an object is projected upward from the surface of the earth with an initial speed of 3.9 km/s. find the maximum height it reaches. m

Answers

Answer 1

The maximum height the object reaches is 925.32 km if it is projected upward from the surface of the earth with an initial speed of 3.9 km/s.

To find the maximum height the object reaches, we need to use the equations of motion. Since the object is projected upward, we can use the following equation:

v^2 = u^2 – 2gh

where v is the final velocity, u is the initial velocity, g is the gravitational acceleration, and h is the maximum height.

Since the object reaches its maximum height, its final velocity is zero. We know the initial velocity is 3.9 km/s. The gravitational acceleration at the surface of the earth is approximately 9.81 m/s^2 (or 0.00981 km/s^2). We can convert the initial velocity to m/s to make the calculations simpler:

u = 3.9 km/s = 3900 m/s

Substituting the values in the equation, we get:

0 = (3900 m/s)^2 - 2 * 9.81 m/s^2 * h

Simplifying this equation, we get:

h = (3900 m/s)^2 / (2 * 9.81 m/s^2) = 925320 m = 925.32 km

Therefore, the maximum height the object reaches is 925.32 km.

An object projected upward from the surface of the earth with an initial speed of 3.9 km/s will reach a maximum height of 925.32 km.

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Answers

formula for net force: force= mass x acceleration

how much charge, in micro-coulombs, must be transferred from the negatively charged to the positively charged plate to increase the potential difference between them by 77 v?

Answers

77 x 10⁶ micro-coulombs of charge must be transferred from the negatively charged to the positively charged plate to increase the potential difference between them by 77 V.

To increase the potential difference between a negatively charged plate and a positively charged plate by 77 V, you must transfer 77 x 10⁶ micro-coulombs of charge. This can be calculated using the equation:

Q = V * (10⁶)

where Q is the charge in micro-coulombs and V is the potential difference in Volts.

Plugging in 77 V for V, you get:

Q = 77 V * (10⁶)

Q = 77 x 10⁶ micro-coulombs.

Therefore, 77 x 10⁶ micro-coulombs of charge must be transferred from the negatively charged to the positively charged plate to increase the potential difference between them by 77 V.

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According to Jean Piaget, unrealistic idealism often occurs in adolescence as a result of __________. Rational thought egocentrism environmental conditions lack of education.

Answers

According to Jean Piaget, unrealistic idealism often occurs in adolescence as a result of egocentrism. The inability to distinguish between self and others is referred to as egocentrism.

What is egocentrism?

The inability to distinguish between self and others is referred to as egocentrism. It is, more precisely, the incapacity to effectively assume or comprehend any viewpoint other than one's own.

Egocentrism may be present in every stage of life, including childhood, adolescence, and maturity.

Hence option B is correct. According to Jean Piaget, unrealistic idealism often occurs in adolescence as a result of egocentrism.

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Answer:

egocentrism

got it right⬇️✅

According to Jean Piaget, unrealistic idealism often occurs in adolescence as a result of __________.

What is the root cause of earths magnetic field?

Answers

Answer:

I'm not sure but I think it is electric currents in the outer core

which atomic particle has no charge?
A. Electron
B. Neutron
C. Nucleus
D. Proton

Answers

Answer:

B. Neutron has no charge

Answer:

B. Neutron

Explanation:

Firstly, the nucleus is what contains the protons and electrons, so it is not an atomic particle. The electron has a negative charge, and the proton has a positive charge (you can remember this by looking at its prefix 'pro'). This means the neutron has no charge (think of it as neutral).

What is the best way to describe the modern understanding of the location of
electrons in an atom?
A. Electrons are placed within a mass of positively charged particles.
B. Electrons exist in specific orbits around the nucleus.
C. Electrons do not move and are in different levels within the atom.
D. Electrons are most likely to be found within certain regions around
the nucleus.

