A 0.75 m3 rigid tank initially contains air whose density is 1.18 kg/m3. The tank is connected to a high-pressure supply link through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 4.95 kg/m3. Determine, in kg, the mass of air that has entered the tank..

Answers

Answer 1

Answer:

2.83kg

Explanation:

Answer:

2.83kg

Explanation:

Given

initial density = 1.18 kg/m3

Final density in the tank = 4.95 kg/m3.

Let us write the mass balance first.

Change in the mass of the system=mass of the air entering the system - Mass of air out the system

Mass that entered= M2 - M1

But DENSITY= MASS/ VOLUME

Mass= volume × Density

We can expressed the mass in terms of density since density is given in the question.

Mass that entered= (volume × density)2 - ( volume × density)1

= (V ρ)2 - (V ρ)1

But V1= V2 the volume remains the same

= ( ρ2 - ρ1)v

= (4.95 kg/m3 - 1.18 kg/m3) 0.75 m3

= 3.77× 0.75

= 2.8275kg

Mass that entered= 2.83kg

therefore, mass of air that has entered the tank= 2.83kg


Related Questions

What are the names and number of of atoms in a molecule of nitrous oxide,N2O?

Answers

Answer:

2 nitrogen and 1 oxygen,

Explanation:

N2=2 nitrogen

O= a single element

2 nitrogen and 1 oxygen

write the following Quantitiesin scientific notation.
a. 10130 Pa to 2 decimal place

b. 978.15m * s-2 to one decimal place

c 0.000001256 A to3 decimal place​

Answers

Answer: a. \(1.01\times 10^{4}Pa\)

b.  \(9.8\times 10^{2}ms^{-2}\)

c.  \(1.256\times 10^{-6}A\)

Explanation:

Scientific notation is defined as the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example : 5000 is written as \(5.0\times 10^3\)

a. 10130 Pa to 2 decimal place is written as \(1.01\times 10^{4}Pa\)

b. \(978.15ms^{-2}\) to 1 decimal place is written as \(9.8\times 10^{2}ms^{-2}\)

c.  \(0.000001256A\) to 3 decimal places is written as \(1.256\times 10^{-6}A\)

Your son forgets to do his chores before leaving for hockey practice. You scold him later that evening when he returns (which he does NOT enjoy). This is an example of...

Answers

The scenario presented is an example of negative punishment.

Negative punishment involves the removal of a desirable stimulus or the addition of an aversive stimulus in response to a behavior, with the goal of decreasing the likelihood of that behavior occurring again in the future.

In this case, the desirable stimulus that was removed is the son's ability to engage in leisure activities like playing hockey, and the aversive stimulus that was added is the scolding from the parent. By experiencing this consequence, the son may be less likely to forget his chores in the future in order to avoid the negative outcome.

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What characteristics determine how easily two substances change temperature? Check all that apply.
volume of the two substances in contact
amount of time the two substances are in contact
Oarea in contact between the two substances
specific heat of the material that makes up the substances
density of the two substances in contact

Answers

Answer:

The characteristics that determine how easily two substances change temperature are:

specific heat of the material that makes up the substancesarea in contact between the two substances

The volume and density of the substances and the amount of time they are in contact do not directly affect how easily they change temperature.

Explanation:

Three packing crates of masses, M1 = 6 kg, M2 = 2 kg
and M3 = 8 kg are connected by a light string of
negligible mass that passes over the pulley as shown.
Masses M1 and M3 lies on a 30o
incline plane which
slides down the plane. The coefficient of kinetic friction
on the incline plane is 0.28.
Determine the acceleration of the system.

