a 114-in-long astm a36 steel rod with a cross-sectional area of 4 in2 is secured between rigid supports. if there is no stress in the rod at a temperature of 88 f, compute the stress (psi) when the temperature drops to 17 f. the proportional limit of the steel is 26 x 103 psi. take e

Answers

Answer 1

Thermal stress σth = 18.3987 Ksi

No deflection of bar = compression by reaction

αΔTΨ = σΨ/e

σth = αΔTE

=  0.0000065 × 26 × \(10^{3}\) × 88

σth = 18.3987 Ksi

The word "thermal stress" refers to a temperature fluctuation that is extreme enough to have an adverse effect on aquatic creatures, their numbers, community structure, or ecosystem. Aquatic creatures have developed to work best within a specific range of water temperature. Thermal stress is mechanical stress that is produced by any change in a material's temperature in mechanics and thermodynamics. Depending on the other heating variables, such as the type of material and restrictions, these stresses may cause fracturing or plastic deformation. [1] Things that can cause thermal stress include temperature gradients, thermal expansion or contraction, and thermal shocks. The thermal expansion coefficient, which differs amongst materials, has a significant impact on this kind of stress. Typically, the higher the temperature.

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Related Questions

Calcular la cantidad de solucion que se encuentra en un recipiente con 670 g de solvente y 22 g de soluto

Answers

Answer:

692 g

Explanation:

La fórmula para encontrar la solución de una mezcla química es agregar el soluto y el solvente juntos. Esto significa

Solución = solvente + soluto

Solución = 670 g + 22 g

Solución = 692 g

es así de simple, y espero que lo entiendas

Energy Representations 3: Power and Efficiency:Question 2
This Sankey diagram shows the energy transformations
in a mixer used to stir ingredients together. If the
percentage of non-useful energy produced by the mixer
is 30%, what is the energy efficiency of the mixer?
Select one:
10%.
70%.
100%.
30%.
Electric energy
Sound
Thermal energy
energy
Kinetic energ

Energy Representations 3: Power and Efficiency:Question 2This Sankey diagram shows the energy transformationsin

Answers

The energy efficiency of the mixer is 70%.

The Sankey diagram shows the amount of energy absorbed, the amount of useful energy, and the amount of non-useful energy.

Input energy = output energyInput energy = useful energy + non-useful energyInput energy (I) = useful energy (U) + waste energy (W)
I = U + W

The efficiency of a device

η = (U/I) × 100%

Input energy is always 100%
I = 100%W = 30%

I = U + W

100% = U + 30%

U = 100% - 30%

U = 70%

The efficiency of the mixer

η = (U/I) × 100%

η = (70%/100%) × 100%

η = (7/10) × 100%

η = 70%

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A massless rod is balanced on a pivot as shown below. If the rod is in static equilibrium, what
magnitude of force (x) must be exerted on the other end of the rod?
A. 7.5 N
B. 13 N
C. 20 N
D. 53 N
E. 80 N

A massless rod is balanced on a pivot as shown below. If the rod is in static equilibrium, whatmagnitude

Answers

Answer:

torques must balance for equilibrium

counterclockwise = clockwise

1.5 X = 4 * 20

x = 80 N-m / 1.5 m = 53 N

(D) is correct

You see a flash of lightning, and then 15 seconds later you hear thunder. How far away is the lightning?.

Answers

If you calculate the seconds between the lightning strike and divide that number by 5, you'll find the distance in miles: 5 seconds = 1 mile, 15 seconds = 3 miles, and 0 seconds = very close.

What is a lighting flash?

The return stroke happens when a charged president makes contact with the ground. The quick discharge the electricity that has built up on the leader is all that happens during the return stroke. This discharge resembles a lightning bolt to us.

What causes lightning to flash?

A stepped leader, or a channel of negative charges, travels towards the ground during the beginning of a cloud-to-ground lightning strike. The stepped leader keeps moving downhill in a sequence of steps that really are each between 50 and 100 meters long. The stepped leader might take many different turns.

