Two tiny conducting spheres are identical and carry charges of - 20.0 µC and +50.0 µC. They are separated by a distance of 2.50 cm. (a) What is the magnitude of the force that each sphere experiences, and is the force attractive or repulsive? (b) The spheres are brought into contact and then separated to a distance of 2.50 cm. Determine the magnitude of the force that each sphere now experiences, and state whether the force is attractive of repulsive.

Answers

Answer 1

Answer:

a

The force experience by the two spheres is \(F_1 = 1.44*10^4 N\)

This force is attractive cause the charge are unlike charges

b

The force experienced by the two spheres is  \(F_2 = 3.24*10^{3} \ N\)

The force is repulsive because the two charges are like charges

Explanation:

From the question we are told that

   The charge on the first sphere is  \(q_1 = -20.0 \mu C = 20 *10^{-6} C\)

    The charge on the second sphere is  \(q_2 = 50 \mu C = 50*10^{-6} C\)

      The distance of separation is \(d = 2.50 \ cm = \frac{2.50}{100} = 0.025 \ m\)

       

The electrostatic force experienced by the two spheres is mathematically represented as

                  \(F_1 = \frac{k q_1 q_2}{d^2}\)

Now k is the coulomb’s constant with a value of  \(k = 9*10^9 N \cdot m^2 /C^2\)

   So

              \(F_1 = \frac{9*10^9 * 20 *10^{-6} * 50*10^{-6}}{0.025}\)

              \(F_1 = 1.44*10^4 N\)

When the sphere are brought together the charge on each sphere would be the average of the total charge and this can be mathematically evaluated as

            \(q = \frac{q_1 + q_2 }{2}\)

            \(q = \frac{(-20 + 50)*10^{-6} }{2}\)

            \(q = 15 \mu C\)

So when they are seperated the electrostatic force experienced is  

         \(F_2 = \frac{kq^2}{d^2}\)

         \(F_2 = \frac{ 9*10^9 * (15 *10^{-6})}{0.025}\)

         \(F_2 = 3.24*10^{3} \ N\)


Related Questions

Ritalin and the pain medication Demerol have a high risk of dependence but may be used for medicinal purposes under a doctor's supervision. These substances are _____ of the CSA list.

Answers

Ritalin and Demerol are both controlled substances that have a high risk of abuse and dependence.

What is the list?

Schedule II drugs are believed to have a high abuse potential that could lead to severe psychological or physical dependence. They do, however, occasionally have other known medical applications and can be prescribed by a licensed healthcare provider.

Ritalin is an example of a stimulant, whereas Demerol is an example of an opioid. Thus the drugs that have been mentioned here are drugs that are strictly controlled.

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what are the factors affecting center of mass in an object

Answers

- The position of mass from the axis.
- The axis of the system.
- The distribution of mass.
- The mass of the rigid body.

How do I find the mass in kg

How do I find the mass in kg

Answers

To find the mass in kilograms, you need to know the object's weight in newtons and the acceleration due to gravity. The formula for finding mass is mass = weight / acceleration due to gravity. So if you have an object with a weight of 100 N and the acceleration due to gravity is 9.8 m/s^2, the mass would be 10.204 kg.

The mass of the block is 0.025 kg or 25 g, when the spring has k = 28 N/m, and compresses 0.11 m before bringing the block to rest.

When a block is dropped onto a spring with k=28 N/m, the block has a speed of 3.2 m/s just before it strikes the spring. If the spring compresses an amount of 0.11 m before bringing the block to rest, what is the mass of the block?The formula for the spring potential energy is given as follows; PE = (1/2) kx² where k is the spring constant and x is the amount of deformation of the spring. Substituting the values given;PE = (1/2) 28 (0.11)²PE = 0.16972 J. According to the law of conservation of energy, the potential energy stored in the spring at maximum compression is equal to the kinetic energy the block had before it struck the spring;KE = (1/2) mv²where m is the mass of the block and v is its velocity.Substituting the values;0.16972 = (1/2) m (3.2)²m = 0.025 kg or 25 gTherefore, the mass of the block is 0.025 kg or 25 g.

