Diego is trying to lift a piano to the second floor of his house. diego uses a pulley system and gives a big lift to the piano.the piano moves upward, then stops, and then it starts to fall to the ground. (the direction of the force of gravity is negative.) which list best describes the forces on the piano in the proper order? positive force → balanced force → negative force negative force → balanced force → positive force positive force → unbalanced force → negative force negative force → unbalanced force → positive force

Answers

Answer 1

The correct order of forces acting on the piano as it moves up, stops, and falls back down is Positive force - balanced force - negative force. Here option A is the correct answer.

Positive force - when Diego gives a big lift to the piano, he applies a positive force to the piano, which helps to overcome the force of gravity and lift the piano upward.

Balanced force - when the piano stops moving upward, the forces acting on it are balanced. The force of gravity pulling the piano downward is equal and opposite to the force applied by Diego lifting the piano upward.

Negative force - when the piano starts to fall back down, the force of gravity pulling the piano downward becomes the dominant force, causing the piano to accelerate downward. This is a negative force acting on the piano.

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Complete question:

Diego is trying to lift a piano to the second floor of his house. Diego uses a pulley system and gives a big lift to the piano. The piano moves upward, then stops, and then starts to fall to the ground. (the direction of the force of gravity is negative.) Which list best describes the forces on the piano in the proper order?

A - positive force - balanced force - negative force

B - negative force - balanced force - positive force

C - positive force - unbalanced force - negative force

D - negative force - unbalanced force - positive force


Related Questions

The temperature measured outside the International Space Station is 2.7 Kelvin. How is it possible for empty space to have a temperature?

Answers

Answer:

people could just have a space heater or they are wearing warm clothes.

Explanation:

COMMON SENSE!!!!!

A graph titled change in temperature versus gravitational potential energy shows gravitational potential energy in kilojoules on the x-axis, numbered 0 to 50, and change in temperature in degrees celsius on the y-axis, numbered 0 to 12. The graph is a straight line from the (5, 1) and slants upward to (50, 11.5). Two additional points on the line are (10, 2.5) and (25, 6). Based on the graph, what kind of relationship exists between the change in temperature of the water and the gravitational potential energy of the cylinder? It is an inverse relationship. It is a direct relationship. It is an indirect relationship. It is a cyclic relationship.

Answers

Answer: (B) It is a direct relationship

Explanation:

Help...
If a machine allows us to apply less force to do work what is the cost?

Answers

If a machine allows us to apply less force to do work, the cost is that we must apply the force over a greater distance.

What is machine?

The above is so because, according to the principle of work and energy, the amount of work done remains constant, but the force and distance can be traded off. In other words, if we decrease the force required to do a certain amount of work, we must increase the distance over which the force is applied in order to compensate.

Therefore, For example, consider a simple lever. By using a lever, we can apply less force to lift a heavy object, but we must move the lever over a greater distance in order to do so. The work done, which is the product of the force and the distance, remains constant. In this case, the force is reduced, but the distance over which it is applied is increased.

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20 A measure of the speed and direction of an object's motion

a. velocity
b. speed.
c. momentum​

Answers

The answer is a. Velocity
Velocity= displacement over change in time

If Emily throws the ball at an angle of 30∘ below the horizontal with a speed of 14m/s, how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 4.0m.

Answers

Emily throws the ball at 30 degree below the horizontal

so here the speed is 14 m/s and hence we will find its horizontal and vertical components

v_x = 14 cos30 = 12.12 m/sv

x

=14cos30=12.12m/s

v_y = 14 sin30 = 7 m/sv

y

=14sin30=7m/s

vertical distance between them

\delta y = 4 mδy=4m

now we will use kinematics in order to find the time taken by the ball to reach at Allison

\delat y = v_y *t + \frac{1}{2} at^2\delaty=v

y

∗t+

2

1

at

2

here acceleration is due to gravity

a = 9.8 m/s^2a=9.8m/s

2

now we will have

4 = 7 * t + \frac{1}{2}*9.8 * t^24=7∗t+

2

1

∗9.8∗t

2

now solving above quadratic equation we have

t = 0.44 st=0.44s

now in order to find the horizontal distance where ball will fall is given as

d = v_x * td=v

x

∗t

here it shows that horizontal motion is uniform motion and it is not accelerated so we can use distance = speed * time

d = 12.12 * 0.44 = 5.33 md=12.12∗0.44=5.33m

I’ll literlly give you points
and make you brainiest

Ill literlly give you points and make you brainiest

Answers

Answer:

a

Explanation:

why is it more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity?