Answers

Answer:

 a = 2.5 m / s²

Explanation:

This is an exercise of Newton's second law, in this case we fix a coordinate system with the x axis parallel to the plane with positive direction

Let's write the second law for bodies in the inclined plane

    W₁ₓ + W₃ₓ - fr = (m₁ + m₃) a

    N₁ - \(W_{1y}\) + N₃- W_{3y} = 0

    N₁ + N₃ = W_{1y} + W_{3y}

let's use trigonometry to find the weight components

    sin 30 = Wₓ/ W

    Wₓ = W sin 30

    cos 30 = W_{y} / W

    W_{y} = W cos 30

we substitute

    N₁+ N₃ = W₁ cos 30 + W₃ cos 30

    W₁ₓ + W₃ₓ - μ (m₁ + m₃) g cos30 = (m₁ + m₃) a

     a = (m₁g sin 30 + m₃g sin 30 - μ (m₁ + m₃) g cos 30) / (m₁ + m₃)

     a = g sin 30 - μ g cos30

let's calculate

     a = 9.8 sin 30 - 0.28 9.8 cos 30

     a = 4.9 - 2,376

     a = 2.5 m / s²

A force does 128-J of work on a 4-kg cart. What mus be the velocity of the cart?

Answers

Answer:

v = 8[m/s]

Explanation:

In this case, the work that is exerted on the cart is the kinetic energy that allows the movement, so we can use the following equation of kinetic energy.

\(E_{kin}=Work\\E_{kin}=\frac{1}{2} *m*v^{2}\)

Now replacing:

\(128=0.5*4*v^{2} \\v=\sqrt{64} \\v=8[m/s]\)

Mike rides his horse with a constant speed of 20 km/h. How far can he travel in 4 hours?

Answers

Answer:

Mike can travel 80 Km in 4 hours

005 (part 1 of 2) 10.0 points
A runner is jogging in a straight line at a
steady v,= 2.1 km/hr. When the runner is
L= 4.4 km from the finish line, a bird begins
flying straight from the runner to the finish
line at us= 10.5 km/hr (5 times as fast as
the runner). When the bird reaches the finish

005 (part 1 of 2) 10.0 pointsA runner is jogging in a straight line at asteady v,= 2.1 km/hr. When the

Answers

A constant speed motion is one in which equal distances are covered in equal times

The bird travels a cumulative distance of 7.\(\overline 3\) km

The reason the above value is correct is as follows:

The known parameters are;

Speed of the runner, \(v_r\) = 2.1 km/hr

The location where the bird begins to fly to the finish line = When the runner is 4.4 km from the finish line

The speed of the bird, \(v_b\) = 10.5 km/hr = 5 times the runners speed

The bird reaches the finish line, turns, and returns back to the runner

Required:

The find cumulative distance traveled by the bird

Solution:

The distance the bird travels is five times the distance the runner travels, therefore,

Let x represent the distance the runner ravels before the bird returns, we have;

The distance the bird travels = 4.4 + 4.4 - x = 8.8 - x

The distance the runner travels = x

The time the runner runs x km = The time the bird flies (8.8 - 4) km

\(From \ velocity = \dfrac{Distance }{Time}\), we have;

\(Time= \dfrac{Distance }{Velocity}\)

Given the time taken by the runner is equal to the time taken by bird, while running, we have;

\(Time= \dfrac{x}{2.1} = \dfrac{8.8 - x}{10.5}\)

Therefore;

10.5·x = 2.1·(8.8 - x) = 2.1×8.8 - 2.1·x

10.5·x + 2.1·x =  2.1×8.8 = 18.84

12.6·x = 18.84

\(x = \dfrac{18.84}{12.6} =\dfrac{22}{15} = 1.4 \overline 6\)

\(The \ distance \ the \ bird \ travels = 8.8 - \dfrac{22}{15} \approx \dfrac{22}{3} = 7. \overline 3\)

The cumulative distance the bird travels is 7.\(\overline 3\) km

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plz help me if it's okay :) and thank you ​

plz help me if it's okay :) and thank you

Answers

Explanation:

I am not sure that this answer will be correct

plz help me if it's okay :) and thank you

Use the following information to answer questions 2-4. Two people are playing a game of
tug-of-war with the rope attached to a mass of 25 kg at the center. The person pulling to
the left pulls with a force of 20 N. The person pulling to the right pulls with a force of 10 N.
2. Which direction will the 25 kg mass move?
a. Left
b. Right
C. It will not move
How do you know?