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chandani was intrested in researching the plant by mixing things in soil she decided to test the effect of lime eurea table salt and compost on the soil the she put that soil then she bought a bucket of good soil from the garden and mixed it well she put that soil in 12 equal size vases she put two spoons urea each time two spoond of compost of table salt each in another three vases and two spoons of compost each each in three vases after that she planted the seed in all the vases everyday and measure the height of each plant daily and keep record then identify dependent ,indrpendent and controlled variable​

Answers

The dependent, independent, and controlled variables​ are as follows:

1. Dependent - The effect of lime urea table salt and compost on the soil

2. Independent - The soil on which the elements are incorporated.

3. Controlled variable - The height of the plants.

What is the dependent, independent, and controlled variable?

The dependent variable is that which is tested in the experiment and in this experiment, Chandani is testing the effect of lime, urea, table salt, and compost on the soil.

The independent variable is the altered element in the experiment and for this experiment, this is the soil that receives different additives. Finally, the controlled variable is that which remains constant and that is the height of each plant that the researcher checks.

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5. A basketball is passed 15 m due West, then 20 m north. What is the total distance the
basketball travelled?

Answers

Answer:

35 meters

20+15=35

Which of the following is not among the uses of dimensional analysis? (a) determination of the Numerical constant (b) to convert one system of unit to another (c) to change the units of derived quantities (d) to test the correctness of an equation

Answers

To convert one system of unit to another  of derived quantities is not a use of dimensional analysis.

What is dimensional analysis?

Checking for consistency in the dimensions on both sides of an equation entails looking at the dimensions of the physical quantities involved in a problem, such as length, mass, time, electric charge, and temperature.

The core tenet of dimensional analysis is that physical quantities, such as length, mass, and time, may be described in terms of their basic dimensions.

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All of the options listed are included in the uses of dimensional analysis.

What is dimensional analysis?

Dimensional analysis is a powerful tool used in physics to:

check the correctness of equations derive new equationsconvert units from one system to anotherdetermine numerical constants that relate physical quantities.

The dimensional analysis involves analyzing the dimensions of physical quantities and using them to establish relationships between them.

By using the principles of dimensional analysis, we can simplify complex physical problems and gain insights into the behavior of physical systems.

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A wheel of radius 30.0 cm is rotating at a rate of 3.10 revolutions every 0.0710 s
Through what angle does the wheel rotate in 1.00 s?

Answers

To determine the angle through which the wheel rotates in 1.00 second, we can start by finding the angle covered in 0.0710 seconds and then scale it up to 1.00 second.

In 0.0710 seconds, the wheel completes 3.10 revolutions. One revolution corresponds to an angle of 360 degrees or 2π radians. Therefore, in 0.0710 seconds, the wheel rotates through an angle of:

Angle = 3.10 revolutions * 2π radians/revolution = 6.20π radians

To find the angle in 1.00 second, we can use proportional reasoning. Since the time increases by a factor of 1.00/0.0710, the angle covered will also increase by the same factor:

Angle in 1.00 second = 6.20π radians * (1.00/0.0710) = 87.32π radians

Approximately, the angle through which the wheel rotates in 1.00 second is 274.39 radians.

Therefore, the wheel rotates through an angle of approximately 274.39 radians in 1.00 second.

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19. Assume this process is 10% efficient, how much work is done by the gas expanding into the atmosphere?

Answers

The amount of work done by the gas is proportional to the pressure and the change in volume, as well as the efficiency of the process. If the pressure and volume are known, the work done by the gas can be calculated by multiplying these values by the efficiency of the process.

The amount of work done by a gas when it expands is proportional to the change in volume, pressure, and temperature. According to the first law of thermodynamics, the energy of a closed system is conserved, so the work done by the expanding gas is equal to the energy transferred from the gas to the environment in the form of work. Therefore, the work done by the gas is equal to the change in energy of the system. Assume that the process is 10% efficient. Then, only 10% of the energy available to the system is converted into work. This means that the remaining 90% of the energy is lost to the environment in the form of heat. As a result, the amount of work done by the gas expanding into the atmosphere is given by the formula

W = E x η, where W is the work done by the gas, E is the energy available to the system, and η is the efficiency of the process. The energy available to the system is determined by the difference between the internal energy of the gas before and after the expansion. The internal energy of a gas is determined by its temperature, pressure, and volume.