Answers

It is more difficult to start moving a heavy carton from rest than it is to keep pushing it with constant velocity because of static friction.

Static friction refers to the resistance encountered when attempting to initiate the movement of two objects that are in contact with each other but not currently in motion relative to each other. When an object is at rest, the force of static friction acts in the opposite direction to any force applied to it.

In this case, the force applied to the carton is the force needed to start moving it from rest. The force of static friction is greater than the force applied to the carton, making it difficult to start moving the carton from rest.

Once the carton is moving with constant velocity, the force of static friction is no longer acting on it. The only force acting on the carton is the force that is applied to keep it moving at a constant velocity. This force is equal to the force of kinetic friction which is less than the force of static friction.

To summarize, the initial effort required to overcome the static friction between a heavy carton and its resting position is greater compared to the continuous force needed to maintain its constant velocity. The force of static friction is greater than the force applied to the carton, making it difficult to start moving the carton from rest.

Once the carton is moving with constant velocity, the force of static friction is no longer acting on it, and the only force acting on the carton is the force that is applied to keep it moving at a constant velocity.

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the weight of a girl with the mass of 40.0kg is ?

Answers

Answer:

392 Newtons

Explanation:

In order to find the weight, you have to multiply the mass by the gravitation constant (9.8), which gives us 40.0 * 9.8 = 392 Newtons.

PLEASE HELP!
A truck pushes a 2030 kg-car with a force 700 N for 5.0 s. The cars starts from rest.
How far will it go?

Answers

Answer:

x = 4.32 [m]

Explanation:

We must divide this problem into three parts, in the first part we must use Newton's second law which tells us that the force is equal to the product of mass by acceleration.

∑F = m*a

where:

F = force = 700 [N]

m = mass = 2030 [kg]

a = acceleration [m/s²]

Now replacing:

\(F=m*a\\700=2030*a\\a = 0.344[m/s^{2}]\)

Then we can determine the final speed using the principle of conservation of momentum and amount of movement.

\((m_{1}*v_{1})+Imp_{1-2}=(m_{1}*v_{2})\)

where:

m₁ = mass of the car = 2030 [kg]

v₁ = velocity at the initial moment = 0 (the car starts from rest)

Imp₁₋₂ = The impulse or momentum (force by the time)

v₂ = final velocity after the impulse [m/s]

\((2030*0) + (700*5)=(2030*v_{2})\\3500 = 2030*v_{2}\\v_{2}=1.72[m/s]\)

Now using the following equation of kinematics, we can determine the distance traveled.

\(v_{2}^{2} =v_{1}^{2}+2*a*x\)

where:

v₂ = final velocity = 1.72 [m/s]

v₁ = initial velocity = 0

a = acceleration = 0.344 [m/s²]

x = distance [m]

\(1.72^{2}=0^{2} +(2*0.344*x) \\2.97 = 0.688*x\\x = 4.32 [m]\)

Describe the properties of waves and explain how they can be measured.
Why is a sound wave considered a mechanical wave?

Answers

The properties of waves are: wavelength, time period.

Sound wave is considered a mechanical wave because it requires medium to travel.

What is mechanical wave?

A mechanical wave is one whose energy cannot be transmitted via a vacuum. To transfer their energy from one place to another, mechanical waves need a medium.

A mechanical wave is something like a sound wave. A vacuum can not be traversed by sound waves.