Answers

Answer:

B. Electrons exist in specific orbits around the nucleus.

Explanation:

Answer:

D

Explanation:

just did it :)




Colegt - Nm (4) Consider the following calculation: (106.7)*(98.2)/(46.210)x(1.01). The number of significant figures in the result: A) 1 B) 5 C) 2 D) 3 or an acceleration of 2.0 m/s2. This means

Answers

A significant digit is defined as a number that is not zero or a leading zero in a number. The number of significant figures in the above result is 3, which is the answer. Therefore, the correct option is D) 3 or an acceleration of 2.0 m/s².

The calculation is:

(106.7) * (98.2) / (46.210) * (1.01)

Calculating the above expression in accordance with BIDMAS/BODMAS rule, the result will be:

226.78473984

The given question is asking about the number of significant figures in the result. A significant digit is defined as a number that is not zero or a leading zero in a number.

The number of significant figures in the above result is 3, which is the answer. Therefore, the correct option is D) 3 or an acceleration of 2.0 m/s².

An acceleration of 2.0 m/s² implies that the velocity of the object is rising at a rate of 2.0 meters per second every second or every one second.

A body that is moving with an acceleration of 2.0 m/s² is experiencing an increase in velocity of 2.0 m/s every second.

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A baseball with a mass of 0. 15 kilograms collides with a bat at a speed of 40 meters/second. The duration of the collision is 8. 0 x 103 seconds. The

ball moves off with a speed of 50 meters/second in the opposite direction. What is the value of the force?

Answers

The value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

When an object collides with another object, they exchange energy. For example, a baseball and bat collision or a car collision. When two objects collide, the force of the collision has to be equal on both sides of the collision according to Newton's Third Law. So, to find the value of force, we will apply the equation:

F = ΔP / ΔT

where F is the force, ΔP is the change in momentum, and ΔT is the time of collision. The equation represents the impulse momentum theorem.

Now, let's apply the given values to the above equation.

Final momentum (p2) = mass × final velocity (v2)

p2 = 0.15 kg × (-50 m/s)

p2 = -7.5 kg.m/s

Initial momentum (p1) = mass × initial velocity (v1)

p1 = 0.15 kg × (40 m/s)

p1 = 6 kg.m/s

Change in momentum (ΔP) = p2 - p1

ΔP = -7.5 kg.m/s - 6 kg.m/s

ΔP = -13.5 kg.m/s

Time of collision (ΔT) = 8.0 × 10³ s

Now, putting the values of ΔP and ΔT in the equation of impulse momentum theorem, we get:

F = ΔP / ΔT

F = -13.5 kg.m/s ÷ 8.0 × 10³ s

F = -1.7 × 10⁻³ N

Thus, the value of force is 1.7 × 10⁻³ N, with the direction opposite to that of the bat's motion.

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BRAINLIEST HERE COME GET IT

Answers

Oh that would be lovely! Thank you!

Answer:

The answers is A lol

Explanation:

Which of these planets has characteristics most similar to Jupiter? (1
point)
O Mercury, Venus, and Neptune
O Venus, Earth, and Mars
O Neptune, Saturn, and Uranus
O Earth, Mars, and Saturn

Answers

Neptune Saturn and Uranus

They’re the Jovian or “Jupiter-like” planets because of their enormous size to the relative terrestrial planets.

1. A capacitor is made of 2 rectangular metal plates with side length of 3cmx6cm separated by a distance of 2. 36cm with water in between the plates. The capacitor has a voltage of 110v and is not connected to a battery. Calculate the capacitance. What is the new capacitance if we replace water with a new dielectric material with a constant of 3. 75 in between the plates? What is the new voltage? What is the charge on each plate?


2. A capacitor of 3. 23µF has an area of 6. 35mm^2. Determine the separation distance between the two plates. If the new capacitance is now 5. 63mF, what is the value of the dielectric inserted to the capacitor? What is the new voltage if the capacitor is connected to a 110 volts source? If the electric field created by two plates 8. 99x10^4 N/C and a working voltage of 63 volts. Will the capacitor experience a dielectric breakdown? Prove your answer.


