How much energy must a stove transfer to completely heat 1g of liquid water from 1o C to 25o C?

Answers

Answer 1

The energy needed by a stove to transfer heat completely to 1 g of liquid water fro 1 °C to 25 °C is 100.37 J.

What is energy?

Energy is the ability or the capacity to do work.

To calculate the  amount of energy, we use the formula below.

Formula:

Q = cm(t₂-t₁).............. Equation 1

Where:

Q = Amount of energyc = Specific heat capacity of the waterm = mass of the watert₂ = Final temperaturet₁ = Initial temperature

From the question,

Given:

m = 1 g = 0.001 kgc = 4182 J/kg°Ct₁ = 1 °Ct₂ = 25 °C

Substitute these values into equation 1

Q = 0.001(4182)(25-1)Q = 100.37 J

Hence, The energy required is 100.37 J.

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Answer 2

Taking into account the definition of calorimetry, the energy that a stove must transfer to completely heat 1 g of liquid water from 1 °C to 25 °C is 100.416 J.

Definition of calorimetry

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

When heat added or removed from a substance causes a temperature change in it without affecting its molecular structure, it is called sensible heat.

So, the expression that allows to calculate heat exchanges is:

Q = c× m× ΔT

where:

Q is the heat exchanged by a body of mass m.c is the specific heat substance.ΔT is the temperature variation.

Energy in this case

In this case, you know:

Q= ?c= 4.184 J/gCm= 1 gΔT= Tfinal - Tinitial= 25 C - 1 C= 24 C

Replacing in the definition of calorimetry:

Q = 4.184 J/gC× 1 g× 24 C

Solving:

Q= 100.416 J

Finally, the energy needed is 100.416 J.

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Related Questions

which of these diagrams may possibly correspond to the situation at point a on the motion diagram? type, in increasing order, the numbers corresponding to the correct diagrams. do not use commas. for instance, if you think that only diagrams 3 and 4 are correct, type 34.

Answers

The force diagrams that may possibly correspond to the situation at point A on the motion diagram are 356.

What are force diagrams?

A force diagram, also known as a free-body diagram, is a graphical representation that shows the forces, moments, and reactions acting on a body under a specific state. It shows a body or group of connected bodies along with all the applied forces, times, and reactions that the bodies experience.

At point A in the motion diagram, the force acting at point A are as follows:

a net force acting in the forward directiona frictional force acting backward in opposition to the direction to the net forcegravitational force or weight of the object acting downwardsnormal reaction acting upwards.

Hence, the correct diagrams are 3, 5, and 6.

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which of these diagrams may possibly correspond to the situation at point a on the motion diagram? type,
which of these diagrams may possibly correspond to the situation at point a on the motion diagram? type,

You are designing a machine for a space exploration vehicle. It contains an enclosed column of oil that is 1.50 m tall, and you need the pressure difference between the top and the bottom of this column to be 0.125 atm. (a) What must be the density of the oil? (b) If the vehicle is taken to Mars, where the acceleration due to gravity is 0.379g, what will be the pressure difference (in earth atmospheres) between the top and bottom of the oil column?

Answers

Answer:

Explanation:

(a) To find the density of the oil, we can use the formula for pressure difference in a fluid column:

ΔP = ρgh

where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

Plugging in the given values, we have:

0.125 atm = ρgh = ρ(9.81 m/s^2)(1.50 m)

Solving for ρ, we get:

ρ = 0.125 atm / (9.81 m/s^2 x 1.50 m) ≈ 0.00847 g/cm^3

Therefore, the density of the oil must be approximately 0.00847 g/cm^3.

(b) On Mars, the acceleration due to gravity is 0.379 times that of Earth, or g_Mars = 0.379g_Earth. The pressure difference between the top and bottom of the oil column will be:

ΔP_Mars = ρgh_Mars = ρg_Earth(0.379)(1.50 m)

Using the density we found in part (a), we have:

ΔP_Mars = (0.00847 g/cm^3)(9.81 m/s^2)(0.379)(1.50 m) / (1 atm/101325 Pa)

ΔP_Mars ≈ 0.019 atm

So, the pressure difference between the top and bottom of the oil column on Mars will be approximately 0.019 atm, or about 0.15 times the pressure difference on Earth.