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A car of mass of 1200 kg is driven around a corner of a radius of 45m at 15 ms-1
.
(a) Calculate the acceleration of the car.
(b) Calculate the centripetal force acting on the car.
(c) Explain how the centripetal force is being produced.

Answers

Explanation:

w = v/r

= 15/ 45 = 1/3 rads-¹

a = w²r

= 1/9 • 45 = 5 ms-²

F = mv²/r

= 1200• 15• 15/45

= 6000N

The car, when rounding the curve, is pulled towards the center by the friction between it's wheels and the road.

A single-phase, 22 kVA, 2400f240 V, 60 Hz distribution transformer has the following characteristics: Core losses at rated voltage are 730 watts; copper losses at half the rated load are 340 watts. (a) Determine the efficiency of the transformer when it delivers full load at 0.46 power factor lagging. (b) Determine the percent of the rated load at which the transformer efficiency is a maximum (In an exam, you may be asked to report this efficiency as a per unit value as well). (c) Determine this efficiency if the power factor of this "optimal" load is 0.9. (d) The transformer has the following daily load cycle. Determine the all-day-efficiency of the transformer. No load for 6 hours; 70% full load for 10 hours at 0.8 PF; 90% full load for 8 hours at 0.9 PF. la) muss = 5!! "/0 (b) Load for mm = as: % (c) hm" with 0.9 power factor load = 555 % % id) name =

Answers

(a) The efficiency of the transformer when it delivers full load at 0.46 power factor lagging can be calculated using the formula:

Efficiency = (Output Power / Input Power) x 100%

The output power can be determined by multiplying the apparent power by the power factor, and the input power is the sum of the core losses and copper losses. By substituting the given values, the efficiency can be computed.

(b) The percent of the rated load at which the transformer efficiency is a maximum can be determined by finding the load level that minimizes the sum of the core losses and copper losses. This can be achieved by varying the load and calculating the total losses until the minimum value is obtained.

(c) To determine the efficiency at the "optimal" load with a power factor of 0.9, the same approach as in part (a) can be used. The output power is calculated by multiplying the apparent power by the power factor, and the input power is the sum of the core losses and copper losses.

(d) The all-day efficiency of the transformer can be found by calculating the weighted average of the efficiencies during each load cycle, considering the duration and power factor of each load condition. By multiplying the efficiency of each load cycle by its corresponding duration and summing them up, the all-day efficiency can be obtained.

To provide a detailed explanation and calculations for each part, I would need the specific numerical values for the apparent power, power factor, load durations, and load power factors. Please provide those values, and I can assist you in solving the problem step by step.

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silicon
sodium
nitrogen
potassium

Use the periodic table to predict which element is nonmetallic AND a gas at room temperature.
A) nitrogen
B) potassium
C.)silicon
D) sodium​

Answers

D)
Jdjdgusnabausbebsbssjwhegdhchhx

kinetic energy is the force that needs to be dissipated in a collision. T/F?

Answers

kinetic energy is the force that needs to be dissipated in a collision.  The following statement is False.

Kinetic energy is not a force; it is a form of energy associated with the motion of an object. In a collision, kinetic energy is not the force that needs to be dissipated but rather a quantity that can be transferred or transformed during the collision. During a collision, forces act on the objects involved, causing them to change their motion. These forces can come from external sources or be generated internally due to interactions between the objects. The forces involved in a collision are responsible for altering the objects' velocities and momentum. Kinetic energy is related to the mass and velocity of an object and can be calculated using the equation:

Kinetic energy = (1/2) × mass × velocity^2

In a collision, the total kinetic energy of the system might change. Some collisions result in a transfer or transformation of kinetic energy between the objects involved, while in other cases, the total kinetic energy is conserved. The forces involved in a collision determine how the kinetic energy is distributed or dissipated. Energy can be transferred into other forms, such as heat, sound, or deformation of the objects involved, depending on the nature of the collision and the materials of the objects.

