All practice questions

Question 341Question →

A painter has $\frac{3}{4}$ of a gallon of blue paint. If they use exactly $\frac{1}{3}$ of this paint to complete a small project, how many gallons of paint did they use? (Express your answer as a decimal.)

Show answer & explanation

Answer: 0.25

Answer

0.25

To find

\frac{1}{3}

of

\frac{3}{4}

, you must multiply the two fractions together. Calculating

\frac{3}{4} \times \frac{1}{3}

results in

\frac{3}{12}

. Simplifying by dividing the numerator and denominator by 3 gives

\frac{1}{4}

. Finally, converting

\frac{1}{4}

to a decimal yields 0.25.

Step-by-Step Solution

1

Identify the mathematical operation

Multiplication:

\frac{3}{4} \times \frac{1}{3}

The phrase '

\frac{1}{3}

of this paint' indicates finding a part of a part, which requires multiplication.

2

Multiply the fractions

\frac{3}{12}

Multiply the numerators together (

3 \times 1 = 3

) and the denominators together (

4 \times 3 = 12

).

3

Simplify the resulting fraction

\frac{1}{4}

Both

3

and

12

share a greatest common factor of

3

. Dividing both by

3

simplifies the fraction.

4

Convert the simplified fraction to a decimal

0.25

The question specifically requests the final answer to be expressed as a decimal.

Key Concept

Fraction multiplication and decimal conversion

Question 342Question →

A motorized winch pulls an $80\text{ kg}$ cargo pallet horizontally from rest across a concrete loading platform. The winch exerts a constant horizontal pulling force of $440\text{ N}$ , while a constant kinetic friction force of $120\text{ N}$ opposes the motion. What is the final speed of the pallet in meters per second ( $\text{m/s}$ ) after being pulled continuously for $5\text{ seconds}$ ?

Show answer & explanation

Answer: 20

Answer

20\text{ m/s}

The correct speed is

20\text{ m/s}

. By finding the net unbalanced force (

440\text{ N} - 120\text{ N} = 320\text{ N}

), the acceleration of the

80\text{ kg}

pallet is calculated as

a = 320 / 80 = 4\text{ m/s}^2

. Multiplying this constant acceleration by the elapsed time of

5\text{ s}

yields the final speed of

20\text{ m/s}

.

Step-by-Step Solution

1

Determine the net horizontal force acting on the cargo pallet by subtracting the opposing friction force from the applied pulling force.

F_{\text{net}} = 440\text{ N} - 120\text{ N} = 320\text{ N}

According to Newton's laws of motion, acceleration is produced only by the unbalanced net force acting on the mass.

2

Calculate the constant horizontal acceleration using Newton's second law of motion (

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

).

a = \frac{320\text{ N}}{80\text{ kg}} = 4\text{ m/s}^2

The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

3

Compute the final speed after

5\text{ seconds}

using the kinematic velocity-time relationship (

v = v_0 + at

) with an initial speed of

0\text{ m/s}

.

v = 0\text{ m/s} + (4\text{ m/s}^2)(5\text{ s}) = 20\text{ m/s}

For an object undergoing constant acceleration from rest, final velocity is the product of acceleration and elapsed time.

Key Concept

Newton's Second Law combined with linear kinematics under constant net force

Estimated Time:1m 30s

Question 343Question →

An electric motor performs $4{}500\text{ J}$ of mechanical work in $15\text{ seconds}$ . What is the power output of the motor, in watts?

Show answer & explanation

Answer: 300

Answer

The power output of the motor is

300\text{ W}

.

Power is calculated by dividing work by time (

P = \frac{W}{t}

). Dividing

4{}500\text{ J}

by

15\text{ s}

yields

300\text{ W}

.

Step-by-Step Solution

1

Identify the relationship between power, work, and time.

P = \frac{W}{t}

Power is defined scientifically as the rate of doing work or transferring energy per unit time.