What will the velocity of the mass be after 1 second?

What will the velocity of the mass be after 2 seconds?

Answers

The direction in which the 25 kg mass will move is to the Left. The correct option is A.

This is because the force pulling to the left is greater than that to the right.

The velocity of the mass after 1 second will be 0.4 m/s

The velocity of the mass after 2 seconds will be 0.8 m/s

What is the net force on the mass of 25 kg?

The net force o the mass of 25 kg is given below:

Net force = 20 N - 10 N

Net force = 10 N

The velocity of the mass is given by the formula below:

Velocity = net force * time / mass

velocity after 1 second = 10 * 1 / 25

velocity after 1 second = 0.4 m/s

velocity after 2 seconds = 10 * 2 / 25

velocity after 2 seconds = 0.8 m/s

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Question No. 11. What is the acceleration of a car that goes from 20 Km/hr to 100 Km/hr in 8 seconds?2. A plane goes from 500 Km/hr to 1,400 Km/hr in 3 minutes. What is its acceleration?3. A car going at 80 mph comes to a complete stop in 6 seconds. Calculate the acceleration4. A train accelerates at a rate of 2 Km/hr/sec for a period of 30 seconds. If its initial speed was 15 Km/hr,what will be its final speed?5. If an object at rest accelerates by 5 meters/sec/sec, what will be its speed after 15 seconds?6. How long will it take for a car to come to a complete stop when traveling at 45 miles per hour if itsacceleration is -3 miles/hr/sec?7. A car going at 75 miles/hr slows down to 25 miles/hr in 2.5 sec; calculate the acceleration.8. What was the initial speed of a truck that ended up with a speed of 65 Km/hr after it accelerated3 Km/hr/sec for a period of 5 seconds?9. If a baseball lands with a speed of 80 miles/hr after traveling with an acceleration of -6 miles/hr/sec for 5 seconds, what was the initial speed at which the ball was hit?10. What distance will a bicyclist cover in 25 seconds if he pedals with an acceleration of 2.5 meters/sec/sec?11. What was the acceleration of a runner that ran a distance of 200 meters in 17 seconds?12. How long will it take for a car accelerating at 4 meters/sec/sec to cover a distance of 500 meters?

Question No. 11. What is the acceleration of a car that goes from 20 Km/hr to 100 Km/hr in 8 seconds?2.

Answers

Given:

The initial velocity of the car is

\(\begin{gathered} v_i=20\text{ km/hr} \\ =20\times\frac{1000\text{ m}}{3600\text{ s}} \\ =5.556\text{ m/s} \end{gathered}\)

The final velocity of the car is

\(\begin{gathered} v_f=100\text{ km/hr} \\ =\text{ 100}\times\frac{5}{18} \\ =\text{ 27.778 m/s} \end{gathered}\)

The time duration is t = 8 s

To find the acceleration of a car.

Explanation:

The acceleration of the car will be

\(\begin{gathered} a=\frac{v_f-v_i}{t} \\ =\frac{27.778-5.556}{8} \\ =2.775\text{ m/s}^2 \end{gathered}\)

Thus, the acceleration of the car is 2.775 m/s.

A car traveling 85 km/h is 250 m behind a truck
traveling 73 km/h.