Units of time and space can be used to measure the fundamental characteristics of waves. The length between wave crests, or wavelength (L), and the time it takes a wave to pass a fixed point, or period (T), are two characteristics that can be measured directly.

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if a tent is touched with a finger on inner surface , when it is raining , it allows the rain water to leak through. give a reason for this observation

Answers

Explanation:

When water vapor in the air comes into contact with something cool, like the ceiling of a tent, its molecules slow down and get closer together. When that happens, the gaseous water vapor turns back into liquid water droplets. That's condensation!

a physics lab instructor is working on a new demonstration. she attaches two identical conducting globes with mass

Answers

A physics lab instructor is working on a new demonstration involving two identical conducting globes with mass. To start, she should ensure the globes are clean and free of any dust or debris, as this can affect their conductivity.

Then, she can attach the globes using a conducting wire or a rod. It is important to make sure that the connection between the globes is secure and does not introduce any resistance. Once the globes are connected, the instructor can introduce a charge to one of the globes using a power source, such as a Van de Graaff generator. This will cause the charges to distribute evenly across both globes due to their conductive properties.

The instructor can then demonstrate various electrical phenomena, such as the repulsion or attraction between the globes, by manipulating the charges. It is crucial to follow safety precautions when dealing with electrical experiments and ensure proper grounding.

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A physics lab instructor is working on a new demonstration involving two identical conducting globes with mass. The main answer is that when these globes are brought into contact and then separated, they will each carry the same amount of charge. This phenomenon is known as charge conservation.



To explain further, when the globes are in contact, electrons are transferred from one globe to the other, equalizing the charge distribution between them. As a result, both globes have the same amount of charge. When they are separated, each globe retains the charge it acquired during contact.

This charge conservation principle is a fundamental concept in physics, and it is applicable in various scenarios. Understanding charge conservation helps explain how charge is distributed and transferred in objects and systems.

In summary, when two identical conducting globes with mass are brought into contact and then separated, they will each carry the same amount of charge due to charge conservation. This explanation highlights the concept of charge distribution and transfer in physics.

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if a truck goes 30 kilometers in 30 minutes what is the average speed ​

Answers

Answer:

60 km per hour

Explanation:

if you drive for 30 min and go 30km then if you drive for 60 min(1hr) then you would have driven 60km.

Answer:

60

Explanation:

hope this helps

Elements in the same group have…
A. A wide range of chemical properties
B. The same atomic radius
C. Number of electrons in its outer shell.
D. Same number of protons
E. The same number of electron shells.

Answers

A wide range of chemical properties

B
1 point
How much force is needed to accelerate a 2500 kg car at a rate of 4m/s²?
625 N
10,000 N
8,400 N
7,500 N

Answers

The force needed to accelerate a 2500 kg car at a rate of 4m/s² will be  10,000 N.Option B is correct.

What is force?

Force is defined as the push or pull applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.

Given data;

Force,F = ?

Mass,m = 2500 kg

Acceleration,a = 4 m/s²

The force is found as;

F=ma

F=2500 kg × 4 m/s²

F= 10,000 N

The force needed to accelerate a 2500 kg car at a rate of 4m/s² will be  10,000 N.

Hence option B is correct.

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Your driver's license is at risk of being cancelled if you: O A. Lied on the license application. O B. Are caught driving under the influence. O C. Cause an accident that injures another person. O D. Have more than three traffic violations in one year​

Answers

Your driver's license is at risk of being cancelled if you have more than three traffic violations in one year​. The correct option is D.

What is driving license?

The license by the central government to an individual to travel on road by his own vehicle on terms and conditions to be strictly followed.

When a driver is moving with his vehicle and come across the traffic signal, he must follow them. If he violates the traffic signals more than three times, he will get his license cancelled.

Thus, your driver's license is at risk of being cancelled if you have more than three traffic violations in one year​. The correct option is D.

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Which best describes the riders' final velocities ? gabriella is speeding up at the same rate that kendall is slowing down, and franklin is not accelerating. gabriella is slowing down at the same rate that kendall is speeding up, and franklin is not accelerating. gabriella and franklin are both slowing down, and kendall is accelerating. gabriella is slowing down, and kendall and franklin are accelerating.