2

Substitute the given work (

4{}500\text{ J}

) and time (

15\text{ s}

) into the power equation.

P = \frac{4{}500\text{ J}}{15\text{ s}} = 300\text{ W}

Dividing total work in joules by elapsed time in seconds yields the power in watts (

1\text{ W} = 1\text{ J/s}

).

Key Concept

Power is the rate at which work is performed over time (

P = \frac{W}{t}

).

Estimated Time:45s

Question 344Question →

A technician performs $750\text{ J}$ of mechanical work while pushing a piece of machinery across a level workshop floor over a distance of $15\text{ meters}$ . Assuming the force is applied parallel to the direction of motion, what is the magnitude of the horizontal force applied, in newtons?

Show answer & explanation

Answer: 50

Answer

The magnitude of the applied horizontal force is

50\text{ N}

.

Mechanical work is defined as

W = F \times d

when force and displacement are in the same direction. Rearranging to solve for force gives

F = \frac{W}{d} = \frac{750\text{ J}}{15\text{ m}} = 50\text{ N}

.

Step-by-Step Solution

1

State the governing formula relating work, force, and displacement

W = F \times d

Work is defined as force multiplied by displacement in the direction of the force.

2

Rearrange the equation to isolate the unknown force variable (

F

)

F = \frac{W}{d}

Dividing both sides of the work formula by displacement yields force.

3

Substitute the given numerical quantities (

W = 750\text{ J}

,

d = 15\text{ m}

) and compute

F = \frac{750}{15} = 50\text{ N}

Carrying out the arithmetic yields the magnitude of the required force in newtons.

Key Concept

Work is the product of the magnitude of displacement and the component of force in the direction of displacement (

W = Fd

).

Estimated Time:1m 0s

Question 345Question →

A model electric car accelerates uniformly along a straight track from rest to a speed of $12\text{ m/s}$ in $4\text{ seconds}$ . What is the magnitude of the car's acceleration in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The magnitude of the acceleration is

3\text{ m/s}^2

.

Acceleration is defined as the change in velocity divided by the time elapsed (

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

). Since the car accelerates from

0\text{ m/s}

to

12\text{ m/s}

in

4\text{ s}

, the acceleration is

\frac{12 - 0}{4} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement

Initial velocity

v_i = 0\text{ m/s}

, final velocity

v_f = 12\text{ m/s}

, time

t = 4\text{ s}

Establishing known variables is necessary before selecting the appropriate kinematic relationship.

2

Apply the definition of constant linear acceleration:

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

Formula set up as

a = \frac{12\text{ m/s} - 0\text{ m/s}}{4\text{ s}}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute acceleration

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

Dividing

12

by

4

yields the constant acceleration magnitude.

Key Concept

Uniform Linear Acceleration

Alternative Method

Using the kinematic equation

v_f = v_i + at

, substitute

12 = 0 + a(4)

, which simplifies directly to

4a = 12

, yielding

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

.

Estimated Time:45s

Question 346Question →

A $3\text{ kg}$ object moving at $20\text{ m/s}$ along a frictionless horizontal surface collides with and sticks to a stationary $7\text{ kg}$ object. Immediately after the collision, the combined mass slides onto a rough surface with a coefficient of kinetic friction of $0.3$ . Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , how many meters will the combined mass slide before coming to a complete stop?

Show answer & explanation

Answer: 6

Answer

6

The problem is solved in two phases. Phase 1 is the perfectly inelastic collision, where momentum is conserved:

p_i = p_f \Rightarrow (3)(20) = (10)v

, which gives a shared velocity of

6\text{ m/s}

. Phase 2 is the sliding on a rough surface, where the only horizontal force is kinetic friction. The acceleration is

a = -\mu_k g = -(0.3)(10) = -3\text{ m/s}^2

. Finally, using the kinematic equation

v_f^2 = v_i^2 + 2ad

(where

v_f = 0

), we get

0 = 36 + 2(-3)d

, yielding

d = 6\text{ meters}

.