USE GRESA

Answers

the electric field is more than the threshold value and the capacitor will experience dielectric breakdown.

1. Given values are,
side length of metal plates, a = 3 cm and b = 6 cm
distance between the plates, d = 2.36 cm
voltage, V = 110 V
dielectric constant of water, k = 80.4
dielectric constant of new material, k2 = 3.75
a) To calculate the capacitance of capacitor, the formula is, C=εA/d  ……………… (1)
where A = area of plate, ε = permittivity, and d = separation distance between two plates.
We know that the permittivity of vacuum is given as, ε0 = 8.854 x 10^-12 F/m
The capacitance of capacitor can be expressed as,
C1 = ε0 (kA/d) …………….. (2)
where, ε0 = permittivity of vacuum, k = dielectric constant and A = area of plate.
Substituting the given values in equation (2),
C1 = 8.854 x 10^-12 x 80.4 x (0.03 x 0.06)/0.0236
C1 = 0.000132 F
Therefore, the capacitance of capacitor is 0.000132 F.

b) To calculate the new capacitance, the formula is given as,
C2 = k2ε0A/d ……………… (3)
where k2 is the dielectric constant of new material.
Substituting the given values in equation (3),
C2 = 3.75 x 8.854 x 10^-12 x (0.03 x 0.06)/0.0236
C2 = 0.000263 F
Therefore, the new capacitance is 0.000263 F.

c) The new voltage can be calculated as,
V2 = V1(C1/C2) …………… (4)
Substituting the given values in equation (4),
V2 = 110 (0.000132/0.000263)
V2 = 55 V
Therefore, the new voltage is 55 V.

d) The charge on each plate is given as,
Q = CV ………….. (5)
Substituting the given values in equation (5),
Q = 0.000132 x 110
Q = 0.0145 C
Therefore, the charge on each plate is 0.0145 C.

2. Given values are,
capacitance, C = 3.23 µF
area of plate, A = 6.35 mm^2
separation distance between two plates, d = ?
new capacitance, C2 = 5.63 mF
new dielectric constant, k2 = ?
voltage, V = 110 V
electric field between two plates, E = 8.99 x 10^4 N/C
working voltage, Vw = 63 V

a) The separation distance between two plates can be calculated as,
C1/C2 = d2/d1  …………….. (6)
where d1 and d2 are the initial and final separation distance, respectively.
Substituting the given values in equation (6),
3.23 x 10^-6/5.63 x 10^-3 = d2/d1
d2 = 5.63 x 10^-3 x (d1/3.23 x 10^-6)
Area of plate, A = 6.35 mm^2 = 6.35 x 10^-6 m^2
The capacitance can be expressed as,
C = εA/d
d = εA/C
where ε = permittivity of dielectric material.
Therefore, substituting the given values in above equation,
d1 = ε x 6.35 x 10^-6/3.23 x 10^-6
d1 = 12.50 ε
Substituting the value of d1 in equation (6),
5.63 x 10^-3 = d2/12.50 ε
d2 = 70.38 ε
The separation distance between two plates is 70.38 ε.

b) The new dielectric constant can be calculated as,
C2 = k2ε0A/d2
k2 = C2d2/ε0A
Substituting the given values in above equation,
k2 = 5.63 x 10^-3 x 70.38 ε/(8.854 x 10^-12 x 6.35 x 10^-6)
k2 = 3.95
Therefore, the new dielectric constant is 3.95.

c) The new voltage can be calculated as,
V2 = V1(C1/C2)
Substituting the given values in above equation,
V2 = 110(3.23 x 10^-6/5.63 x 10^-3)
V2 = 0.063 V
Therefore, the new voltage is 0.063 V.

d) The electric field can be expressed as,
E = V/d
d = V/E
Substituting the given values in above equation,
d = 63/8.99 x 10^4
d = 7.01 x 10^-4 m
The voltage, V = 110 V > working voltage, Vw = 63 V

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A car and a truck round a curve of radius r at constant speeds. The speed of the car is twice the speed of the truck. What is the ratio of the acceleration of the car to that of the truck?