Answers

Time needed = t = 20.83 s

Further explanation

Given

car speed = 85 km/h

truck speed = 73 km/h

Required

the time it takes for the car to reach the truck

Solution

When the car reaches the truck, the distance between them will be the same

x car - 250 m = x truck

General formula for distance (d) :

d = v.t

So the equation becomes :

85t-250 = 73t

12t=250

t = 20.83 s

g What is the CD's moment of inertia for rotation about a perpendicular axis through the edge of the disk

Answers

Answer:

Explanation:

A CD has an OD of 120 mm and an ID of 15 mm and has a mass between 14 and 33 grams. Let's call it m

Lets call the outer and inner radii R and r respectively

Find the moment of inertia about a line perpendicular to the surface of the disc through its center. We can integrate or look up the result from standard tables

I = ½m(R² + r²)

then use the parallel axis theorem to shift the position of the axis

I = ½m(R² + r²) + md²

where d is the distance of the shift. In this case d = R

I = ½m(R² + r²) + mR²

I = m(1.5R² + 0.5r²)

If we select a mass of say 20 grams

I = 0.020(1.5(0.060²) + 0.5(0.0075²))

I = 0.0001085625 kg•m²

Find the current flowing across the 30 Ohm resistor. I = [?] A
9.0 V 30 Ω 40 Ω 50 Ω 20 Ω 10 Ω​

ANSWERED: 0.143 A

Find the current flowing across the 30 Ohm resistor. I = [?] A9.0 V 30 40 50 20 10 ANSWERED: 0.143 A

Answers

The current flowing over the 30 Ω resistor is 0.4 A.

How to solve

To discover the current streaming over the 30 Ohm resistor, able to apply Ohm's Law, which states that the current (I) is break even with to the voltage (V) partitioned by the resistance (R). In this case, the voltage over the circuit is given as 9.0 V.

To calculate the full resistance of the circuit, we ought to consider the resistors in arrangement and parallel. The resistors with values of 40 Ω and 50 Ω are in serie.

Hence, the sum of their value (R_series )= 40 Ω + 50 Ω = 90 Ω. The 20 Ω and 10 Ω resistors are in parallel, hence, their resistance is represented as (1/R_parallel) = 1/20 Ω + 1/10 Ω = 1/10 Ω. Disentangling this expression gives R_parallel = 6.67 Ω.

Presently, ready to calculate the entire resistance of the circuit. The resistors with values of 30 Ω and 90 Ω (from the arrangement combination) are in parallel, so their identical resistance is given by 1/R_total = 1/30 Ω + 1/90 Ω = 1/22.5 Ω. Rearranging this expression gives R_total = 22.5 Ω.

At last, able to apply Ohm's Law to discover the current over the 30 Ω resistor. I = V / R_total = 9.0 V / 22.5 Ω ≈ 0.4 A.

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(b) Figure 11.1 shows a uniform meter rule balanced horizontally on a knife-edge placed at the 58cm mark when a mass of 20g is suspended from the end. 0cm 58cm Figure 11.1 (i) Find the mass of the rule. (ii) What is the weight of the rule. (taking g = 10m/s²)? 100cm 20g [2] [2]​

Answers

The mass of the rule is 3.36 kg and the weight of the rule is 33.6 N.

A knife should be balanced somewhere, right?

The butt of the blade is designed to balance the majority of fine chef's knives. This is due to the fact that a pinch grip is used in both Western and Eastern cutting styles for improved control. Therefore it makes sense that you'd want your knife to be balanced where you'll be holding it.

To balance the meter rule, Assume the mass of the rule "M".

It is possible to determine the rule's magnitude and weight, which act downward:

weight of rule = M * g

where g = acceleration due to gravity.

weight of rule * (50 cm) = (20 g) * (100 cm - 58 cm)

M * g * (50 cm) = (20 g) * (42 cm)

M = (20 g * 42 cm) / (50 cm * g)

M = 33.6 g / g

M = 33.6 g / 10 m/s^{2}

M = 3.36 kg

(ii) The weight of the rule:

weight of rule = M * g

weight of rule = 3.36 kg * 10 m/s^{2}

weight of rule = 33.6 N

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How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of kinetic energy?