Answers

"While Kendall is accelerating and Gabriella was slowing down in lockstep, Franklin is not doing so.

What does the term "acceleration" in physics mean?

When an object accelerates, its acceleration also moves in the same direction as its velocity. This indicates that the situation is developing. Example B shows an object moving in reverse while accelerating (i.e., having a negative velocity).

What do you call something that accelerates?

By dividing that velocity change but by time it takes for change to occur, acceleration is determined. Similar to velocity, acceleration has a direction. When something speeds up, it moves more quickly in the area it is moving.

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Assume that a satellite with a mass of 500kg orbits Earth 225km above its surface. Given that the mass of Earth is 5.97 x 10^24 kg and the radius of Earth is 6.38 x 10^6 m. (A)
What is the force of gravity that acts on the satellite? (B) What is the speed of the Satellites orbit

Answers

With the use of formulas,  the force of gravity on the satellite is 4563.8 N and the speed of the Satellites is 7764.5 m/s

What is Newton's Law of Gravitation ?

It states that the force of attraction between two object is proportional to the product of the masses and inversely proportional to the square of the distance between them.

Assume that a satellite with a mass of 500kg orbits Earth 225km above its surface. Given that the mass of Earth is 5.97 x 10^24 kg and the radius of Earth is 6.38 x 10^6 m.

(A) The force of gravity that acts on the satellite will be

F = GMm/r²

Where

G = 6.67 × 10^-11 Nm²/kg²M = 5.97 x 10^24 kgm = 500kgr = 6.38 x 10^6 m + 225 000 m = 6605000 mF = ?

Substitute all the parameters

F = (6.67 × 10^-11 × 5.97 x 10^24  × 500)/6605000²

F = 4563.8 N

(B) The speed of the Satellites orbit will be

v = √GM/r

v = √(6.67 × 10^-11 × 5.97 x 10^24 )/6605000

v = √60287509.5

v = 7764.5 m/s

Therefore, the force of gravity that acts on the satellite is 4563.8 N and the speed of the Satellites orbit is 7764.5 m/s

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Just like Coke is a type of soda, __________ is a type of ___________.
A.concentration,.equilibrium
B..equilibrium, concentration
C.diffusion, osmosis
D.osmosis. diffusion​

Answers

Answer:

osmosis diffusion

Explanation:

ok it's correct

When soda bottles are sealed in a factory, the bottles are all the same temperature with the same pressure of gas inside. A student decides to perform an experiment to determine what changes will result from adjusting the temperatures of two sealed soda bottles. One bottle of soda is heated, while the other is cooled.
Which statement describes a result of the experiment?

Answers

Answer: changes will result from adjusting the temperatures of two sealed soda

Explanation:

the preasure builds up and makes the bottle expand so it might crack but the other one will become ice then will crack the sides

Answer:

changes

Explanation:

1. List a similarity between magnetic force and electrical force.

Answers

Answer:

Both are attractive as well as repulsive.

Explanation:

(Like poles repel, like charges repel; unlike poles attract, unlike charges attract).

There are two types of charges that form electric fields: positive and negative charges. Magnetic fields are formed by charges and are related with two magnetic poles, north and south (but moving charges).

The attraction and repulsion of electric charges produce both electric and magnetic fields.

The force released by magnets when they attract or repel each other is known as magnetism. An electric force is the attracting or repulsive interaction between any two charged things.

Similarities are as follows:

There are two types of charges that form electric fields: positive and negative charges. Magnetic fields are formed by charges and are related with two magnetic poles, north and south (but moving charges).The attraction and repulsion of electric charges produce both electric and magnetic fields.

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STATE THE NUMBER OF IMAGES FORMED WHEN AN OBJECT IS BETWEEN TWO PLANE MIRRORS PLACED

Answers

When an object is placed between two parallel plane mirrors, an infinite number of images are formed. This is because each mirror reflects multiple images of the object, and those images are reflected by the other mirror, resulting in a never-ending series of reflections.