Answer:

The pressure difference (in Earth's atmosphere) between the top and bottom of the oil column on Mars is 0.045 atm.

Explanation:

(a) To find the density of the oil, we can use the formula for pressure difference in a fluid column: ΔP = ρgh, where ΔP is the pressure difference, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

We know that the pressure difference is 0.125 atm, the height of the column is 1.50 m, and the acceleration due to gravity on Earth is 9.81 m/s². Plugging in these values, we get:

0.125 atm = ρ(9.81 m/s²)(1.50 m)

Solving for ρ, we get:

ρ = 0.00803 g/cm³

Therefore, the density of the oil must be 0.00803 g/cm³.

(b) If the vehicle is taken to Mars, where the acceleration due to gravity is 0.379g, we can use the same formula to find the pressure difference:

ΔP = ρgh

We know that the height of the column is still 1.50 m, but the acceleration due to gravity is now 0.379g. Plugging in these values, we get:

ΔP = (0.00803 g/cm³)(9.81 m/s²)(0.379)(150 cm)

Solving for ΔP, we get:

ΔP = 0.045 atm

Therefore, the pressure difference (in Earth's atmosphere) between the top and bottom of the oil column on Mars is 0.045 atm.

A 15 kg box is pushed with a force of 35 N in the +x direction, and the box accelerates to the right. It does not accelerate up or down

Answers

The box accelerates to the right due to the applied force of 35 N in the +x direction.

Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the net force acting on the box is 35 N in the +x direction, and its mass is 15 kg. Therefore, we can calculate the acceleration using the formula:

acceleration = net force / mass

acceleration = 35 N / 15 kg = 2.33 m/s² (rounded to two decimal places)

Since the box is not accelerating up or down, we can conclude that the force applied is only causing the box to accelerate in the horizontal direction.

Other forces such as gravity and friction are not considered in this scenario. Thus, the 15 kg box will experience an acceleration of approximately 2.33 m/s² in the +x direction due to the applied force of 35 N.

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A flat sheet of paper of area 0.450 m2 is oriented so that the normal to the sheet is at an angle of 600 to a uniform electric field of magnitude 18 N C-1. What is the magnitude of the electric flux through the sheet? A. 3.22 N m2 C-1 B. 21.42 N m2 C-1 C. 5.04 N m2 C-1 D. 11.72 N m2 C-1 E. 4.05 N m2 C​

Answers

The magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹ (Option E).

The electric flux through a surface is given by the product of the electric field strength and the area of the surface projected perpendicular to the electric field.

In this case, the electric field strength is 18 N C⁻¹, and the area of the sheet projected perpendicular to the electric field is 0.450 m²

(since the normal to the sheet makes an angle of 60° with the electric field). Multiplying these values gives the electric flux:

Electric flux = Electric field strength × Area

Electric flux = 18 N C⁻¹ × 0.450 m²

Electric flux = 8.1 N m² C⁻¹

In summary, the magnitude of the electric flux through the sheet is 4.05 N m² C⁻¹. This value is obtained by multiplying the given electric field strength by the projected area of the sheet perpendicular to the electric field.

The angle of 60° is taken into account to determine the effective area for calculating the flux.(Option E).

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Is frictional force the only example of non-conservative force?​

Answers

Answer: NO, there are many examples of non-conservative forces.

Explanation: Conservatives forces are special forces whose work is zero in a closed path.

Magnetic and Electric fields are Non- Conservative.

An airplane is built to withstand a maximum acceleration of 4 g. If its mass is 1,140 kg, what size force would cause this acceleration?

Answers

The size of force that would cause this acceleration is 4560N.

How to calculate force?

