{ m/s}$

Answer

19.6 \text{ m/s}

The correct answer applies the impulse-momentum theorem. First, the mass is found by dividing the weight by gravity (

2,940 \text{ N} / 9.8 \text{ m/s}^2 = 300 \text{ kg}

). Then, the impulse is calculated as the braking force multiplied by time (

588 \text{ N} \times 10 \text{ s} = 5,880 \text{ N}\cdot\text{s}

). Because impulse equals the change in momentum (

m \times \Delta v

), dividing the impulse by the mass yields the sled's initial velocity (

5,880 \text{ N}\cdot\text{s} / 300 \text{ kg} = 19.6 \text{ m/s}

).

Step-by-Step Solution

1

Calculate the mass of the sled from its given weight.

m = 2,940 \text{ N} / 9.8 \text{ m/s}^2 = 300 \text{ kg}

Momentum and kinematic equations require mass (in kg), not weight (in N).

2

Calculate the total impulse applied by the friction track.

\text{Impulse} = F \times t = 588 \text{ N} \times 10 \text{ s} = 5,880 \text{ N}\cdot\text{s}

Impulse is defined as the product of the average force and the time duration over which it acts.

3

Relate the impulse to the change in velocity.

5,880 = 300 \times \Delta v

, which solves to

\Delta v = 19.6 \text{ m/s}

.

The impulse-momentum theorem states that impulse equals the change in momentum (

\Delta p = m \times \Delta v

). Since the sled stops, the change in velocity equals its initial velocity.

Key Concept

Impulse and Momentum Conservation

Alternative Method

You can also solve this using Newton's Second Law and basic kinematics. First, find the deceleration:

a = F / m = 588 / 300 = 1.96 \text{ m/s}^2

. Then, use the kinematic equation

v_f = v_i - a \times t

. Since

v_f = 0

,

v_i = a \times t = 1.96 \times 10 = 19.6 \text{ m/s}

.

Estimated Time:1m 30s

Question 116Question →

A naval response boat is towing a disabled speedboat through choppy waters. The disabled speedboat has a mass of $4,000 \text{ kg}$ . The response boat's winch maintains a constant forward tension of $14,000 \text{ N}$ on the tow cable. Meanwhile, the water and wind create a combined resistive drag force of $4,400 \text{ N}$ acting against the speedboat.

What is the forward acceleration of the disabled speedboat in $\text{m/s}^2$ ?

Show answer & explanation

Answer: 2.4

Answer

2.4

The acceleration is determined by first finding the net force (

14,000 \text{ N} - 4,400 \text{ N} = 9,600 \text{ N}

) and then dividing it by the mass (

4,000 \text{ kg}

) according to Newton's Second Law (

a = F_{net}/m

), resulting in

2.4 \text{ m/s}^2

.

Step-by-Step Solution

1

Identify all horizontal forces acting on the speedboat.

Forward tension force =

14,000 \text{ N}

, Backward resistive drag force =

4,400 \text{ N}

.

Newton's Second Law requires the total net force, not just the applied force, to find the resulting acceleration.

2

Calculate the net horizontal force (

F_{net}

).

F_{net} = 14,000 \text{ N} - 4,400 \text{ N} = 9,600 \text{ N}

.

The drag force acts in the opposite direction of the tow cable, so it must be subtracted.

3

Use Newton's Second Law to solve for acceleration.

a = \frac{F_{net}}{m} = \frac{9,600 \text{ N}}{4,000 \text{ kg}} = 2.4 \text{ m/s}^2

.

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

Key Concept

Newton's Second Law (

F=ma

) requires first calculating the net force by combining all opposing forces (like applied tension and drag friction) before dividing by the mass to find the resulting acceleration.

Question 117Question →

An industrial robotic actuator pushes a $2,000 \text{ kg}$ steel casting along a horizontal assembly rail. The actuator applies a continuous forward force of $5,000 \text{ N}$ , while friction from the rail creates an opposing force of $1,000 \text{ N}$ . What is the forward acceleration of the steel casting?

0.5 \text{ m/s}^2

2.0 \text{ m/s}^2

2.5 \text{ m/s}^2

20.0 \text{ m/s}^2

Show answer & explanation

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

Answer

The correct forward acceleration is

2.0 \text{ m/s}^2

.

The correct answer is found by first determining the net force acting on the casting. Subtract the

1,000 \text{ N}

opposing friction from the

5,000 \text{ N}

applied force to get a net force of

4,000 \text{ N}

. Then, apply Newton's Second Law (

a = F/m

) by dividing the

4,000 \text{ N}

net force by the

2,000 \text{ kg}

mass, resulting in

2.0 \text{ m/s}^2

.

Step-by-Step Solution

1

Determine the net force acting on the steel casting.

F_{\text{net}} = 5,000 \text{ N} \text{ (applied)} - 1,000 \text{ N} \text{ (friction)} = 4,000 \text{ N}

When multiple forces act on an object, you must find the overall net force before calculating acceleration. Opposing forces are subtracted.

2

Use Newton's Second Law (

F = ma

) to solve for acceleration (

a = F/m

).

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

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

Key Concept

Newton's Second Law and Net Force Calculation

Question 118Question →

A carpenter uses a $5\text{ kg}$ pneumatic nail gun. The gun fires a $50\text{ gram}$ nail forward with a velocity of $100\text{ m/s}$ . Based on the conservation of momentum, if the gun is unrestrained, what is its backward recoil speed?