However, the intensity of each image decreases as the number of reflections increases, and the images get closer and closer together. In practical applications, only a few images are usually visible due to the limited amount of light available and the decreasing intensity of the images. Plane mirrors are flat mirrors that reflect light in a predictable manner. They are commonly used in many different applications, such as in mirrors for personal grooming or as reflective surfaces in optical instruments.

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When two swimmers are under water in a swimming pool, it is possible for
the interface between the water and the air to act as a mirror, allowing the
swimmers to see images of each other if they look up at the underside of
the surface. Explain this phenomenon.

Answers

Answer:

If they are looking at a large enoug h angle of incidence against a relatively calm surface, all the light will be internally reflected, allowing the  swimmers to see each other.

Explanation:

I need help with the 1st and the 3rd one plzzzzzzzzzzzzz

I need help with the 1st and the 3rd one plzzzzzzzzzzzzz

Answers

Answer for the first one is 2. The answer for the 3rd one is 8

Which animals are cold-blooded, obtain dissolved oxygen in water through gills, have scales, have fins, and live in water

Answers

Answer:

Sea fish

Explanation:

Sea fish doesn't breath through their gills but dissolved oxygen in water through gills

a truck of mass 2 500 kg travelling at the speed of 20 ms–1 to the right collide head-on with another car of mass 1 000 kg. If both the truck and the car stop after collision, what is the velocity of the car before the collision?​

Answers

Answer:

50 m/s opposite direction to the motion of the truck

Explanation:

From the question,

Applying the law of conservation of momentum

mu+m'u' = V(m+m')...….. Equation 1

Where m = mass of the truck, u = initial velocity of the truck, m' = mass of the car, u' = initial velocity of the car, V = Final velocity after collision

Given: m = 2500 kg, u = 20 m/s, m' = 1000 kg, V = 0 m/s (both car stop after collision)

Substitute these values into equation 1

2500(20)+1000(u') = 0(2500+1000)

2500(20)+1000(u') = 0

Solve for u'

u' = -[2500(20)]/1000

u' = -50 m/s

The negative sign shows that the car travels in opposite direction to the truck

Hence the car initial velocity before collision is 50 m/s in opposite direction to the motion of the truck

Please help me, I am following along diligently. V(t) = t^2 -9t+18, with distance, s measured in meters, left or right of 0, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t=0 sec is 1 meter right of 0, that is s(0)= 1Part I: Average velocity over the interval 0 to 8 secondsPart II: The instantaneous velocity and speed at time 5 secsPart III: The time intervals when the particle is moving rightPart IV: The time intervals when the particle is going faster, and slowing downPart V: Total distance the particle has traveled between 0 and 8 seconds

Please help me, I am following along diligently. V(t) = t^2 -9t+18, with distance, s measured in meters,

Answers

Given that the velocity at any time t is

\(v(t)=t^2-9t+18\)

Also, the time interval is from t = 0 to t = 8 seconds

The position at time t = 0 s is s(0) = 1 m towards right of zero.

The initial time is t = 0 s, so the initial velocity will be

\(\begin{gathered} v_i(t=0)=0^2-9\times0+18\text{ } \\ v_i(0)\text{ = 18 m/s} \end{gathered}\)

The final time is t = 8 s, so the final velocity will be

\(\begin{gathered} v_f(t=8)=8^2-9\times8+18 \\ v_f(8)\text{ = 64-72+18} \\ =\text{ 10 m/s} \end{gathered}\)

The average velocity will be

\(\begin{gathered} v_{av}=\frac{v_i+v_f}{2} \\ =\frac{18+10}{2} \\ =14\text{ m/s} \end{gathered}\)

Thus, the average velocity is 14 m/s.

Part II:

The instantaneous velocity at time t =5 s will be

\(\begin{gathered} v(t=5)=5^2-9\times5+18 \\ =25-45+18 \\ =-2\text{ m/s} \end{gathered}\)

The instantaneous speed is the magnitude of instantaneous velocity.