The force acting on a body can be calculated by multiplying the mass of the body by its acceleration as follows:

Force = mass × acceleration

According to this question, an airplane is built to withstand a maximum acceleration of 4m/s². If its mass is 1,140 kg, the magnitude of the force required is as follows:

Force = 1140kg × 4m/s²

Force = 4560N

Therefore, 4560N is the force acting on the airplane.

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represent the reading of a vernier caliper with a diagram showing the reading 45.75mm

Answers

The reading on a vernier caliper can be represented as 45.75mm.

1. Understand the components of a vernier caliper: A vernier caliper consists of two main scales - the main scale and the vernier scale. The main scale is typically graduated in millimeters, while the vernier scale is a smaller scale that slides along the main scale.

2. Locate the main scale: Identify the main scale on the vernier caliper. The main scale is usually marked on the fixed jaw of the caliper and extends in a linear fashion.

3. Identify the vernier scale: The vernier scale is attached to the movable jaw of the caliper. It slides along the main scale and consists of smaller divisions.

4. Align the zero marks: Close the jaws of the caliper and ensure that the zero marks on both the main and vernier scales are aligned.

5. Determine the main scale reading: Read the main scale value that aligns with the zero mark on the vernier scale. In this case, the main scale reading will be 45mm.

6. Locate the vernier scale reading: Examine the vernier scale and identify the division on the vernier scale that lines up perfectly with a division on the main scale. This will give you the additional measurement beyond the main scale reading.

7. Determine the vernier scale reading: Find the division on the vernier scale that aligns with a division on the main scale. The value of this vernier division corresponds to the additional measurement. In this case, the vernier scale reading will be 0.75mm.

8. Add the main scale and vernier scale readings: Combine the main scale reading and the vernier scale reading to get the final measurement. In this case, the final reading will be 45.75mm.

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Tasks
Task 2 - Compare and contrast the use of D'Alembert's principle with
the principle of conservation of energy to solve an
engineering problem
A motor vehicle having a mass of 800 kg is at rest on an incline of 1 in 8 when the
brakes are released. The vehicle travels 30 m down the incline against a constant
frictional resistance to motion of 100 N where it reaches the bottom of the slope.
a) Using the principle of conservation of energy, calculate the velocity of the
vehicle at the bottom of the incline.
b) Using an alternative method that does not involve a consideration of energy,
cacluate the velocity of the vehicle at the bottom of the incline.
c) Discuss the merits of the two methods you have used for parts a) and b) of
this question. Justify the use of an energy method for these types of
problems.​

Answers

Answer:

NE DIYON INGILIZ MISIN SEN

Calculate the net force exerted on a box.

Calculate the net force exerted on a box.

Answers

Answer:

35 N to the left

Explanation:

Do 65 minus 30, and you get 35 N to the left

Because force is a vector quantity, you have to mention both magnitude and direction in your answer.

The linear expansion coefficient of aluminium is 24 × 10^-6 (°C)^-1. When thetemperature is 33 °C, a spherical aluminium ball has a diameter of 11.21 cm.A) Calculate the diameter (in cm) of the aluminium ball when the temperature is raisedto 257° C? (Round your answer to 3 decimal places.)B) Calculate the change in temperature (in °C) needed to increase the volume of thealuminium ball by 3.24%.

Answers

A) Use the following formula for the linear expansion, in this case, of the diameter of the spherical ball:

\(d=d_o\lbrack1+\alpha(T_2-T_1)\rbrack\)

where,

do: initial diameter = 11.21cm

d: final diameter = ?

α: linear expansion coefficient = 24*10^6 /°C

T2: final temperature = 257°C

T1: intial temperature = 33°C

Replace the previous values of the parameters into the formula for d and simplify:

Hence, the diameter of the spherical ball is 11.27cm

B) First, consider what is the change in the radius of the sphere, as follow:

\(\Delta V=0.0324V_o\)

Now, use the following formula for the change in volume with the temperature:

\(\Delta V=\beta V_o\Delta T=3\alpha V_o\Delta T\)

where you have used the equivalence β = 3α.