Answers

Answer:

*1) 100 Joule energy

*2) 101.2 m/s

Explanation:

*1) 1J = 1w

100J = 100w

*2) A 70-kg person will have to run at a speed of 101.2 m/s to have that amount of kinetic energy.

Which one of the following is not a part of the Particle Theory?
1 All matter is made of particles
2 particles move faster when cooled
3 particles move faster when heated
4 particles are attracted to each other​

Answers

The only option that is not a part of the particle theory is, particles move faster when cooled.

What is particle theory of matter?

The particle theory of matter states that all matter consists of tiny particles which are in state of constant motion, colliding with one another and with of the containing vessel.

These theory can be summarized as;

All matter is made of particlesParticles move faster when heatedParticles are attracted to each other​

Thus, the only option that is not a part of the particle theory is, particles move faster when cooled.

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A sports car accelerates at a constant rate from rest to a speed of 90 km/hr in 8 s. What is its acceleration?

3.13 m/s2

4.22 m/s2

5.31 m/s2

6.67 m/s2

none of the above

Answers

First convert 90km/hr to m/s.

Initiate velocity = 0m/s (car was at rest)

Final velocity is 25m/s (90km/hr converted)

25m/s - 0m/s / 8s = 3.125 m/s^s

Therefore the answer is option A (3.13m/s^2)

Which type of wave does the illustration depict?
transverse wave
longitudinal wave
surface wave

Which type of wave does the illustration depict?transverse wavelongitudinal wavesurface wave

Answers

The graphic shows a longitudinal wave, a type of wave.

Option B is the best choice.

What is the most accurate way to define a longitudinal wave?

Longitudinal waves are waves in which the medium is displaced either in the same direction as or in the opposite direction from the wave's direction of propagation.

How can a wave type be determined?

There are two types of waves: longitudinal and transverse. While longitudinal waves resemble sound waves in that they alternate between compressions and rarefactions in a medium, transverse waves are like those on the surface of water that rise and fall.

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Answer:

Surface Wave

Explanation:

Im from k12 i took the test

What is the velocity of a dropped object after it has fallen for 12 s?

Answers

Hellow!

For this use the next formula:

Vf = Vo + gt

Initial velocity is zero, so the formula simplificate:

Vf = gt

Data:

Vf = Final velocity = ?

g = Gravity = 9.8 m/s²

t = Time = 12 s

Replacing according our data:

Vf = 9.8 m/s² * 12 s

Vf = 117.8 m/s

The final velocity will be 117.8 meters per second.

The largest stars we know of have masses of a little over 1035 kilograms, while the lowest mass stars have masses of about 1032 kilograms. How many times more massive are the most massive stars than the lowest mass stars?
Group of answer choices

a thousand times more massive.

a hundred times more massive.

ten times more massive.

ten thousand times more massive

Answers

Answer:

the bigger stars tend to be hotter and burn through their fuel more quickly than smaller stars they also tend to ether be turned into a black hole or a huge nebula with a neutron star the smaller stars have a tendency to go through their fuel slower and don't get as hot as big stars until the red giant stage.

Explanation:

Which direction do longitudinal waves travel?

Answers

Answer:

If the particles of the medium vibrate in a direction parallel to the direction of propagation of the wave, it is called a longitudinal wave. In longitudinal waves, the particle movement is parallel to the direction of wave propagation.

Explanation:

What is the vector sum of a vector T~ given by 40 m, 30 degrees and a vector U~ given by 12
m, 225 degrees?

Answers

Hence, R = 28.97 m, 24.5 degrees is the vector sum of T and U.

Is a vector at 30 degrees?

A vector's direction is frequently stated as a rotation of the vector's "tail" anticlockwise with respect to due East. In accordance with this practise, a vector having a direction of 30 degrees is a vector that has been anticlockwise rotated 30 degrees with respect to due east.