Thus, the instantaneous speed will be 2 m/s.

Part III:

The particle will move towards the right when v(t) > 0

The time intervals will be

\(\begin{gathered} t^2-9t+18>0 \\ t^2-6t-3t+18>0 \\ t(t-6)-3(t-6)>0 \\ (t-6)(t-3)>0 \\ t-6>0\text{ or t>6} \\ t-3>0\text{ ot t>3} \end{gathered}\)

Thus, time intervals are t > 3 and t > 6 when the particle is moving towards the right.

Part IV :

The particle will move faster if the acceleration, a(t) > 0

The particle will slow down if the acceleration, a(t) < 0

So, first, we need to find the acceleration, it can be calculated as

\(\begin{gathered} a(t)=\text{ }\frac{d(v(t))}{dt} \\ =\frac{d(t^2-9t+18)}{dt} \\ =2t-9 \end{gathered}\)

For the particle moving faster,

\(\begin{gathered} a(t)>0 \\ 2t-9>0 \\ 2t-9+9>9+0 \\ 2t>9 \\ \frac{2t}{2}>\frac{9}{2} \\ t>\frac{9}{2} \\ t>4.5\text{ s} \end{gathered}\)

For particle slowing down,

\(\begin{gathered} a(t)<0 \\ 2t-9<0 \\ 2t-9+9<9+0_{} \\ 2t<9 \\ \frac{2t}{2}<\frac{9}{2} \\ t<4.5\text{ s} \end{gathered}\)

The total distance can be calculated as

\(\begin{gathered} s(t)=\int ^8_0v(t)dt \\ =\text{ }\int ^8_0(t^2-9t+18)\mathrm{d}t \\ =\lbrack\frac{t^3}{3}\rbrack^8_0-9\lbrack\frac{t^2}{2}\rbrack^8_0+18\lbrack t^{}\rbrack^8_0 \\ =\frac{1}{3}\lbrack512-0\rbrack-9\lbrack64-0\rbrack+18\lbrack8-0\rbrack \\ =\text{ 170.67-576+144} \\ =-261.33\text{ m} \end{gathered}\)

Here, the negative symbol indicates it is towards the left from zero.

A duck is 12 m from the edge of a pond. A student stands in the middle of the pond
and creates ripples that travel past the duck and towards the edge of the pond. The
ripples are produced uniformly at 2 ripples per second. The student determines that
the ripples take 3.0 seconds after they pass the duck to reach the edge of the pond.
Determine the wavelength of the ripples.

Answers

Answer:

The wavelength is 2 meters

Explanation:

The relationship between the frequency, the speed and the wavelength is given by the relation;

v = f × λ

The given parameters are;

The distance of the duck from the edge of the pond = 12 m

The number of ripples produced per second = Frequency, f = 2 Hz

The time it takes the ripple to reach the edge of the pond after travelling past the duck = 3 seconds

Therefore, speed of the wave, v = Distance/time = 12 m/(3 s) = 4 m/s

The wavelength, λ, is therefore;

λ = v/f = (4 m/s)/(2 Hz) = 2 meters.

The x and y components of a vector r are > rx = 14 m and ry = -9.5 m, respectively. Find (a) the direction and (b) the magnitude of the vector r > . (c) If both rx and r are doubled how do you predict your answers to parts (a) and (b) will change? (d) Verify your prediction in part (c) by calculating the magnitude and direction for this new case.

Answers

The direction of the vector is given by the angle θ, where θ = arctan(ry / rx). The magnitude of the vector is given by the formula |r| = sqrt(rx^2 + ry^2).

(a) To find the direction of the vector, we can use the formula θ = arctan(ry / rx). Substituting the given values, θ = arctan(-9.5 / 14) ≈ -32.9 degrees (measured counterclockwise from the positive x-axis).