Step-by-Step Solution

1

Apply the law of conservation of momentum to find the velocity of the combined mass immediately after the collision.

v = 6\text{ m/s}

In a perfectly inelastic collision, momentum is conserved (

m_1v_1 + m_2v_2 = (m_1+m_2)v

). Therefore,

3(20) + 7(0) = 10v

.

2

Calculate the deceleration of the combined mass due to kinetic friction.

a = -3\text{ m/s}^2

The net force is kinetic friction (

F_k = \mu_k m g

). Using Newton's second law, acceleration

a = -F_k / m = -\mu_k g = -0.3(10)

.

3

Use kinematics to find the distance required for the mass to come to a stop.

d = 6\text{ m}

Using the time-independent kinematic equation

v_f^2 = v_i^2 + 2ad

with

v_f = 0\text{ m/s}

,

v_i = 6\text{ m/s}

, and

a = -3\text{ m/s}^2

.

Key Concept

Conservation of Momentum and Kinematics

Question 347Question →

A $15\text{ kg}$ sled slides across a smooth ice rink at a constant velocity of $4\text{ m/s}$ . What is the magnitude of the sled's momentum in kilogram-meters per second ( $\text{kg}\cdot\text{m/s}$ )?

Show answer & explanation

Answer: 60

Answer

60 kg·m/s

Linear momentum is calculated using the formula

p = m \times v

. For an object with a mass of

15\text{ kg}

moving at

4\text{ m/s}

, the momentum is

15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

.

Step-by-Step Solution

1

Identify the given mass and velocity values.

m = 15\text{ kg}

and

v = 4\text{ m/s}

Linear momentum depends directly on an object's mass and its velocity.

2

Apply the momentum formula

p = m \times v

.

p = 15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

Multiplying mass by velocity calculates the magnitude of linear momentum.

Key Concept

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

p = mv

).

Estimated Time:45s

Question 348Question →

A rectangular glass container with internal base dimensions of $5\text{ cm}$ by $4\text{ cm}$ contains water. A solid mineral specimen with a mass of $130\text{ g}$ is completely submerged into the water, causing the water level to rise by $2.5\text{ cm}$ without spilling. What is the density of the mineral specimen in $\text{g/cm}^3$ ?

Show answer & explanation

Answer: 2.6

Answer

The density of the mineral specimen is

2.6\text{ g/cm}^3

.

Density is calculated by dividing mass by volume (

\rho = \frac{m}{V}

). The water displacement method reveals the object's volume:

\text{Volume} = \text{length} \times \text{width} \times \Delta h = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

. Dividing the given mass of

130\text{ g}

by the displaced volume of

50\text{ cm}^3

yields exactly

2.6\text{ g/cm}^3

.

Step-by-Step Solution

1

Calculate the volume of the displaced water inside the rectangular container.

V = 5\text{ cm} \times 4\text{ cm} \times 2.5\text{ cm} = 50\text{ cm}^3

The volume of fluid pushed upward corresponds to the area of the base multiplied by the change in water height.

2

Equate the volume of the submerged solid to the displaced fluid volume.

V_{\text{specimen}} = 50\text{ cm}^3

By the principle of fluid displacement, a completely submerged solid displaces a volume of fluid exactly equal to its own physical volume.

3

Calculate the density of the specimen using the mass-to-volume ratio.

\rho = \frac{m}{V} = \frac{130\text{ g}}{50\text{ cm}^3} = 2.6\text{ g/cm}^3

Density is an intensive physical property defined as mass per unit volume.

Key Concept

Density is an intensive physical property of matter defined as mass per unit volume (

\rho = m/V

), determinable for irregular or submerged solids via fluid displacement.