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calculate the relative density of a block having dimension 4m x 3m x 2m given its mass in 48000g​

Answers

Answer:

in the picture

Explanation:

CARRY ON LEARNING

calculate the relative density of a block having dimension 4m x 3m x 2m given its mass in 48000g

How does your collected data help you to see if you meet your criteria for success

Answers

Collected data plays a crucial role in evaluating whether the criteria for success have been met. By analyzing the collected data, one can assess the progress made towards achieving the desired goals and determine if the criteria have been fulfilled.

Data provides an objective measure of performance or outcomes, allowing for an evidence-based assessment of success. It helps to quantify and track key metrics or indicators related to the criteria for success. By comparing the actual data with the predetermined benchmarks or targets, one can determine if the criteria have been met or if further improvements are required.

Data analysis also enables the identification of trends, patterns, and correlations, providing insights into the factors influencing success. It helps in identifying areas of strength and areas that need improvement. Additionally, data can be used for comparative analysis, benchmarking against previous periods or similar projects, to gain a broader perspective on success.

In summary, collected data provides an objective basis for evaluating progress and success by comparing actual performance against predetermined criteria, identifying areas of improvement, and gaining insights for future decision-making.

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E) Would you expect the temperature of the water to continue rising above 20°C? Explain your answer.​

Answers

Answer:

No, when water converts to steam on heating, the temperature remains constant at the boiling point and the heat supplied to the water is used for the vaporisation of water, rather than increasing the temperature of water.

This energy used for the vaporisation is termed as the latent heat of vaporisation.

You’ll find similar observations if you try heating ice - the temperature remains at 0∘ Celsius. Here, it’s the latent heat of fusion.

if you 235lb traviling north at 75mph and strike a 150 lb deer going 35mph east what is the force

Answers

We need to use the formula: Force = Mass × Acceleration Let's use the given values to calculate the force exerted on the deer when it is hit by the car. The car weighs 235 lb and it is traveling north at 75 mph. The deer weighs 150 lb and it is going 35 mph east. Force = 44045 lbSince the force is a vector quantity, it has both magnitude and direction.

Step 1: Convert the velocities into feet per second.1 mile = 5280 feet1 hour = 3600 seconds So, the velocity of the car is:75 mph = (75 × 5280) ÷ 3600 = 110 feet/secondThe velocity of the deer is:35 mph = (35 × 5280) ÷ 3600 = 51.3 feet/second

Step 2: Find the components of velocity of the deer. The velocity of the deer is in the east direction, so we need to find its horizontal component, vx, and its vertical component, vy. If the angle between the deer's velocity and the x-axis is θ, then: vx = v × cosθandvy = v × sinθv = 51.3 feet/secondθ = 90° - arctan(0 / 110) = 90°So,vx = 51.3 × cos90° = 0 feet/second vy = 51.3 × sin90° = 51.3 feet/second

Step 3: Find the net velocities of the car and the deer. Since the car is moving north and the deer is moving east, the net velocity of the car and deer together can be found using the Pythagorean theorem. Net velocity = √[(vx + 110)² + vy²]Net velocity = √[(0 + 110)² + (51.3)²]Net velocity = √(12100 + 2631.69)Net velocity = √14731.69Net velocity = 121.3 feet/second

Step 4: Find the net momentum of the car and the deer. Net momentum = (mass of car × velocity of car) + (mass of deer × velocity of deer)Net momentum = (235 × 110) + (150 × 121.3)Net momentum = 25850 + 18195Net momentum = 44045 lb ft/second

Step 5: Find the force exerted on the deer. Force = Net momentum ÷ time Here, time is the duration of the collision which is not given in the problem. We will assume it to be 1 second. Force = 44045 ÷ 1

Force = 44045 lb Since the force is a vector quantity, it has both magnitude and direction. The direction of force is along the line of impact which is not given in the problem.