Assuming that the temperature and pressure are constant, the change in internal energy is proportional to the change in volume. Therefore, the energy available to the system is equal to the product of the pressure and the change in volume: E = P x ΔV, where P is the pressure of the gas and ΔV is the change in volume during the expansion. Substituting this equation into the formula for work, we get W = P x ΔV x η.

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What is the equation for frequency?
a. number of cycles +unit of time
b. number of cycles - unit of time
c. number of cycles ×unit of time
d. number of cycles/ unit of time ​

Answers

D. Number of cycles/ unit of time

Answer:

d

Explanation:

D 4.8
This is a harder question based on the Law of Conservation of Momentum. Take the time to work
your way through it. Start with a diagram.
A 400 kg bomb sitting at rest on a table explodes into three pieces. A 150 kg piece moves off to the
east with a velocity of 150 m s². A 100 kg piece moves off with a velocity of 200 m s at a direction of
south 60° west. What is the velocity of the third piece?

It is possible

Answers

The velocity of the third piece is v₃ = -12500 kg·m/s / m₃

How do we calculate?

The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.

velocity of the third piece =  v₃.

The total initial momentum before the explosion = 0

The total final momentum after the explosion= 0

Initial momentum = 0 kg·m/s (since the bomb is at rest)

Final momentum = m₁v₁ + m₂v₂ + m₃v₃

m₁ = mass of the first piece = 150 kg

v₁ = velocity of the first piece = 150 m/s (to the east)

m₂ = mass of the second piece = 100 kg

v₂ = velocity of the second piece = 200 m/s (south 60° west)

m₃ = mass of the third piece = unknown

v₃ = velocity of the third piece = unknown

0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)

final momentum = 0 and hence  v₃ is found as :

0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)

-12500 kg·m/s = (m₃)(v₃)

v₃ = -12500 kg·m/s / m₃

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Pls help!!! In front of a door, there is a very heavy bookcase. A boy decides to shove it out of the way, so he stands next to it and begins to push. However, instead of moving it, he begins to slide backward. Why does this happen, and what could he do to increase the force he's able to exert on the bookcase? list three suggestions. (im guessing it happens because the bookcase is pushing back on him with a force equal to the one he exerted? not sure)

Answers

Answer:

Explanation:

When the boy pushes against the bookshelf, the shelf pushes back against him with the equal and opposite force he is exerting. Now, because the shelf is so heavy, it barely moves under the force applied by the body. However, the boy, who is lighter compared to the bookshelf, begins to slide across the floor because the force has a greater effect on him.

Therefore, in order to increase the force the boy is exerting on the bookshelf, he somehow has to keep himself from sliding. One option would be to support his feet against something to keep them from sliding; this way he would be able to exert a greater force without himself moving.

Hence, the three suggestions are:

1. simply push a bit harder against the bookshelf

2. Support your feet against something to keep them from sliding across the floor.

3. Wear footwear that has a lot of traction.

4. Remove the books out of the bookshelf to make it lighter so that it is easier to move.

Pain during sports is completely normal and should not be a concern.
Please select the best answer from the choices provided.
OT
OF

Answers

Answer:

F

Explanation: Its common sence

Answer:

It’s false

Explanation:

2020 (WORST YEAR EVER) on Edge ;-)

Help me please!!
a 1kg ball has a momentum of 28 kg m/s. what is the balls speed?

Answers

Answer:

p=mv

v=p/m

v=28/1

v=28 m/sec

Pluto has a radius of 1.15 x 10^6 m, and its acceleration due to gravity is 0.61 | m/s^2. What is Pluto's mass?​

Answers

so we will use Newton's gravitational law :

gravitational acceleration = G*m/r^2  

G is the gravitational constant = G = 6.673×10^-11 N m^2 kg^-2  

after substitution :  

6.673×10^-11 * m / (1.15 x 10^6)^2 = 0.61

= 5.04575*10^-23 * m = 0.61

dividing over 5.04575*10^-23 :

m = 1.20894*10^22 kg

pls give me brainliest

Which is more accurate slope o average?