Select one:

a. 0

b. 3

c. 2

d. 4

e. 1

Answers

The ratio of the acceleration of the car to that of the truck can be determined based on the relationship between centripetal acceleration and speed.

Centripetal acceleration (ac) is given by the equation:

ac = (v^2) / r

where v is the speed and r is the radius of the curve.

Given that the speed of the car is twice the speed of the truck, we can denote the speed of the truck as v and the speed of the car as 2v.

The centripetal acceleration of the car (acar) is then:

acar = ((2v)^2) / r = 4(v^2) / r

The centripetal acceleration of the truck (atruck) is:

atruck = (v^2) / r

Therefore, the ratio of the acceleration of the car to that of the truck is:

acar / atruck = (4(v^2) / r) / ((v^2) / r) = 4

The ratio of the acceleration of the car to that of the truck is 4.

Therefore, the correct answer is d. 4.

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An object, experiencing no friction, keeps moving at a constant speed. What can we say about the net force on the object?

a) the net force keeping the object going is the same as the force that would be required to stop it
b)the net force is in the same direction as the object's velocity
c)the object is not changing its speed but its velocity might be changing in Direction so if there is a net force it is that right angles to the velocity
d)since the object has no acceleration there is no net force
e)the net force is equal to the weight of the object ​

Answers

Answer:

Explanation:

Let's look at a mathematical representation of this. The equation for tis is just a souped up version of Newton's 2nd Law:

F - f = ma. It an object is moving at a constant speed, the acceleration of that object is 0. That changes this equation to

F = f which states that the applied Force equals the frictional force, choice a.

Even though ome thing may be impoible uch a raining cat and dog, and human turning into a different pecie, realitically, it can happen but at a very extremley low percent?

Answers

In the above case, It is not possible for it to rain cats and dogs as it is a figure of speech and not a literal occurrence. Similarly, humans cannot turn into a different species as it goes against the laws of science .

What is the species about?

The statement above is not entirely accurate. Raining cats and dogs is a phrase used to describe heavy rain, it is not a real phenomenon. And humans cannot turn into a different species, it is a biological impossibility.

What does it imply when it says it's raining cats and dogs?

Consequently, a storm with strong winds (cats) and heavy rain may be described as "raining cats and dogs" (cats). Greek word cata doxa, which means "contrary to experience or conviction," may have been the source of the phrase "cats and dogs." It is raining exceptionally or ridiculously hard if it is raining cats and dogs.

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a bicyclist traveled from 15.6 m/s to 21.1 m/s over a distance of 30 meters

a) what is the acceleration of the bicyclist?

b) How much time does it take the bicyclist to travel the 30 meters

Answers

The acceleration of the bicyclist is 3.35 m / s². It takes the bicyclist 1.64 s to travel the 30 meters

We know that,

a = ( v - u ) / t

s = ut + 1 / 2 at²

where,

a = Acceleration

v = Final velocity

u = Initial velocity

t = Time taken

s = Distance travelled

Given that,

u = 15.6 m / s

v = 21.1 m / s

s = 30 m

a = ( 21.1 - 15.6 ) / t = 5.5 / t

s = ut + 1 / 2 at²

30 = 15.6 t + 1 / 2 ( 5.5 t )

30 = 15.6 t + 2.75 t

t = 30 / 18.35

t = 1.64 s

a = 5.5 / t = 5.5 / 1.64

a = 3.35 m / s²

Equations of motion are used to describe the position of an object using the motion of the object with respect to time. It is done using speed, acceleration, distance and time.

Therefore,

a) The acceleration of the bicyclist is 3.35 m / s²

b) Time taken by the bicyclist =

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v
\( v = v1 + v2 + v3\)
five resistance of value 0.1ohm 2.0ohms 1.0 ohms and 0.9 ohms are connected in series calculate the value of
the combined resistance ​

Answers

Answer:

v

Explanation:

bv

Solar energy stored in large bodies of water, called solar pounds, is being used to generate electricity. If such a solar power plant has an efficiency of 3 percent and a net power output of 180 kW, determine the average value of the required solar energy collection rate, in Btu/h.