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Given w= 4+,- 0.02 A=2.0+,-0.2 and 3.0+,-0.6 what is the value of w\ A y square

Answers

Explanation:

w = (4.52 ± 0.02) cm, x = ( 2.0 ± 0.2) cm, y = (3.0 ± 0.6) cm. Find z = x + y - w and its uncertainty.

z = x + y - w = 2.0 + 3.0 - 4.5 = 0.5 cm

Dz = Dx + Dy + Dw = 0.2 + 0.6 + 0.02 = 0.82 rounding to 0.8 cm

So z = (0.5 ± 0.8) cm

Solution with standard deviations, Eq. 1b, Dz = 0.633 cm

z = (0.5 ± 0.6) cm

Notice that we round the uncertainty to one significant figure and round the answer to match.

1. The force on the last car of a train with a mass of 4.5 kg is 8.0 N. What is the train's acceleration in m/s2?

2. Observe the table. How many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true?
Enter your answer as a whole number, like this: 4

1. The force on the last car of a train with a mass of 4.5 kg is 8.0 N. What is the train's acceleration

Answers

1. The force on the last car of a train with a mass of 4.5 kg is 8.0 N. What is the trains acceleration in m/s2?
answer = 1.78
1. The force on the last car of a train with a mass of 4.5 kg is 8.0 N. What is the train's acceleration
The Fortnite of a steam locomotive is the park in a while the president of president in a

Is it ok for some help pwease?

What is the area of calm winds near the equator called?


doldrums


polar easterlies


trade winds


horse latitudes

Answers

Answer:

doldrums

Explanation:

Just need to type something more to be able to post

10. Duncan needs to lift a 31.0kg rock. If he exerts an upward force of 500 N on the rock, what is the rock's acceleration?​

Answers

Explanation:

(taking g = 10 m/s^2)

F - W = m * a

500 - 310 = 31 * a

190 = 31 * a

a (Acceleration of rock ) = 6.12 m/s^2

A 2.0-kilogram ball rolls down a ramp. if the ball accelerates at a rate of 12 m/s2, the net force causing the acceleration is:
a:6 newtons
b:10 newtons
c:12 newtons
d:24 newtons

Answers

Answer:

D

Explanation:

f = ma

2 x 12 = 24

answer could differ since it's rolling down a ramp. if an angle is given our approach differs.


A forensic investigator is collecting hair samples from the victims and possible suspects of a violent attack. How many control
samples of full length scalp hairs and how many full length pubic hairs are collected for the control samples?
A)
25/10
B)
50/24
50/50
D)
100/50

Answers

Answer: B. 50/24

Explanation: just took the usatestprep

Question 2 - A circuit breaker is designed to operate with a voltage capacity between 110-220 Volts
and a current capacity in the range of 15-30 Amp. How would you test the circuit for its tripping
behavior. (Hint: Identify the type of test that is applicable for range of values)

Answers

To test the circuit breaker's tripping behavior, you can perform an overload test.

A circuit breaker is a mechanical switching device that interrupts an electric circuit's current when it detects an overcurrent condition. A circuit breaker is designed to operate with a voltage capacity between 110-220 Volts and a current capacity in the range of 15-30 Amps.

The following are the procedures for testing the circuit breaker:

Inspection:

Examine the circuit breaker for any visual harm or defects.

Ensure that all screws and terminals are secure and free of debris.

Continuity:

Use a multimeter to check the circuit breaker's continuity.

Ensure that there is continuity between the input and output wires of the circuit breaker and that the multimeter's resistance reading is zero when the breaker is closed.

Load:

Examine the circuit breaker's load-carrying capacity.

To do so, use a power source that is within the circuit breaker's current range and attach the circuit breaker to it.

As a result, the power source's current would flow through the circuit breaker.

Observe the tripping behavior:

After the power source has been connected, increase the current gradually to see if the circuit breaker trips at the appropriate value.

To do this, use a variable resistor or a load bank device to regulate the current flowing through the circuit breaker.