Solve the equation above for the change in temperature and replace the values of the other parameters:

\(\Delta T=\frac{\Delta V}{3\alpha V_o}=\frac{0.0324V_o}{3(24\cdot10^{-6}(\degree C)^{-1})V}=450\degree C\)

Hence, the change in temperature is 450°C

The linear expansion coefficient of aluminium is 24 10^-6 (C)^-1. When thetemperature is 33 C, a spherical

Find distance between two object of radius 6 cm and 2 cm

Answers

The distance between two objects of radius 6 cm and 2 cm is zero

To find the distance between two objects with radii of 6 cm and 2 cm, we need to consider the center-to-center distance between the objects and subtract the sum of their radii.

Let's denote the radii of the objects as r1 = 6 cm and r2 = 2 cm.

The distance between the centers of the objects can be represented as d = r1 + r2. Adding the radii ensures that we account for the space occupied by both objects.

Substituting the values, we have d = 6 cm + 2 cm = 8 cm.

Now, to find the actual distance between the objects, we subtract the sum of their radii from the center-to-center distance:

Distance = d - (r1 + r2) = 8 cm - (6 cm + 2 cm) = 8 cm - 8 cm = 0 cm.

The resulting distance is 0 cm, indicating that the objects are in direct contact with each other. This means that their surfaces are touching. When the distance between two objects is zero, it implies that they are overlapping or in physical contact. In this case, since the distance is equal to 0 cm, the two objects are touching each other, with their surfaces coming into contact.

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A closely wound, circular coil with radius 2.80 cm has 790 turns. Part A What must the current in the coil be if the magnetic field at the center of the coil is 0.0760 T

Answers

Answer:

\(I=11.1A\)

Explanation:

From the question we are told that:

Radius \(R=2.80\)

Turns \(N=790\)

Magnetic field B=0.0760

Generally the equation for Magnetic field at the center of the coil is mathematically given by

 \(B=\frac{\mu NI}{2r}\)

 \(0.076=\frac{4\p*10^-^7*790*I}{2*0.028}\)

 \(I=\frac{0.076*2*0.028}{4\p*10^{-7}*790}\)

 \(I=11.1A\)

A rocket ship carrying passengers blasts off to go from New York to Hong Kong, a distance of about 13,000 km. (a) How fast (in terms of c) must the rocket ship go to have its own length shortened by 1%? c (b) Ignore effects of general relativity and determine how much time (in s) the rocket ship's clock and the ground-based clocks differ when the rocket ship arrives in Hong Kong.

Answers

Answer:

0.14c

0.003 s

Explanation:

See attachment

A rocket ship carrying passengers blasts off to go from New York to Hong Kong, a distance of about 13,000

what is general relativity​

Answers

Explanation:

General relativity is a theory of space and time. ... The central idea of general relativity is that space and time are two aspects of spacetime. Spacetime is curved when there is matter, energy, and momentum resulting in what we perceive as gravity. The links between these forces are shown in the Einstein field equations.

You have two flashlights that have 0.500-A currents flowing through them. One flashlight has a single 1.50-V battery in its circuit, and the second flashlight has three 1.50-V batteries connected in a chain that provides 4.50 V. How much power is the battery in the first flashlight providing

Answers

Answer: 0.75 W

Explanation:

Given

Current flowing \(I=0.5\ A\)

The first flashlight has a single 1.5 V battery

The second flashlight has three 1.5 V batteries connected to provide 4.5 V

Power is the product of voltage and current.

For the first flashlight

\(\Rightarrow P=1.5\times 0.5\\\Rightarrow P=0.75\ W\)

Thus, the first flashlight providing 0.75 W of power.

A 7500 kg truck is speeding up at 5 m/s down a 1000m on-ramp to the highway.
What is the force exerted on the truck?