0.1\text{ m/s}

1\text{ m/s}

100\text{ m/s}

1,000\text{ m/s}

Show answer & explanation

Answer: $1\text{ m/s}$

Answer

The nail gun will have a backward recoil speed of

1\text{ m/s}

.

According to the law of conservation of momentum, the forward momentum of the nail must be perfectly balanced by the backward momentum of the nail gun. First, convert the nail's mass to standard units (

50\text{ g} = 0.05\text{ kg}

). The nail's momentum is

0.05\text{ kg} \times 100\text{ m/s} = 5\text{ kg}\cdot\text{m/s}

. Because the gun's mass is

5\text{ kg}

, dividing the total momentum (

5

) by its mass (

5

) gives a recoil speed of

1\text{ m/s}

.

Step-by-Step Solution

1

Convert the nail's mass from grams to kilograms to ensure consistent standard units.

50\text{ grams} = 0.05\text{ kg}

.

Momentum equations require matching mass units on both sides, typically kilograms.

2

Calculate the forward momentum of the nail.

p_{nail} = m \times v = 0.05\text{ kg} \times 100\text{ m/s} = 5\text{ kg}\cdot\text{m/s}

.

Momentum is the product of mass and velocity.

3

Apply the principle of conservation of momentum.

Initial momentum is zero, so

p_{gun} = p_{nail}

. The gun's backward momentum must be

5\text{ kg}\cdot\text{m/s}

.

In a closed system with no external forces, the total momentum before and after firing must remain equal.

4

Calculate the backward recoil speed of the nail gun.

v_{gun} = \frac{p_{gun}}{m_{gun}} = \frac{5\text{ kg}\cdot\text{m/s}}{5\text{ kg}} = 1\text{ m/s}

.

Rearranging the momentum formula (

p = mv

) solves for the unknown velocity.

Key Concept

Conservation of Momentum (Recoil)

Question 119Question →

Match each modification of a transport vehicle's engine thrust (net force) and cargo load (mass) to its resulting effect on the vehicle's acceleration. Assume all other conditions remain constant, based on Newton's Second Law ( $F = ma$ ).

Click a left item, then click its matching right item

Show answer & explanation

Answer

Each scenario is solved by substituting the modified multipliers for Force (

F

) and mass (

m

) into the acceleration formula

a = \frac{F}{m}

.

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

a = \frac{F}{m}

). By applying the respective multipliers given in each scenario to the numerator and denominator, the resulting change in acceleration can be accurately calculated as a multiple of the original state.

Step-by-Step Solution

1

Rearrange Newton's Second Law to solve for acceleration.

a = \frac{F}{m}

This isolates the variable we need to evaluate to compare proportional changes.

2

Evaluate the first condition: doubled thrust, unchanged mass.

a_{new} = \frac{2F}{m} = 2a

Force increases by a factor of 2, directly doubling acceleration.

3

Evaluate the second condition: halved thrust, doubled mass.

a_{new} = \frac{0.5F}{2m} = 0.25a

Reducing the numerator by half and doubling the denominator divides the overall quotient by 4.

4

Evaluate the third condition: doubled thrust, halved mass.

a_{new} = \frac{2F}{0.5m} = 4a

Dividing by 0.5 in the denominator is equivalent to multiplying by 2, which compounds with the doubled force in the numerator.

5

Evaluate the fourth condition: doubled thrust, doubled mass.

a_{new} = \frac{2F}{2m} = 1a

The equal proportional increases in both the numerator and denominator cancel each other out entirely.

Key Concept

Proportional Reasoning using Newton's Second Law

Question 120Question →

An electromagnetic catapult on a flight deck is used to launch a $2,500 \text{ kg}$ unmanned surveillance drone. The catapult applies a continuous forward thrust of $25,000 \text{ N}$ to the drone. During the launch run, the launch track components exert a constant resistive friction force of $5,000 \text{ N}$ against the drone's motion. What is the forward acceleration of the drone?

8 \text{ m/s}^2

10 \text{ m/s}^2

0.8 \text{ m/s}^2

0.125 \text{ m/s}^2

Show answer & explanation

Answer: $8 \text{ m/s}^2$

Answer

The drone experiences a forward acceleration of

8 \text{ m/s}^2

.

To find the acceleration, the net force must first be calculated by subtracting the opposing friction force (

5,000 \text{ N}

) from the forward thrust (

25,000 \text{ N}

), yielding

20,000 \text{ N}

. Using Newton's Second Law (

F = ma

), dividing this net force by the drone's mass (

2,500 \text{ kg}

) results in an acceleration of

8 \text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the net force acting on the drone.

F_{net} = 25,000 \text{ N} - 5,000 \text{ N} = 20,000 \text{ N}

.

According to Newton's Second Law, the acceleration is determined by the net force, which is the applied thrust minus the opposing friction.

2

Apply Newton's Second Law (

F = ma

) to calculate acceleration.

a = \frac{20,000 \text{ N}}{2,500 \text{ kg}} = 8 \text{ m/s}^2

.

Rearranging the formula to

a = \frac{F}{m}

isolates the acceleration for the calculation.

Key Concept

Newton's Second Law and Net Force

Force, Mass, and Motion

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