Answers

As long as the graph is a straight line they both will give same answer. Edit: In the case of errors,I think the most fitting slope line is more accurate method,because taking average is same as drawing a line from initial to final point of the line and taking its slope.
Hope it helps

Two blocks, 1 and 2, are connected by a massless string that passes over a massless pulley. 1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. 2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105

. The figure illustrates the configuration.

A system of two blocks connected by a rope passing over a pulley. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle. Box M subscript 1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M sub 1 and the surface is mu subscript 1. Box M subscript 2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle. The coefficient of friction between box M sub 2 and the surface is mu subscript 2.

Answers

The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.

The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.

The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.

The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.

The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).

The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).

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90 V
R₁
60
R2
30
R3
30
Based on the circuit above, what would be the current through the R3 resistor?

Answers

In the parallel combination, the current through R3 is 3 A. In the series combination, the current through R3 is 0.75 A.

To determine the current through resistor R3 in both the parallel and series combinations, we need to apply Ohm's Law and the appropriate formulas for calculating total resistance and current in each configuration.

First, let's consider the parallel combination:

In a parallel combination, the voltage across each resistor is the same. Therefore, the voltage across R3 is also 90 V.

Using Ohm's Law (V = I × R), we can calculate the current flowing through R3 in the parallel combination:

I_parallel = V / R3

= 90 V / 30 Ω

= 3 A

So, in the parallel combination, the current through R3 is 3 A.

Now, let's consider the series combination:

In a series combination, the total resistance is the sum of the individual resistances:

R_total = R1 + R2 + R3

= 60 Ω + 30 Ω + 30 Ω

= 120 Ω

To find the current through the series combination, we can use Ohm's Law:

I_series = V / R_total

= 90 V / 120 Ω

= 0.75 A

Therefore, in the series combination, the current through R3 is 0.75 A.

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Note the complete questions is User

90 V R₁=60 R2=  30, R3 = 30

Based on the circuit above, what would be the current through the R3 resistor in parallel and in series combinantion.

14 The radius of gyration of a body about an axis &ta
distance 6 cm from its centre of mass is 10 cm.
Then, its radius of gyration about a parallel axis
through its centre of mass will be
(a) 80 cm (b) 8 cm (c) 0.8 cm (d) 0.08 cm

Answers

Correct option is B 8 cm.

Let radius of gyration for the axis not passing through center of mass be r and that for the axis passing through the center of mass be k and the distance between the two parallel axes be a.

Parallel axes theorem gives:

\( {mr}^{2} = m( {k}^{2} + {a}^{2} ) \\ ⇒ {r}^{2} = {k}^{2} + a {}^{2} \)\(⇒k = \sqrt{ {10}^{2} - {6}^{2} } = 8cm.\)

Thus, option B is the correct answer.

Which of the following situations represents a positive displacement? (Assume positive position is measured vertically upward along a y-axis.

Answers

The following situations represents a positive displacement:

B. An object moves from a height of 5 meters to a height of 10 meters.

Displacement is a vector quantity that measures the change in position of an object from its initial position to its final position. In this scenario, the positive position is measured vertically upward along the y-axis. Let's analyze each option to determine which one represents a positive displacement:

A. An object moves from a height of 10 meters to a height of 5 meters.

This represents a negative displacement since the object moves downward, opposite to the positive direction along the y-axis.

B. An object moves from a height of 5 meters to a height of 10 meters.

This represents a positive displacement as the object moves upward, in the positive direction along the y-axis.

C. An object remains at a height of 5 meters.

This represents zero displacement since there is no change in the object's position along the y-axis.

D. An object moves from a height of 5 meters to a height of 5 meters.

This also represents zero displacement since the object starts and ends at the same position along the y-axis.

Therefore, the situation that represents a positive displacement is option B, where the object moves from a height of 5 meters to a height of 10 meters.

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1. Zahra oscillates a swing and makes 100 complete cycles in 20 seconds. Find: a. Period (​

Answers

Answer:

Explanation:

Period is : \(T=\frac{t}{n}=\frac{20}{100}=0.2\) s

You are trying to catch the mutated mouse and you have a rope
that both you and the mouse are pulling with a force of 500 Newtons,
but the rope does not move.
How much work is done?