Answers

The required solar energy collection rate, in Btu/h is 6,000,000.

Solar energy stored in large bodies of water, called solar pounds, is being used to generate electricity. If such a solar power plant has an efficiency of 3 percent and a net power output of 180 kW, the average value of the required solar energy collection rate, in Btu/h can be calculated as follows:

Given, efficiency of solar power plant = 3%Net power output = 180 kW We know that the solar power is given by ;P = ηQWhere, P = Power outputη = efficiency Q = Solar energy collection rate Substituting the values of η and P in the above equation, we get;180,000 W = 0.03Q

Therefore, Q = 180,000 / 0.03Q = 6,000,000 Btu/hence, the required solar energy collection rate, in Btu/h is 6,000,000.

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An artillery shell of mass 30 kg has a velocity of 250 m/s vertically upward. The shell explodes into two pieces; immediately after the explosion a fragment of mass 10 kg has a velocity of 120 m/s straight downward. How high above the point of the explosion does the larger fragment rise?

Answers

Answer:

9654.34 m

Explanation:

from conservation of momentum

\($$\begin{aligned}30 \times 250 &=-10 \times 120+20 \times V \\20 V &=30 \times 250+10 * 120 \\V &=\frac{30 \times 250+10 \times 120}{20}=435 \mathrm{~m} / \mathrm{s}\end{aligned}$$\)

And from Conservation of Energy

\(\frac{1}{2} m v^{2}=m g h\\h=\frac{v^{2}}{2 g}\\h=\frac{(435(m/s))^{2}}{2 \times 9.8(m/s^{2} )}\\h=9654.34 (m)\)

when preparing wiring diagrams for a bedroom circuit using the method presented in your reading material the first step is to

Answers

When creating wiring diagrams for a bedroom circuit using the method described in your reading material, the initial step involves creating a layout of cables that includes all the lighting and receptacle outlets. Hence, option 4. aligns well with the answer.

This is the most crucial step as it helps to define the overall scope of the wiring and the potential locations of the outlets. In the next step, draw a line between each switch and the outlet it controls. This will give a clear indication of the number of switches and outlets required for the room.

The third step is to draw the traveler conductors for any three-way switches. A traveler wire is used in a 3-way switch configuration and is used to connect the two switches together so that both switches can control the same light.A traveler wire is required to connect each 3-way switch to the other switch in the circuit.

The fourth and final step is to draw a line from the grounded terminal on the lighting panel to each outlet. Grounding wires are an important safety feature of all wiring systems. They help to prevent electrical shock and protect equipment from damage.

To summarize, when creating wiring diagrams for a bedroom circuit, it is important to:

Create a comprehensive cable layout that encompasses all outlets.

Draw lines connecting each switch to its corresponding outlet.

Include traveler conductors for any three-way switches.

Draw lines from the grounded terminal on the lighting panel to each outlet.

The wiring diagrams should be made as per the wiring codes to ensure the safety and quality of work. The bedroom circuit wiring diagrams will help the electrician in charge to install the wiring systems with more efficiency.

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4. What is the amplitude of the waves shown in the diagram below?

4. What is the amplitude of the waves shown in the diagram below?

Answers

Answer:

7.5 m

Explanation:

the amount of energy at the end of the system (output) is different from the starting energy (input). How does this not violate (break) the law of the conservation of energy. This question is based on solar and wind energy

Answers

Answer:

Because some of the energy escaped or was used.

Explanation:

If you were trying to get out of the way of a storm, you would need to know the speed at which it was moving.
a. true
b. false

Answers

This statement is false that If you were trying to get out of the way of a storm, you would need to know the speed at which it was moving.

How can we conclude that If you were trying to get out of the way of a storm, you would need to know the speed or the velocity at which it was moving?