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A car is parked on a cliff overlooking the sea. The cliff is inclined at an angle of 40.0 degrees below the horizontal. The
negligent driver leaves the car in neutral and it begins rolling from rest towards the cliff's edge with an acceleration 5.00
m/s/s. The car moves a linear distance of 70.0 to the edge of the cliff before plunging into the ocean below. The cliff is
50.0 m above the sea. Round everything to 3 significant digits! Use 9.80 for gravity. (hint - because the initial velocity is
down, this causes the cosine rule to flip. Use sin to find Vox. Use cosine to find Viy)

Answers

Fact: Parking a car on a cliff? That is unsafe and probably also illegal.

Given a parallel runtime of 20s on eight cores and a serial runtime of 80s, what is the runtime in seconds on 16 cores assuming the same efficiency (do not include any units in the answer)?

Answers

If we assume the same efficiency, then we can use Amdahl's Law to calculate the new runtime on 16 cores.

Amdahl's Law states that the speedup of a parallel program is limited by the portion of the program that must be executed sequentially. In this case, the portion that must be executed sequentially is (80-20)/80 = 0.75 or 75%. This means that only 25% of the program can be parallelized. Therefore, the speedup we can expect from doubling the number of cores is limited to 1/((1-0.25) + 0.25/8) = 1.85.
Using this speedup, we can calculate the new runtime on 16 cores as 20/1.85 = 10.81 seconds.

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at about 10.∘c, a sample of pure water has a hydronium concentration of 5.4×10−8 m. what is the equilibrium constant, kw, of water at this temperature?

Answers

The equilibrium constant (Kw) of water at 10°C is 5.4×10^(-14) mol^2/L^2.

At 25°C, the commonly used value for Kw is 1.0×10^(-14) mol^2/L^2, which represents the equilibrium constant for the autoionization of water, where water molecules dissociate into hydronium ions (H3O+) and hydroxide ions (OH-).

Kw is defined as Kw = [H3O+][OH-], where [H3O+] and [OH-] are the concentrations of hydronium and hydroxide ions in mol/L, respectively. However, at lower temperatures, the concentration of hydronium ions decreases due to the lower ionization rate of water.

In this case, the given concentration of hydronium ions at 10°C is 5.4×10^(-8) mol/L, so Kw can be calculated as

Kw = [H3O+][OH-] = (5.4×10^(-8))(5.4×10^(-8)) = 2.916×10^(-15) mol^2/L^2, which is the equilibrium constant for water at 10°C.

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for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.a. 3Pb. P/3c. 3P/Td. 9P

Answers

The volume of the gas varies inversely with pressure, and the correct answer is (b) P/3.

According to Boyle's Law, at a constant temperature, the volume of a gas is inversely proportional to its pressure. Mathematically, this can be expressed as:

PV = k

where P is the pressure of the gas, V is its volume, and k is a constant.

If we assume that the mass of the gas remains constant, then k is also constant. So we can write:

\(P_1V_1 = k and P_2V_2 = k\)

where\(P_1 and V_1\) are the initial pressure and volume, and \(P_2 and V_2\) are the final pressure and volume.

If we divide these two equations, we get:

\(P_1V_1/P_2V_2 = 1\)

Since\(V_1\) is inversely proportional to \(P_1\), we can write:

\(V_1 = k/P_1\)

Similarly, \(V_2 = k/P_2.\)

Substituting these values in the above equation, we get:

\((k/P_1)/(k/P_2) = 1\)

Simplifying this, we get:

\(P_2/P_1 = V_1/V_2\)

Since we are given that the temperature remains constant, we can assume that k is constant, and therefore:

\(V_1/P_1 = V_2/P_2\)

If we let \(P_2 = 3P_1\), then we get:

\(V_1/P_1 = V_2/(3P_1)\)

Simplifying this, we get:

\(V_1/V_2 = 1/3\)

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You are asked to analyze the efficiency of a new battery-powered toy, and in your assessment, you are told you need to comment on and calculate its efficiency.