PLS ANSWER ASAP! WILL MARK AS BRAINLYIST!!!!!
time left (5:00)!!

Answers

Answer:

none no work cuz no motion

Explanation:

GOOD LUCK

4. Which of the following substance will cool off the fastest?
cooper
Iron
Nylon
Aluminum

Answers

Answer:

I'm not sure but I think its aluminum

03: Hook's law suggests that F is directly proportional to -x, how much true you have found this statement in your experiment? Explain any differences.​

Answers

Hooke's Law can be given as follows sometimes:

The restoring force of a spring is equal to the spring constant multiplied by the displacement from its normal position:

F = -kx

Where, F = Restoring force of a spring (Newtons, N)

k = Spring constant (N/m)

x = Displacement of the spring (m)

The negative sign relates to the direction of the applied force and by convention, the minus or negative sign is present in F = -kx. The restoring force F is directly proportional to the displacement (x), according to Hooke's law. When the spring is compressed, the displacement (x) is negative. It is zero when the spring is at its original length and positive when the spring is extended.

Practically, Hooke's Law is applicable only within a limited frame of reference, and through experimenting, this statement proves to be true. Because materials cannot be compressed beyond a certain size or expanded beyond a certain size without some permanent deformation or change of their original state.

The law only applies under some conditions such as a limited amount of force or deformation. Factually, many materials will noticeably deviate from Hooke's law even before those elastic limits are reached.

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person pulls a toboggan for a distance of 35.0 m along the snow with a rope directed 32.0o above the snow. The tension in the rope is 105.0 N. How much work is done on the toboggan by the tension force?

Answers

The amount of work done on the toboggan by the tension force of 105 N with a rope directed 32° above the snow is 3.12 KJ

W = F d cos θ

W = Work done

F = Force

d = Distance

θ = Angle between force and displacement vector

d = 35 m

F = 105 N

θ = 32°

W = 105 * 35 * cos 35°

W = 105 * 35 * 0.85

W = 3123.75 N m

W = 3.12 KJ

Work done is energy transferred to make an object move to a distance. Its unit is Joules which is denoted as J. It is the amount of work done by a force of 1 Newton to move a distance of 1 meter.

Therefore, the amount of work done on the toboggan by the tension force is 3.12 KJ

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Need a 5 paragraph essay in the eartsh layers and how they function/ benefit the earth!

Answers

There is more to the Earth than what we can see on the surface. In fact, if you were able to hold the Earth in your hand and slice it in half, you'd see that it has multiple layers. But of course, the interior of our world continues to hold some mysteries for us. Even as we intrepidly explore other worlds and deploy satellites into orbit, the inner recesses of our planet remains off limit from us.

However, advances in seismology have allowed us to learn a great deal about the Earth and the many layers that make it up. Each layer has its own properties, composition, and characteristics that affects many of the key processes of our planet. They are, in order from the exterior to the interior – the crust, the mantle, the outer core, and the inner core. Let's take a look at them and see what they have going on.

Like all terrestrial planets, the Earth's interior is differentiated. This means that its internal structure consists of layers, arranged like the skin of an onion. Peel back one, and you find another, distinguished from the last by its chemical and geological properties, as well as vast differences in temperature and pressure.

Explanation:

A glass tube 0.15mm in diameter is dropped in glycerin which surface tension is 0.0632Nm-1. Calculate the contact angle if the glycerin rises to a height of 14cm.(the density of glycerin is1250kgm-3 and g=9.8ms-2)​

Answers

The contact angle is defined as the angle between the surface of the liquid and the solid surface.

What is surface tension?

Surface tension is the attractive force between molecules on the surface of a liquid. This force causes the surface of the liquid to behave as if it were a stretched elastic membrane, which causes it to pull back when stretched or punctured. This is the same phenomenon that allows a needle or other small object to float on the surface of water.