Let's begin by separating the components of the vector T:

T~ = 40 m, 30 degrees

T_x = 40 cos(30) = 34.64 m

T_y = 40 sin(30) = 20 m

Let's now decompose the vector U into its constituent parts:

U~ = 12 m, 225 degrees

U_x = 12 cos(225) = -8.49 m

U_y = 12 sin(225) = -8.49 m

It is possible to combine elements of the same type (x and y):

R_x = T_x + U_x = 34.64 m - 8.49 m = 26.15 m

R_y = T_y + U_y = 20 m - 8.49 m = 11.51 m

The Pythagorean theorem can be used to determine the size of the resulting vector R:

|R~| = sqrt(R_x² + R_y²) = sqrt((26.15 m)² + (11.51 m)²) = 28.97 m

The inverse tangent function can be used to determine the direction of the resulting vector R:

theta = tan⁻¹(R_y/R_x) = tan⁻¹(11.51 m/26.15 m) = 24.5 degree.

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How do you add sound waves?

Answers

The addition of two sound waves produces a new wave of higher amplitude if their compressions and refractions line up. It is also known as constructive interference.

What is interference?

Interference can be described as a phenomenon in which two waves combine by adding at every single point in space and time, to form a resultant wave of greater or lower amplitude.

Constructive and destructive interference occurs in the interaction of waves that are correlated with each other because they come from the same source.

When two sound waves propagate in the same direction in phase with each other, their amplitude gets added, and the resultant wave is produced from constructive interference.

When two waves interfere with each other and have a displacement in the opposite direction.  When a crest of a wave meets the trough of another wave, the waves undergo destructive interference.

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How do you add sound waves?

Problem No. 5: The results for one patient show that the blood in the aorta begins at a speed of 0.10 m/s and undergoes constant acceleration for 38 ms, reaching a peak speed of 1.29 m/s. (a) What is the acceleration reflected in these data? (b) How far does the blood travel during this period?

Answers

A. The acceleration reflected in the data is 38 m/s²

B. The distance traveled by the blood during the period is 0.02 m

How do i determine the acceleration reflected?

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

From the question given, we were told the the blood undergoes constant acceleration for 38 m/s².

Thus, we can say that the acceleration reflected in this data is 38 m/s²

How do i determine the distance travel by the blood?

The distance traveled by the blood can be obtain as follow:

Initial speed (u) = 0.10 m/sFinal speed (v) = 1.29 m/s Acceleration(a) = 38 m/s²Distance traveled (s) =?

v² = u² + 2as

1.29² = 0.1² + (2 × 38 × s)

1.6641 = 0.01 + 76s

Collect like terms

76s = 1.6641 - 0.01

76s = 1.6541

Divide both sides by 76

s = 1.6541 / 76

s = 0.02 m

Thus, we can conclude that the distance traveled by the blood during the period is 0.02 m

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If a charge is doubled, what happens to electric potential and electric potential energy?

Answers

The required charge on an object is doubled, and the electric potential energy stored in the system also doubles.

What is electric charge?

Electric charge is the property of subatomic particles that causes them to experience a force when placed in an electric and magnetic field.

Here,
If the charge on an object is doubled, the electric potential at a given point around the object also doubles. The electric potential energy stored in an object with a given charge at a certain distance from another charged object is proportional to the product of the two charges and inversely proportional to the distance between them. Thus, if the charge on an object is doubled, the electric potential energy stored in the system also doubles.

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In a DC generator, the generated emf is directly proportional to the

Answers

In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.

This relationship is described by the equation for the generated emf in a DC generator:

Emf = Φ * N * A * Z / 60

Where:

Emf is the generated electromotive force (in volts),

Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),

N is the number of turns in the armature winding,

A is the effective area of the armature coil (in square meters),

Z is the total number of armature conductors, and

60 is a constant representing the conversion from seconds to minutes.

From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.

The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.

The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.

Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.

By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.