Estimated Time:1m 30s

Question 349Question →

An electric winch applies a constant horizontal pulling force of $220\text{ N}$ to drag a heavy storage crate across a level concrete floor for a distance of $15\text{ meters}$ in $6\text{ seconds}$ . What is the average power output delivered by the winch in watts?

Show answer & explanation

Answer: 550

Answer

The average power output of the winch is

550\text{ W}

.

Work equals force multiplied by distance (

220\text{ N} \times 15\text{ m} = 3300\text{ J}

). Power is the rate of work done per second (

3300\text{ J} / 6\text{ s} = 550\text{ W}

).

Step-by-Step Solution

1

Calculate the work done by multiplying force by distance

W = 220\text{ N} \times 15\text{ m} = 3300\text{ J}

Work measures the energy transferred by a force acting over a displacement in the direction of the force (

W = Fd

).

2

Calculate the power output by dividing work done by elapsed time

P = \frac{3300\text{ J}}{6\text{ s}} = 550\text{ W}

Power represents the rate at which work is done over time (

P = \frac{W}{t}

).

Key Concept

Work is calculated as the product of force and displacement (

W = Fd

), and power is the rate of doing work over time (

P = \frac{W}{t}

).

Estimated Time:1m 0s

Question 350Question →

A sealed, hollow cylinder made of solid metal (density $= 6.0 \text{ g/cm}^3$ ) is placed in a liquid solvent (density $= 1.5 \text{ g/cm}^3$ ). The cylinder achieves neutral buoyancy, meaning it floats completely submerged without sinking or rising. If the total outer volume of the cylinder is $400 \text{ cm}^3$ , what is the volume of the hollow cavity inside the cylinder in $\text{cm}^3$ ?

Show answer & explanation

Answer: 300

Answer

300

For the cylinder to be neutrally buoyant, its total mass divided by its total volume must equal the fluid's density of

1.5 \text{ g/cm}^3

. With a total volume of

400 \text{ cm}^3

, the cylinder's total mass is

600 \text{ g}

. Since the entire mass comes from the metal shell, dividing this

600 \text{ g}

by the metal's true density (

6.0 \text{ g/cm}^3

) reveals that the actual metal occupies

100 \text{ cm}^3

. The remaining volume (

400 - 100

) must be the

300 \text{ cm}^3

hollow cavity.

Step-by-Step Solution

1

Determine the average density required for neutral buoyancy.

Average density =

1.5 \text{ g/cm}^3

An object that floats completely submerged (neutrally buoyant) must have an overall density exactly equal to the fluid it displaces.

2

Calculate the total mass of the cylinder.

Total mass =

600 \text{ g}

Mass equals the overall average density multiplied by total volume (

1.5 \times 400

).

3

Calculate the volume occupied by the solid metal itself.

Metal volume =

100 \text{ cm}^3

The solid metal volume equals the total mass divided by the solid metal's density (

600 / 6.0

). The hollow cavity contributes essentially zero mass.

4

Calculate the volume of the hollow cavity.

Cavity volume =

300 \text{ cm}^3

The cavity volume is the total outer volume minus the volume of the solid metal (

400 - 100

).

Key Concept

Density, extensive/intensive properties, and buoyancy of composite objects

Question 351Question →

A divalent metal cation ( $M^{2+}$ ) contains $18$ electrons. In the nucleus of this isotope, the number of neutrons is $4$ greater than the number of protons. What is the mass number of this isotope?

Show answer & explanation

Answer: 44

Answer

The mass number of this isotope is

44

.

A neutral atom that forms a divalent cation (

M^{2+}

) loses

2

electrons. Since the cation has

18

electrons, the neutral atom has

20

electrons and therefore

20

protons. The isotope has

4

more neutrons than protons, giving

20 + 4 = 24

neutrons. The mass number is the sum of protons and neutrons:

20 + 24 = 44

.

Step-by-Step Solution

1

Determine the atomic number (number of protons) from the cation's charge and electron configuration.