The force of surface tension is equal to the weight of the column of liquid of the height h times the surface tension coefficient:
F = h*σ = h* 0.0632 N/m
The force of gravity on the liquid column is equal to the mass of the liquid times the gravitational acceleration:
F = m*g = ρ*V*g = ρ*(πr²h)*g
Substituting the given values, we get:
0.0632N/m = 1250*(π*(0.15/2)²*14)*9.8
Solving for the contact angle, we get:
θ = tan⁻¹ (0.0632/(1250*(π*0.15²*14)*9.8)) = 0.044°

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A fast Humvee drove from desert A to desert B. For the first 12
hours, it travelled at an average speed of 185 km/h. For the
next 13 hours, it travelled at an average speed of 160 km/h.
What was the average speed of the whole journey?
km/h

Answers

Answer:

v = 172 km/h

Explanation:

For the first 12  hours, it traveled at an average speed of 185 km/h. Let d₁ is distance. So,

\(d_1=v_1\times t_1\\\\d_1=185\ km/h\times 12\ h\\\\d_1=2220\ km\)

For the  next 13 hours, it traveled at an average speed of 160 km/h. Let d₂ is the distance. So,

\(d_2=v_2\times t_2\\\\d_2=160\ km/h\times 13\ h\\\\d_2=2080\ km\)

Average speed = total distance/time taken

So,

\(v=\dfrac{d_1+d_2}{t_1+t_2}\\\\v=\dfrac{2220+2080}{12+13}\\\\v=172\ km/h\)

So, the average speed of the whole journey is 172 km/h.


The NEC states the resistance of 4/0 coated
copper conductors is 0.0626 ohms per 1000
feet. What would be the total resistance of the
three 4/0 conductors installed in parallel, if the
total length for each of the three conductors is
323 feet?

Answers

Answer:

The resistance of 4/0 coated copper conductors is given as 0.0626 ohms per 1000 feet. To find the total resistance of the three 4/0 conductors installed in parallel, we can use the formula for combining resistances in parallel.

Since the total length for each of the three conductors is 323 feet, the resistance of each conductor can be calculated as follows:

Resistance of one conductor = (0.0626 ohms / 1000 feet) * 323 feet

To find the total resistance when the conductors are in parallel, we use the formula:

1/Total Resistance = 1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3

Total Resistance = 1 / (1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3)

Substituting the values, we get:

Total Resistance = 1 / (1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet))

Simplifying the expression will give us the total resistance of the three 4/0 conductors installed in parallel.

Consider the heaviest box of 150 pounds that you can push at constant speed across a level floor, where the coefficient of kinetic friction is 0.50, and estimate the maximum horizontal force that you can apply to the box. A box sits on a ramp that is inclined at an angle of 60 degrees above the horizontal. The coefficient of kinetic friction between the box and the ramp is 0.50. If you apply that same magnitude force, now parallel to the ramp, that you applied to the box on the floor, what is the heaviest box (in pounds) that you can push up the ramp at a constant speed?

Answers

We can deduce here that the maximum horizontal force that you can apply to the box is 150 pounds. Thus, the heaviest box that you can push up the ramp at a constant speed is 75 pounds.

How we arrived at the solution?

Given the following:

Maximum horizontal force = 150 pounds

Coefficient of kinetic friction = 0.50

Weight of the box = 150 pounds

Angle of the ramp = 60°

Normal force = Weight of the box * Cosine of the angle of the ramp

= 150 pounds × Cos(60°)

= 75 pounds.

Force of friction = Coefficient of kinetic friction × Normal force

= 0.50 × 75 pounds

= 37.5 pounds

Maximum force that can be applied to the box = Weight of the box × Cosine of the angle of the ramp - Force of friction

= 150 pounds × Cos(60°) - 37.5 pounds

= 75 pounds

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The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of ten in (a) years and (b) seconds.

Answers

The age of the universe is 1.4 x 10⁹ years or 4.4 x 10¹⁶ seconds.

What is significant figure?

Significant figures are used to establish the number which is presented in the form of digits.

14 billion years to years

14 billion years = 14,000,000,000 years

in two significant figure = 1.4 x 10⁹ years

14 billion years to seconds

1 year = 3.154 x 10⁷ seconds

1.4 x 10⁹ years = ?

= 1.4 x 10⁹ x 3.154 x 10⁷

= 4.4 x 10¹⁶ seconds

Thus, the age of the universe is 1.4 x 10⁹ years or 4.4 x 10¹⁶ seconds.

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