If you were trying to get out of the way of a storm, you would need to know the velocity at which it was moving because,

According to the definition of the speed we can state that, Speed is the time rate at which an object is moving along a path, While according to the definition of velocity we can state that, velocity is the rate and direction of an object's movement.

However the mathematical formula doesn't make any difference,

\(S=\frac{d}{t}\) or \(V=\frac{d}{t}\)

d= This is the distance the storm going to cover.

t= The time within the storm going to cover the distance.

S and V is the speed and velocity of the storm respectively.

Seeing the mathematical formula we cannot make difference. But from the definition we can surely conclude that If you were trying to get out of the way of a storm, you would need to know the velocity at which it was moving. Because to get out of the way of the storm not only we have to know the path but also we have to know the storm's direction of movement.

So from the above discussion we can conclude that this statement is false.

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Find the x-component of this
vector:

Find the x-component of thisvector:

Answers

Answer:

4.978 m

Explanation:

\(\mathsf v_x\) , the x-component of a vector is given by \(\boldsymbol v\cos\theta\) where \(\theta\) is the angle formed by the vector with the x-axis. The sign of the x-component depends on which quadrant the vector is

Here \(\theta = 77.1\)°

\(\cost\theta = \cos(77.1) = 0.22325\)

The vector has magnitude of 22.3 m

So the x-component = 22.3 x 0.22325 = 4.978 m

a 45 kg block of ice slides down a frictionless incline 1.5 m long and 0.91 m high. a worker pushes up against the ice, parallel to the incline, so that the block slides down at constant speed. (a) find the magnitude of the worker's force. how much work is done on the block by (b) the worker's force, (c) the gravitational force on the block, (d) the normal force on the block from the surface of the incline, and (e) the net force on the block?

Answers

The factor of the pressure of gravity exerted at the ice block (of mass m) along the incline is mg sin θ. The resultant force \(\vec{F_{net} }\) is zero since there is no acceleration.

(a) The factor of the pressure of gravity exerted at the ice block (of mass m) along the incline is mg sin θ ,

In which θ=sin ^−1 (zero.ninety one/1.five) offers the attitude of inclination for the willing plane.

Since the ice block slides down with uniform pace, the employee need to exert a force \(\vec{F}\) “uphill” with a magnitude equal to mg sin θ.

Consequently,

F=mg sinθ=(45 kg)(9.8 m/s^2)( 1.5 m x 0.91 m)=2.7×10^2N

(b) For the reason that “downhill” displacement is contrary to \(\vec{F}\), the work done by the worker is \(W_1 =-(2.7*10^2 N)(1.5 m)=-4.0*10^2J\).

(c) Because the displacement has a vertically downward thing of value zero.ninety one m (in the same route as the force of gravity), we find the paintings achieved by gravity to \(W_2=(45 kg)(9.8 m/s^2 )(0.91 m)=4.0*10^2J.\)

(d) Since \(\vec{F_{N}}\) is perpendicular to the course of movement of the block, and cos 90°=0,paintings done via the normal pressure is \(W_3\) =0 by Eq. 7-7.

(e) The resultant force \(\vec{F_{net} }\) is zero since there is no acceleration. For that reason, its paintings is 0, as may be checked by means of including the above outcomes \(W_1+W_2 +W_3=0\).

Gravity is the fundamental force of attraction between any two objects with mass. It is a fundamental force of nature that governs the motion of planets, stars, galaxies, and other celestial bodies. According to the theory of general relativity, gravity arises due to the curvature of spacetime caused by the presence of massive objects.

Gravity is responsible for the motion of the planets around the sun, the moon around the earth, and the formation of stars and galaxies. It is a universal force that affects all objects in the universe, regardless of their size or composition. The strength of the gravitational force depends on the mass of the objects and the distance between them. The greater the mass of an object, the stronger its gravitational pull. Similarly, the closer two objects are, the stronger the gravitational force between them.

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ACTIVITY 3: THE CHOICE IS YOURS!