Protons =

20

A divalent cation (

M^{2+}

) has lost

2

electrons relative to its neutral state. The neutral atom therefore has

18 + 2 = 20

electrons and, correspondingly,

20

protons.

2

Calculate the total number of neutrons in the nucleus.

Neutrons =

24

The problem specifies that the number of neutrons exceeds the number of protons by

4

, giving

20 + 4 = 24

neutrons.

3

Sum the protons and neutrons to obtain the mass number (

A

).

Mass number =

44

The mass number of an isotope is defined as the total number of nucleons (protons plus neutrons):

20 + 24 = 44

.

Key Concept

Calculation of atomic number and mass number from ionic charge and subatomic particle relationships.

Estimated Time:1m 30s

Question 352Question →

A technician inspects a solid metal component with a mass of $108\text{ g}$ and a volume of $12\text{ cm}^3$ . What is the density of the component in grams per cubic centimeter ( $\text{g/cm}^3$ )?

Show answer & explanation

Answer: 9

Answer

9 g/cm^3

Density measures the amount of mass contained per unit volume of a substance. Dividing the component's mass of

108\text{ g}

by its volume of

12\text{ cm}^3

gives a density of

9\text{ g/cm}^3

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement

Mass (

m

) =

108\text{ g}

, Volume (

V

) =

12\text{ cm}^3

Density is a fundamental physical property defined as mass per unit volume.

2

Calculate the density using the formula

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

\text{Density} = \frac{108\text{ g}}{12\text{ cm}^3} = 9\text{ g/cm}^3

Dividing the total mass of the object by its volume determines the mass contained in each cubic centimeter.

Key Concept

Density as a characteristic physical property of matter relating mass and volume

Estimated Time:45s

Question 353Question →

A motorized winch pulls a cable, accelerating a load from rest ( $0\text{ m/s}$ ) to a final velocity of $18\text{ m/s}$ in $6\text{ seconds}$ at a constant rate. What is the acceleration of the load in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The acceleration of the load is

3\text{ m/s}^2

.

Acceleration is calculated by dividing the total change in velocity by the elapsed time (

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

). Because the load accelerates uniformly from

0\text{ m/s}

to

18\text{ m/s}

over

6\text{ s}

, the acceleration is

\frac{18\text{ m/s} - 0\text{ m/s}}{6\text{ s}} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the initial velocity, final velocity, and elapsed time from the given problem.

v_i = 0\text{ m/s}

,

v_f = 18\text{ m/s}

, and

t = 6\text{ s}

These parameters are required to calculate uniform linear acceleration.

2

Set up the acceleration formula:

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

.

a = \frac{18 - 0}{6}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute the numerical value.

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

Dividing

18\text{ m/s}

by

6\text{ s}

yields

3\text{ m/s}^2

.

Key Concept

Linear acceleration is defined as the change in velocity divided by the time interval over which the change occurs (

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

).

Estimated Time:45s

Question 354Question →

An automotive technician pours a sample of hydraulic fluid with a density of $0.85\text{ g/cm}^3$ into a graduated container. If the fluid sample occupies a volume of $200\text{ cm}^3$ , what is the mass of the fluid in grams?

Show answer & explanation

Answer: 170

Answer

The mass of the hydraulic fluid sample is

170\text{ g}

.

Density is defined as the amount of mass contained within a given unit volume (

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

). Rearranging this formula to solve for mass gives

\text{Mass} = \text{Density} \times \text{Volume}

. Multiplying the fluid's density of

0.85\text{ g/cm}^3

by its volume of

200\text{ cm}^3

yields a total mass of

170\text{ g}

.

Step-by-Step Solution

1

State the formula relating mass, density, and volume:

\text{Mass} = \text{Density} \times \text{Volume}

.

\text{Mass} = 0.85\text{ g/cm}^3 \times 200\text{ cm}^3

Density represents mass per unit volume (

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

), so rearranging to solve for mass requires multiplying density by volume.