Answers

Answer:

37500 N

Explanation:

F = ma

F = 7500 (5 m/s^2) = 37500 N


After 5.2 seconds of uniform acceleration from rest, a spacecraft reaches an
altitude of 5.7 x 102 m [up]. What is the final velocity of the spacecraft? What is the
acceleration of the spacecraft?

Answers

Answer:

Final Velocity:  109.615 m/s

Acceleration:  21.08 m/s²

Explanation:

Distance traveled is given by

Velocity v = Δx/Δt

where Δx is the distance covered and Δt the time to cover that distance

Here Δx = 5.7 x 10² m and t = 5.2 seconds

So v = 5.7 x 10²/5.2 = 109.615 m/s

Acceleration is Δv/Δt where Δv is the change in velocity from an initial velocity and Δt the time taken to reach that initial velocity

Here initial velocity is 0, so Δv= 109.615 - 0 = 109.615m/s

Time to reach this velocity = 5.2 s

So acceleration a =  109.615/5.2 = 21.08 m/s²

Compare the relative strengths of the nuclear force and the electric force

Answers

Answer:

To establish this relationship we must examine the potentials that these forces create. The electrical potential is described by

        Ve = k q / r

The potential for strong nuclear force is

       Vn (r) = - gs / 4pir exp (-mrc / h)

Where gs is the stacking constant and r the distance between the nucleons,

We can compare these potentials where the force is derived from the relationship

       E = -dU / dr

       F = q E

Explanation:

Question 1
Imagine running one hour straight west at 12 km/h and then changing direction
quickly and running one hour straight north at 12 km/h. What was your total
distance? Round to the nearest whole number.
O 34 km NW
O 12 km
O 24 km
O 17 km NW
1 pts

Answers

Answer: 24km

Explanation:

hope this helps

10. In a laboratory experiment, students recorded the
following length data: 12.2 cm, 12.1 cm, 12 cm,
11.9 cm, and 12.20 cm. (a) Determine the average
length and express the answer using the correct
number of significant figures. (b) Based on your
average length calculation in part (a), discuss the
importance of recording measurements to the
appropriate number of significant figures.

Answers

a) 12.1 Average.

B) It is important to record measurements to the correct number of significant figures because otherwise, the integrity of the number is compromised.

What does the average?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint.The mean, median, and mode are the three primary varieties of average. Each of these methods operates slightly differently and frequently yields values typically a little off. The average that is most frequently used is the mean. You add all the values and divide this sum by the total number of values to obtain the mean value.Averages are mostly used to track changes over time within a sample group or cohort.Since averages can be used to compare different quantities of the same category, we employ them. The calculation of averages has limits since it cannot reveal how something is distributed among individuals. For instance, the distribution of income is not shown by per capita income.

A) Determine the average length and express the answer using the correct number of significant figures:

12.2+12.1+12=36.3/3 = 12.1 Average.

B)  Based on your average length calculation in part a, discuss the importance of recording measurements to the appropriate number of significant figures:

It is important to record measurements to the correct number of significant figures because otherwise, the integrity of the number is compromised.

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An astronaut named Sandra Bullock has drifted too far away from her spaceshuttle while attempting to repair the Hubble Space telescope. She realizes that theshuttle is moving away from her at 3 m/s. On her back is a 10 kg jetpack which consistsof an 8 kg holding tank filled with 2 kg of pressurized gas. Without the jetpack, sheand her space suit have a mass of 80 kg.

Required:
a. She is able to use the gas to propel herself in the same direction as the shuttle. The gas exits the tank at a uniform rate with a constant velocity of 100 m/s, relative to the tank (and her). After the gas in the tank has been released, what is her velocity?
b. After this, she throws her empty tank into space and relies on the conservation of momentum to increase her speed to match that of the shuttle. With what velocity (in her frame of reference!) will she have to throw the tank?