Directions: Read each item carefully. Choose the letter of the best answer.

____1. What is the advantage of an electromagnet compared to a permanent magnet?

A. Electromagnet is lighter.

B. Electromagnet can be turned on and off.

C. Permanent magnet cannot be used to pick up metals.

D. Electromagnet can be used for attracting more metals.

____2. What are the factors that affect the strength of an electromagnet?

A. Battery, magnet, and core

B. Dry cells, nail, and magnet

C. Number of coil, number of magnets, and wire

D. Number of coils/wire, number of batteries/dry cells, and properties of the core

____3. What could make an electromagnet stronger?

A. Use a weaker battery.

B. Reverse the poles of the magnet.

C. Remove all the coils and the nail.

D. Add more coils of wire to the nail.

____4. Complete this sentence:

"In order to form an electromagnet, a/an _______ current should flow through a coil of

______ covered around a/an ______ core. "

A. Electric, wire, iron C. Iron, electric, wire

B. Iron, wire, electric D. Wire, iron electric

_____5. You conducted an experiment using a very strong electromagnet. How can

you make it weaker?

A. Add more loops. C. Add more batteries.

B. Use a thicker wire. D. Wrap the wire loosely.

(LAS)-Science week 6 QR-3​

Answers

Answer:

1 B      2 D  3  D    4 DC  wire  ferrite   5 D

Explanation:




4) In a spring mass system the displacement, x meters, of an object from its equilibrium position with time, t, in seconds follows the differential equation d²x dx 4 +4= -17x. Given x(0) = 1 and x'(0

Answers

The differential equation governing the displacement of an object in a spring mass system is given by \(\(\frac{{d^2x}}{{dt^2}} + 4\frac{{dx}}{{dt}} + 4x = -17x\)\), with initial conditions \(\(x(0) = 1\)\) and \(\(x'(0)\)\) to be determined.

To solve the differential equation, we can use the method of characteristic equations. First, let's rewrite the equation in a more standard form:

\(\(\frac{{d^2x}}{{dt^2}} + 4\frac{{dx}}{{dt}} + 21x = 0\)\)

The characteristic equation corresponding to this differential equation is given by:

\(\(r^2 + 4r + 21 = 0\)\)

Solving this quadratic equation, we find that the roots are complex:

\(\(r = -2 \pm \sqrt{5}i\)\)

The general solution of the differential equation is then given by:

\(\(x(t) = c_1 e^{(-2 + \sqrt{5}i)t} + c_2 e^{(-2 - \sqrt{5}i)t}\)\)

Applying the initial condition \(\(x(0) = 1\)\), we have:

\(\(c_1 + c_2 = 1\)\)

To determine the value of \(\(x'(0)\)\), we differentiate \(\(x(t)\)\) with respect to \(\(t\)\) and evaluate it at \(\(t = 0\)\):

\(\(x'(t) = (-2 + \sqrt{5}i)c_1 e^{(-2 + \sqrt{5}i)t} + (-2 - \sqrt{5}i)c_2 e^{(-2 - \sqrt{5}i)t}\)\\\\\(x'(0) = (-2 + \sqrt{5}i)c_1 + (-2 - \sqrt{5}i)c_2\)\)

Since we are given \(\(x'(0)\)\) but not the specific values of \(\(c_1\)\) and \(\(c_2\)\), we cannot determine the final answer without additional information.

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Brad has three beakers of water. Each beaker contains 500 mL of water. The temperature of the water in the first beaker is 40°C. The water in the second beaker is at 100°C, and the water in the third beaker is at 60°C. As part of a lab experiment he will carefully combine the water in all three beakers. He predicts that the combined water will have a final temperature of 50°C.

Evaluate Brad’s claim and clearly state whether he is correct or not. Explain your answer to support your evaluation.