2

Multiply the numerical values to compute the total mass.

\text{Mass} = 170\text{ g}

0.85 \times 200 = 170

.

Key Concept

Calculating mass from density and volume (

m = \rho \times V

)

Estimated Time:45s

Question 355Question →

A warehouse forklift applies a constant horizontal forward force of $300\text{ N}$ to a $120\text{ kg}$ cargo pallet moving across a level floor. A constant opposing friction force of $60\text{ N}$ acts against the pallet. What is the magnitude of the pallet's acceleration in $\text{m/s}^2$ ?

Show answer & explanation

Answer: 2

Answer

The magnitude of the pallet's acceleration is

2\text{ m/s}^2

.

According to Newton's second law of motion, the acceleration of an object equals the net unbalanced force acting upon it divided by its mass (

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

). The net force is the forward applied force minus opposing friction (

300\text{ N} - 60\text{ N} = 240\text{ N}

). Dividing

240\text{ N}

by the mass of

120\text{ kg}

yields an acceleration of

2\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the net horizontal force acting on the object by combining all horizontal force components.

F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 300\text{ N} - 60\text{ N} = 240\text{ N}

Forces in opposite directions subtract to yield the overall resultant force causing acceleration.

2

Use Newton's second law (

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

) to solve for acceleration (

a

).

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

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

Key Concept

Newton's Second Law of Motion (

F_{\text{net}} = ma

) with opposing frictional forces

Estimated Time:1m 0s

Question 356Question →

An isotope of potassium has an atomic number of $19$ and a mass number of $39$ . How many neutrons are present in the nucleus of this atom?

Show answer & explanation

Answer: 20

Answer

The nucleus of this potassium atom contains

20

neutrons.

The mass number (

39

) represents the combined count of protons and neutrons in the nucleus. Because the atomic number is

19

, the atom has

19

protons. Subtracting the protons from the mass number yields

39 - 19 = 20

neutrons.

Step-by-Step Solution

1

Identify the atomic number and mass number from the problem statement.

Atomic number

Z = 19

, Mass number

A = 39

.

The atomic number indicates the number of protons (

19

), and the mass number indicates the total number of nucleons (

39

).

2

Subtract the atomic number from the mass number to calculate the number of neutrons.

N = 39 - 19 = 20

The number of neutrons is determined by subtracting the number of protons from the mass number (

N = A - Z

).

Key Concept

Calculating subatomic particle counts in an isotope using the relationship between mass number, atomic number, and neutrons (

N = A - Z

).

Estimated Time:40s

Question 357Question →

A student places an irregularly shaped mineral sample with a mass of $84\text{ g}$ into a graduated cylinder containing $40\text{ mL}$ of water. The water level rises to $68\text{ mL}$ . What is the density of the mineral in grams per cubic centimeter ( $\text{g/cm}^3$ )?

Show answer & explanation

Answer: 3

Answer

The density of the mineral is 3 g/cm³.

The volume of the mineral is found through liquid displacement:

68\text{ mL} - 40\text{ mL} = 28\text{ mL} = 28\text{ cm}^3

. Dividing the mass of the mineral (

84\text{ g}

) by its volume (

28\text{ cm}^3

) yields a density of

3\text{ g/cm}^3

.

Step-by-Step Solution

1

Determine the volume of the mineral using the water displacement method.

Volume = 68 mL - 40 mL = 28 mL = 28 cm³

When a solid is completely submerged, the volume of liquid displaced is equal to the volume of the solid.

2

Calculate the density of the mineral using the formula Density = Mass / Volume.

Density = 84 g / 28 cm³ = 3 g/cm³

Density is a characteristic physical property defined as the amount of mass per unit volume of a substance.

Key Concept

Density and Volume Determination via Water Displacement

Estimated Time:45s

Question 358Question →

A conveyor system accelerates a $15\text{ kg}$ package along a straight horizontal track from an initial speed of $2\text{ m/s}$ to a final speed of $8\text{ m/s}$ in $3\text{ seconds}$ . What is the magnitude of the net horizontal force acting on the package, in newtons?