(b) To find the magnitude of the vector, we can use the formula |r| = sqrt(rx^2 + ry^2). Substituting the given values, |r| = sqrt((14)^2 + (-9.5)^2) ≈ 16.6 m.

(c) If both rx and ry are doubled, the new values would be rx' = 2 * 14 = 28 m and ry' = 2 * (-9.5) = -19 m. The direction of the vector will remain the same, θ' = arctan(-19 / 28) ≈ -32.9 degrees. The magnitude of the vector will be doubled, |r'| = sqrt((28)^2 + (-19)^2) ≈ 33.3 m.

(d) Calculating the magnitude and direction for the new case with doubled values, we find |r_new| = 33.3 m and θ_new = -32.9 degrees. These values match the predicted changes, with the magnitude being doubled and the direction remaining the same.

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(a) The direction of the vector r is approximately -32.66 degrees. (b) the magnitude of the vector r is approximately 16.52 m. (c) the magnitude will be doubled since the magnitudes of both rx and ry are doubled. (d) our prediction in part (c) is verified.

The vector r has x and y components of rx = 14 m and ry = -9.5 m, respectively. To find the direction and magnitude of the vector, we can use trigonometry. The direction can be determined by calculating the angle θ using the inverse tangent function, and the magnitude can be found using the Pythagorean theorem. If both rx and ry are doubled, we can predict that the direction will remain the same, but the magnitude will also be doubled. This prediction can be verified by recalculating the magnitude and direction using the new values.

(a) To find the direction of the vector r, we can use trigonometry. The direction is given by the angle θ, which can be calculated using the inverse tangent function:

θ = arctan(ry / rx) = arctan(-9.5 m / 14 m) ≈ -32.66 degrees

Therefore, the direction of the vector r is approximately -32.66 degrees.

(b) The magnitude of the vector r can be found using the Pythagorean theorem. The magnitude, denoted as |r|, is given by:

|r| = sqrt(rx^2 + ry^2) = sqrt((14 m)^2 + (-9.5 m)^2) ≈ 16.52 m

Hence, the magnitude of the vector r is approximately 16.52 m.

(c) If both rx and ry are doubled, we can predict that the direction will remain the same because the ratio of ry to rx does not change. However, the magnitude will be doubled since the magnitudes of both rx and ry are doubled.

(d) To verify our prediction, we calculate the new magnitude and direction using the doubled values. The new rx becomes 2 * 14 m = 28 m, and the new ry becomes 2 * (-9.5 m) = -19 m.

The new magnitude, denoted as |r'|, can be calculated as:

|r'| = sqrt((28 m)^2 + (-19 m)^2) ≈ 33.24 m

The new direction, θ', can be calculated as:

θ' = arctan(-19 m / 28 m) ≈ -33.94 degrees

Comparing these values with our prediction, we can see that the magnitude has indeed doubled, and the direction remains in the same quadrant but with a slightly different value. Therefore, our prediction in part (c) is verified.

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A circular loop ( radius = 0.5 m) carries a current of 3.0 A and has unit normal vector of (2i - j +2k)/3 what is x component of the torque on this loop when it is placed in a uniform magnetic field of (2i-6j) T

Answers

Answer:

\(T=9.42Nm\)

Explanation:

From the question we are told that:

Radius \(r= 0.5 m\)

Current \(I= 3.0 A\)

Normal vector \(n=\frac{(2i - j +2k)}{3}\)

Magnetic field \(B= (2i-6j) T\)

Generally the equation for Area is mathematically given by

 \(A=\pi r^2\)

 \(A=3.1415 *0.5^2\)

 \(A=0.7853 m^2\)

Generally the equation for Torque is mathematically given by

 \(T=A(i'*B)\)

Where

 \(i'*B= \begin{bmatrix}2&-1&2\\2&-6&0\end{bmatrix}\)

 \(X\ component\ of\ i'*B= [(-1 * 0)-(2*-6)]\)

 \(X\ component\ of\ i'*B=12\)

Therefore

 \(T=0.7853*12\)

 \(T=9.42Nm\)

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