Answers

Answer:

a) v_f = 0.898 m / s, b)   v₂ = -6.286 m / s

Explanation:

a) For this exercise we use the conservation of momentum, we define a system formed by the astronaut, her equipment and the expelled gases. We must also define a stationary frame of reference, let's place the system on the platform, so the speed of the subject is v = -3 m / s

Initial instant. Before you start to pass gas

        p₀ = (M + Δm) v

M is the mass of the astronaut M  = 80Kg and Δm the masses of the gases

Final moment. When you expel the gases

        p_f = M (v + Δv) + Δm (v-v_e)

where v_e is the gas velocity v_e = 100 m / s

momentum is conserved

        p₀ = p_f

        M v + Δm v = Mv + M Δv + Δm v -Δm ve

          0 = M Δv - Δm v_e

         

if we make the very small quantities Δv → dv and Δm → dm, furthermore the quantity of output gas is equal to the decrease in the total mass dm = -dM

         M dv = -v_e dM

         ∫ dv = - v_e ∫ dM / M

We solve, between the lower limits v₀ = v with M = M₀   and the upper  limit v = v_f for M = M_f

 

         v_f - v₀ = - v_e (ln M_f - Ln M₀)

         v_f - v₀ = v_e ln (\(\frac{M_o}{M_f}\))

         v_f = v₀ + v_e ln (\frac{M_o}{M_f})

let's calculate

         v_f = -1.3 + 100 ln (80 + 10 + 2/80 + 10)

          v_f = -1.3 +2.20

          v_f = 0.898 m / s

b) launch the jetpack to increase its speed up to the speed of the platform

  initial instant. Before launching the tanks

        p₀ = (M + m') v_f

final instnte. After launching the tanks

       p_f = M v₁ + m' v₂

indicate that the final velocity of the astronaut is the platform velocity v₁=0 m / s, since the reference system is fixed on it

       p₀ = p_f

       (M+ m) v_f = M v₁ + m v₂2

       v₂ = \(\frac{ M ( v_f - v_o) + m' v_f}{m'}\)

        v₂ = \(\frac{M}{m}\) (v_f -v₁) + v_f

let's calculate

        v₂ = 80/10 (0.898 - 0) + 0.898

        v₂ = -7.1874 + 0.898

        v₂ = -6.286 m / s

What would be the net force and in what direction for the motion to be? The first one* and explain

What would be the net force and in what direction for the motion to be? The first one* and explain

Answers

Answer:

11. 5 N to the left.

12. 10 N to the right.

Explanation:

11. Determination of the net force.

Force in the left direction (Fₗ) = 10 N

Force in the right direction (Fᵣ) = 5 N

Net force (Fₙ) =?

The net force can be obtained as follow:

Fₙ = Fₗ – Fᵣ (Since the forces act in opposite direction)

Fₙ = 10 – 5

Fₙ = 5 N to left

Thus, the net force is 5 N to the left.

12. Determination of the net force.

Force in the right direction 1 (Fᵣ₁) = 5 N

Force in the right direction 2 (Fᵣ₂) = 5 N

Net force (Fₙ) =?

The net force can be obtained as follow:

Fₙ = Fᵣ₁ + Fᵣ₂ (Since the forces act in the same direction)

Fₙ = 5 + 5

Fₙ = 10 N to the right

Thus, the net force is 10 N to the right.

The reason uranium mining is dangerous is that chain reactions occur naturally in uranium ore deposits
O True
O False

Answers

Answer:

False po cguro yung sagot d ko po kac Alam e Kaya I Wil study hard to get the correct answer and I will share to you pero I try to be a good friend of mine and I will be a great help to you and your family and your family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and friends and family and friends with you and your family and and I hope I hope you you will be will be able to come to the next event in the future and hope to see you see you soon and hope you have a great day and I will see you see you soon and and will see you soon and hope you have a great day and I will see you soon and hope you have a great day and I will see you soon and hope you have a great day and I will see you soon and hope you have a great day and I will see you soon and hope you have a great day and I will see you soon and hope you have a great day and I will see you soon soon and and thank you for your thank you

What is the freezing point (in degrees Celcius) of 4.67 kg of water if it contains 171.9 g of C a B r 2

Answers

Answer:

c

Explanation:

changes from a liquid to a solid

Explain the working and principle of perisocope.​

Answers

Answer:

a periscope use total internal reflection to allow us to see things

the reflection happens at 45°

Explanation:

HELP THIS LAST DAY!!!