What measurements would you need to collect to do a complete assessment of the new toy? (1 mark)
How could the information gathered help you comment on the efficiency of the toy? (1 mark)

Answers

To fully evaluate the effectiveness of a new battery toy, the following measurements should be taken.

1. Battery voltage:

Measure the voltage of the battery that powers the toy. This information helps determine the energy input into the toy.

2. Battery power:

Measure the current drawn from the battery while the toy is running. This measurement gives information about the toy's energy consumption.

3. Duration:

Measure how long the toy runs on battery. Indicates the period during which the energy conversion takes place.

Four. Energy consumption:

Calculate the toy's energy consumption by multiplying the battery voltage by the battery current and operating time. This measurement quantifies the energy the toy uses.

5. Output power:

Evaluate toy output. B. Other relevant indicators that characterize work done, speed, or intended function.

The information obtained from these measurements helps us assess the effectiveness of the toy by:

Efficiency is defined as the ratio of available output energy (or work) to input energy (or work). By calculating the energy used and considering the output of the toy, we can compare the energy input and energy output. If a toy is designed to perform a specific task, such as moving an object or emitting sound or light, we can measure how effectively it performs that task compared to the energy input. can be evaluated. The higher the energy output relative to the energy input, the more efficient the toy is, while the lower the energy output, the less efficient it is.

Also, by analyzing the voltage and current of the battery, you can determine the energy consumption of the toy. If a toy's energy consumption is high compared to its intended function, it may indicate inefficiency in the energy conversion process. Taking all these measurements together, we can make a comprehensive assessment and comment on the effectiveness of new battery-operated toys. 

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Final answer:

To assess the efficiency of the new battery-powered toy, you need to collect measurements of energy input and output, and calculate efficiency using a formula. The gathered information helps you comment on how effectively the toy utilizes the battery's energy.

Explanation:

To assess the efficiency of the new battery-powered toy, you would need to collect measurements related to its energy input and output. Specifically, you would need to measure the amount of energy the toy consumes from the battery (input) and the amount of work or useful energy it produces (output). With this information, you can calculate the efficiency of the toy using the formula Efficiency = (Output Energy/Input Energy) x 100%.

The information gathered will help you comment on the efficiency of the toy by providing quantitative data on how effectively the battery's energy is utilized. If the toy has high efficiency, it means it converts a large portion of the energy it receives into useful work or motion. On the other hand, a low efficiency suggests that a significant amount of energy is wasted as heat or in other non-useful forms. In summary, to assess the efficiency of the new battery-powered toy, you need to collect measurements of energy input and output. This information will allow you to calculate the toy's efficiency and make comments on how effectively it utilizes the battery's energy.

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Why are streams and rivers important for ecosystems?

Answers

Streams are a crucial part of Earth's circulatory system. They carry sediments, nutrients and other materials into rivers and lakes and on to the ocean. But streams are also vital ecosystems on their own, providing wildlife habitat, protecting us from floods and supplying much of our drinking water.
Rivers provide vital advantages, referred to as ecosystem services, that have an impact on our daily life. Drinking water, irrigation, transportation, and other services are provided by them. They also serve as spawning grounds for significant fish species. Rivers provide us with drinking water, irrigate our crops, provide hydroelectricity to our towns, support fish and other aquatic species, and offer a variety of recreational and commercial options. Small streams (such as headwater streams) and the wetlands they support are just as essential.
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A 905kg car travels around a circular track with a radius of 525 m. If the


magnitude of the centripetal force is 2140 N, what is the car's tangential


speed?

Answers

When a 905kg car travels around a circular track with a radius of 525 m and with the magnitude of the centripetal force is 2140 N, then car's tangential speed would be approximately 23.8 m/s.