Show answer & explanation

Answer: 30

Answer

The magnitude of the net horizontal force acting on the package is

30\text{ N}

.

By finding the acceleration through

a = \frac{v_f - v_i}{t} = \frac{8 - 2}{3} = 2\text{ m/s}^2

and applying Newton's second law (

F = ma

), the resulting net force is

15\text{ kg} \times 2\text{ m/s}^2 = 30\text{ N}

.

Step-by-Step Solution

1

Determine the horizontal acceleration of the package using 1D kinematics.

a = \frac{8\text{ m/s} - 2\text{ m/s}}{3\text{ s}} = \frac{6\text{ m/s}}{3\text{ s}} = 2\text{ m/s}^2

Acceleration measures the rate of change of velocity over elapsed time (

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

).

2

Calculate the net force by applying Newton's second law of motion.

F_{\text{net}} = m \times a = 15\text{ kg} \times 2\text{ m/s}^2 = 30\text{ N}

Net force is directly proportional to the mass and the acceleration of the object (

F = ma

).

Key Concept

Newton's Second Law and Uniform Acceleration

Estimated Time:1m 0s

Question 359Question →

A quartermaster is distributing supplies to a unit. The unit requires $4\frac{3}{4}$ pallets of rations. If $2\frac{1}{4}$ pallets have already been delivered, how many more pallets are needed?

Show answer & explanation

Answer: 2.5

Answer

2.5

To find how many more pallets are needed, subtract the amount already delivered (

2\frac{1}{4}

) from the total required (

4\frac{3}{4}

). Subtracting the whole numbers gives

4 - 2 = 2

. Subtracting the fractions gives

\frac{3}{4} - \frac{1}{4} = \frac{2}{4}

, which simplifies to

\frac{1}{2}

. The remaining amount is

2\frac{1}{2}

pallets, which can be expressed as the decimal

2.5

.

Step-by-Step Solution

1

Identify the total pallets required and the amount already delivered.

Total =

4\frac{3}{4}

pallets, Delivered =

2\frac{1}{4}

pallets.

Understanding the given values is necessary to determine the remaining balance.

2

Set up a subtraction equation to find the remaining pallets needed.

4\frac{3}{4} - 2\frac{1}{4}

Subtracting the part that has been delivered from the required total gives the remaining amount.

3

Subtract the whole numbers and the fractions.

4 - 2 = 2

and

\frac{3}{4} - \frac{1}{4} = \frac{2}{4}

.

Since the fractions already have a common denominator, they can be subtracted directly.

4

Simplify the fraction and convert to a decimal format.

\frac{2}{4}

simplifies to

\frac{1}{2}

. The mixed number

2\frac{1}{2}

equals

2.5

.

Numeric answers are typically expressed as decimals.

Key Concept

Subtracting mixed numbers with like denominators

Estimated Time:45s

Question 360Question →

An uncharged atom of chlorine has $17$ electrons and $18$ neutrons in its structure. What is the mass number of this chlorine atom?

Show answer & explanation

Answer: 35

Answer

The mass number of the chlorine atom is

35

.

For an uncharged atom, the number of protons equals the number of electrons (

17

). The mass number is the sum of protons and neutrons (

17 + 18 = 35

).

Step-by-Step Solution

1

Determine the number of protons in the atom

17

protons

In any electrically neutral atom, the number of positively charged protons is equal to the number of negatively charged electrons.

2

Add the number of protons and neutrons together

17 + 18 = 35

The mass number (

A

) of an atom is defined as the total number of protons plus neutrons located in its nucleus.

Key Concept

The mass number of an atom is the sum of its protons and neutrons. In a neutral atom, the number of protons equals the number of electrons.

Estimated Time:45s

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