Answers

Explanation:

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A 0.225 kg sample of tin initially at 97.5°c is dropped into 0.115 kg of water. the initial temperature of the water is 10.0°c. if the specific heat capacity of tin is 230 j/kg • °c, what is the final equilibrium temperature of the tin-water mixture

Answers

Answer:

The final equilibrium temperature of the tin-water mixture is approximately 18.468 °C

Explanation:

The parameters of heat energy transfer from the tin to the water are given as follows;

The mass of the sample of tin, m₁ = 0.225 kg

The initial temperature of the tin, T₁ = 97.5 °C

The mass of the water into which the tin is dropped, m₂ = 0.115 kg

The initial temperature of the water, T₂ = 10.0 °C

The specific heat capacity of tin, c₁ = 230 J/(kg·°C)

The specific heat capacity of water, c₂ = 4,200 J/(kg·°C)

Let 'T' represent the final equilibrium temperature of the tin-water mixture, we have;

The heat lost by the tin, ΔQ\(_{tin}\) = The heat gained by the water ΔQ\(_{water}\)

∴  ΔQ\(_{tin}\) = ΔQ\(_{water}\)

Where;

ΔQ\(_{tin}\) = m₁·c₁·(T₁ - T)

ΔQ\(_{water}\) = m₂·c₂·(T - T₂)

By substitution, we have;

ΔQ\(_{tin}\) = 0.225 kg × 230 J/(kg·°C) × (97.5°C - T)

ΔQ\(_{water}\) = 0.115 kg × 4,200 J/(kg·°C) × (T - 10.0°C)

From ΔQ\(_{tin}\) = ΔQ\(_{water}\), we have;

0.225 kg × 230 J/(kg·°C) × (97.5°C - T) = 0.115 kg × 4,200 J/(kg·°C) × (T - 10.0°C)

∴ 5,045.625 J - 51.75 J/°C × T = 483 J/°C × T - 4,830 J

5,045.625 J + 4,830 J = 534.75 J/°C × T

∴ 534.75 J/°C × T = 9,875.625 J

T =  9,875.625 J/(534.75 J/°C) = 18.4677419 °C ≈ 18.468 °C

The final equilibrium temperature of the tin-water mixture, T ≈ 18.468 °C.

What is shown by the pattern of iron filings around these two magnets?

A. Opposite poles repel because no magnetic field forms between them.
B. Like poles attract because the magnetic field lines extend between them.
C. Like poles repel because the magnetic lined bend away from each other.
D. Opposite poles attract because the magnetic field lines cross each other.

What is shown by the pattern of iron filings around these two magnets?A. Opposite poles repel because

Answers

The pattern of iron fillings around the magnet depicts that like poles repel because the magnetic lined bend away from each other. Thus, option C is correct.

What are magnetic field lines?

The North Magnetic Pole would move via magnetic field lines, which are hypothetical lines. The magnet's oppositely polarized poles attract and repel one another.

Since the magnetic field lines inside the magnet run from the south pole to the north pole, Never do magnetic field lines cross one another. A closed loop is formed by magnetic field lines.

Because magnetic force lines are bending in the direction of the south pole in the illustration, like poles repel one another. If the magnetic lines are bent away from one another, like poles repel one another.

Thus, image given has the presence of lines bending away from each other, thereby are like poles repel. Hence, option C is correct.

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The speed of light traveling through an unknown material is 1.98×108 m/s. Given that the speed of light in a vacuum is 3.00×108 m/s, what is the dielectric constant of the unknown material?

Answers

The dielectric constant of the unknown material is 2.3.

What is dielectric constant?

Dielectric constant is referred as a relative permittivity or amount of charge required to produce one unit of electric flux in a given medium.

Given the speed of light in vacuum c =3 x 10⁸ m/s and the speed of light through an unknown material v = 1.98 x 10⁸ m/s.

The dielectric constant is related to the velocity by the following relation,

v = c/√K

Rearranging for dielectric constant, we get

K = (c/v)²

Substitute the value into the expression ,we get

K =(3 x 10⁸ / 1.98 x 10⁸)²

K = 2.3

Thus, the dielectric constant of the unknown material is 2.3.

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