The centripetal force acting on an object moving in a circular path is given by the formula Fc = m * v^2 / r, where Fc is the centripetal force, m is the mass, v is the tangential speed, and r is the radius of the circular path. Rearranging the formula, we have
v^2 = Fc * r / m
Substituting the given values, we have v^2 = (2140 N) * (525 m) / (905 kg). Solving for v, we find v ≈ 23.8 m/s. Therefore, the car's tangential speed is approximately 23.8 m/s.

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How does Earth’s tilt affect climate?(1 point) It produces uneven heating of Earth’s surface by the sun. It causes some areas to be closer to the sun and others farther away. It produces winds that have a cooling effect in areas close to the poles. It causes days to be warmer and nights to be cooler.

Answers

Answer: It produces uneven heating of Earth's surface by the sun

Explanation:

The Earth's tilt affect the climate by producing uneven heating of the Earth's surface by the Sun. Thus, the correct option is A.

What is the effect of Earth's tilt on climate?

The earth's spin axis is tilted with respect to the orbital plane of the planet. This is what actually causes the change in seasons. When the earth's axis points are towards the sun, it is summer for that hemisphere. However, when the earth's axis points are away, winter season can be expected.

The greater the Earth's axial tilt angle, the more extreme will be the seasons are, as each of the hemisphere receives more solar radiation during its summer season, when the hemisphere is tilted towards the Sun, and less during the winter season, when it is tilted away.

Therefore, the correct option is A.

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a hole in a copper plate has a diameter of 1.325 cm at 21C°. At what tempreture is the diameter equal to 1.164 cm

Answers

Answer:14C

Explanation:

A bob attached to a string of length L = 1.25 m, initially found at the equilibrium
position, is given an initial velocity v = 0.8 m/s. The maximum displacement angle,
Omax, is: (Take g=10 m/s)
17
3.2
13
10.2
6.4
Clear selection
A hoh attached to a string of length 2 m is displaced by an angle of 8º and then

A bob attached to a string of length L = 1.25 m, initially found at the equilibriumposition, is given

Answers

The maximum displacement angle of the bob is 13⁰.

The given parameters;

Length of the pendulum, L = 1.25 mInitial velocity of the bob, v = 0.8 m/s

The maximum displacement of the bob is calculated by applying the principle of conservation of energy;

\(P.E = K.E\\\\mgh = \frac{1}{2} mv^2\\\\h = \frac{v^2}{2g} \\\\h = \frac{0.8^2}{2\times 10} \\\\h = 0.032 \ m\)

The maximum displacement angle is calculated as follows;

\(cos \theta = \frac{L-h}{L} \\\\cos \theta = \frac{1.25 - 0.032}{1.25} \\\\\cos \theta = \frac{1.218}{1.25} \\\\cos \theta = 0.9744\\\\\theta = cos^{-1}(0.9744)\\\\\theta = 13\ ^0\)

Thus, the maximum displacement angle of the bob is 13⁰.

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a fan is turned off when it is running at 850 rpm. it turns 1500 revolutions before it comes to a complete stop. find the fan’s angular acceleration.

Answers

The angular acceleration of the fan is -4.7 rad/s², indicating that it is slowing down. The initial angular velocity is 53.08 rad/s, and it comes to a complete stop in 11.28 seconds.

The angular acceleration of the fan is given by the following formula:

α = \((\omega_f - \omega_i)\) / t

where:

α is the angular acceleration (in rad/s²)

\(\omega_f\) is the final angular velocity (in rad/s)

\(\omega_i\) is the initial angular velocity (in rad/s)

t is the time (in seconds)

We are given that:

\(\omega_f\) = 0 rad/s (the fan comes to a complete stop)

\(\omega_i\) = 850 * 2π / 60 rad/s = 53.08 rad/s

t = 1500 / (60 * 2π) s = 11.28 s

Substituting the given values, we get:

α = (0 - 53.08) / 11.28 = -4.7 rad/s²

Therefore, the fan's angular acceleration is -4.7 rad/s².

The negative sign indicates that the fan is slowing down.

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