HELP THIS LAST DAY!!!

Answers

Answer:

The proton has much greater mass

Explanation:

Protons and electrons are part of an atomProton exists inside nucleus whereas electron keep moving around the nucleusElectrons have negative charge where as protons have positive charge .

Answer:

D, a proton has a much greater mass.

Explanation:

An electron has a mass close to nothing.

6. Show that the weight of an object on the moon is 1/6 its weight on earth.​

Answers

Taking ratio of W & w. ≈ 6 . w = 1/6 W. Therefore , Weight of an object on the moon is 1/6 of its weight on the earth.

2. Which process is used by plants to cycle water from the ground, through the roots, and out the leaves as water vapor?
sublimation
O perspiration
O transpiration
O runoff

Answers

Answer:

The answer is transpiration

Perspiration is the answer

Define invariant transformations

Answers

Answer:

For a given system, there can be particular transformations for which the explicit equations of motion are the same for both the old and new variables. Transformations for which the equations of motion are invariant, are called invariant transformations. It will be shown that if the Lagrangian does not explicitly contain a particular coordinate of displacement  qi, then the corresponding conjugate momentum,  pi, is conserved. This relation is called Noether’s theorem which states “For each symmetry of the Lagrangian, there is a conserved quantity".

B6. [9 Marks] 30⁰ 20140X20 DE Ofe OTO A stainless-steel orthodontic wire is applied to a tooth as shown in the diagram below. The wire has an unstretched length of 3.1 cm and a diameter of 0.22 mm. If the wire is stretched by 0.10 mm during the procedure, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Young's modulus for stainless-steel is 18 × 10¹0 Nm-². ​

Answers

The magnitude of the force on the tooth is approximately 0.022 N.

To find the magnitude and direction of the force on the tooth, we can use Hooke's Law, which states that the force exerted on an object is directly proportional to the change in length of a material when it is stretched or compressed.

First, we need to calculate the strain (ε) of the stainless-steel wire.

Strain is defined as the change in length divided by the original length:

ε = ΔL / L₀

Given that the change in length (ΔL) is 0.10 mm \((0.10 \times 10^{-3} m)\) and the unstretched length (L₀) is 3.1 cm \((3.1 \times 10^{-2} m)\), we can calculate the strain:

\(\epsilon=(0.10 \times 10^{-3} m)/(3.1 \times 10^{-2} m)=0.003225\)

Next, we can use Young's modulus (E) to calculate the stress (σ) in the wire.

Stress is defined as the force per unit area:

σ = E * ε

Given that Young's modulus (E) for stainless-steel is 18 × 10¹⁰ N/m², we can calculate the stress:

σ = (18 × 10¹⁰ N/m²) * 0.003225 = 5.805 × 10⁸ N/m²

Now, we can find the force (F) on the tooth by multiplying the stress by the cross-sectional area (A) of the wire:

F = σ * A

The cross-sectional area (A) can be calculated using the formula for the area of a circle:

A = π * (d/2)²

Given that the diameter (d) of the wire is 0.22 mm\((0.22 \times 10^{-3} m)\), we can calculate the cross-sectional area:

\(A = \pi * (0.22 \times 10^-3 m / 2)^{2} = 3.802 \times 10^{-8} m^2\)

Finally, we can calculate the force:

\(F = (5.805 \times 10^{8} N/m^{2}) * (3.802 \times 10^-8 m^{2}) \approx 2.206 \times 10^{-2} N\)

Therefore, the magnitude of the force on the tooth is approximately 0.022 N.

Since the wire is stretched, the force is pulling the tooth in the direction opposite to the stretching.

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