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The engine in the car from question 1 uses a force of 1200 N to cause the car to accelerate at 3.5 m/s2. What is the car's mass?​

Answers

Answer:

Mass of car's engine = 342.85 kg (Approx.)

Explanation:

Given values:

Force applied by car = 1,200 N

Acceleration of car' engine = 3.5 m/s²

Find:

Mass of car's engine

Computation:

⇒ Mass = Force / Acceleration

⇒ Mass of car's engine = Force applied by car / Acceleration of car

⇒ Mass of car's engine = 1,200 / 3.5

⇒ Mass of car's engine = 342.85 kg (Approx.)

What is the power in watts of a 2.30 ✕ 10^2 MV lightning bolt having a current of 1.99 ✕ 10^4 A?

Answers

Given:

The potential difference between the bolt is

\(\begin{gathered} V=2.30\times10^2\text{ MV} \\ =2.30\times10^8\text{ V} \end{gathered}\)

The current is

\(I=1.99\times10^4\text{ V}\)

To find:

The power

Explanation:

The power is

\(\begin{gathered} P=VI \\ =2.30\times10^8\times1.99\times10^4 \\ =4.58\times10^{12}\text{ W} \end{gathered}\)

Hence, the power is

\(4.58\times10^{12}\text{ W}\)

what is the Vector product of A=2.00i+3.00j+1.00k and B= 1.00i -3.00j -2,00k

Answers

The vector product of A=2.00i+3.00j+1.00k and B=1.00i-3.00j-2.00k is C=9.00i+4.00j-9.00k.

To find the vector product (also known as the cross product) of two vectors, A and B, we can use the following formula:

C = A × B

Where C is the resultant vector, A and B are the given vectors, and × denotes the cross product.

Given A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k, we can substitute these values into the formula to find the vector product:

C = (2.00i + 3.00j + 1.00k) × (1.00i - 3.00j - 2.00k)

Now, let's expand the cross product using the properties of vector products:

C = (2.00i × 1.00i) + (2.00i × -3.00j) + (2.00i × -2.00k) +

   (3.00j × 1.00i) + (3.00j × -3.00j) + (3.00j × -2.00k) +

   (1.00k × 1.00i) + (1.00k × -3.00j) + (1.00k × -2.00k)

Now, let's calculate each of these cross products:

C = (2.00 × 1.00) \(i^2\) + (2.00 × -3.00) i × j + (2.00 × -2.00) i × k +

   (3.00 × 1.00) j × i + (3.00 × -3.00) \(j^2\) + (3.00 × -2.00) j × k +

   (1.00 × 1.00) k × i + (1.00 × -3.00) k × j + (1.00 × -2.00) \(k^2\)

Since i × j = k, j × k = i, and k × i = j, we can simplify the expression further:

C = 2.00k - 6.00i + 4.00i - 9.00j + k - 3.00j - 2.00j - 2.00k

Combining like terms, we get:

C = (2.00i + 4.00i) + (-6.00i - 9.00j - 3.00j) + (2.00k + k - 2.00k)

Simplifying further:

C = 6.00i - 12.00j + k

Therefore, the vector product of A and B is C = 6.00i - 12.00j + k, which can be written as C = 9.00i + 4.00j - 9.00k in terms of i, j, and k.

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Final answer:

The vector product of A and B is -3i - 5j - 9k.

Explanation:

The vector product, also known as the cross product, of two vectors A and B is denoted as A x B. It is a vector that is perpendicular to both A and B. To calculate the vector product, you can use the formula A x B = (Ay * Bz - Az * By)i + (Az * Bx - Ax * Bz)j + (Ax * By - Ay * Bx)k.

In this case, we have A = 2.00i + 3.00j + 1.00k and B = 1.00i - 3.00j - 2.00k. Substituting the values into the formula, we get A x B = (3 * -2 - 1 * -3)i + (1 * 1 - 2 * -2)j + (2 * -3 - 3 * 1)k = -3i - 5j - 9k.

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