Answer:
(a) The power wasted for 0.289 cm wire diameter is 15.93 W
(b) The power wasted for 0.417 cm wire diameter is 7.61 W
Explanation:
Given;
diameter of the wire, d = 0.289 cm = 0.00289 m
voltage of the wire, V = 120 V
Power drawn, P = 1850 W
The resistivity of the wire, ρ = 1.68 x 10⁻⁸ Ω⋅m
Area of the wire;
A = πd²/4
A = (π x 0.00289²) / 4
A = 6.561 x 10⁻⁶ m²
(a) At 26 m of this wire, the resistance of the is
R = ρL / A
R = (1.68 x 10⁻⁸ x 26) / 6.561 x 10⁻⁶
R = 0.067 Ω
Current in the wire is calculated as;
P = IV
I = P / V
I = 1850 / 120
I = 15.417 A
Power wasted = I²R
Power wasted = (15.417²)(0.067)
Power wasted = 15.93 W
(b) when a diameter of 0.417 cm is used instead;
d = 0.417 cm = 0.00417 m
A = πd²/4
A = (π x 0.00417²) / 4
A = 1.366 x 10⁻⁵ m²
Resistance of the wire at 26 m length of wire and 1.366 x 10⁻⁵ m² area;
R = ρL / A
R = (1.68 x 10⁻⁸ x 26) / 1.366 x 10⁻⁵
R = 0.032 Ω
Power wasted = I²R
Power wasted = (15.417²)(0.032)
Power wasted = 7.61 W
Which best compares the temperatures of the substances?
O Substance X has the highest temperature because its particles have more kinetic energy.
O Substance X has the highest temperature because it has fewer particles.
O Substance Y has the highest temperature because its particles have more kinetic energy.
O Substance Y has the highest temperature because it has more particles.
The temperature of a substance is determined by the average kinetic energy of its particles, so Substance X and Substance Y have higher temperatures because their particles have more kinetic energy. The number of particles does not affect temperature. The correct options are (A) and (C).
The temperature of a substance is a measure of the average kinetic energy of its particles. When two substances are compared, the substance with the higher temperature has a higher average kinetic energy. The temperature of a substance is affected by the number of particles in it, as well as their kinetic energy. In general, if two substances have the same number of particles but different temperatures, the substance with the higher temperature has more kinetic energy. The options provided include two statements for each substance that describe why it has a higher temperature. Substance X has the highest temperature because its particles have more kinetic energy and Substance X has the highest temperature because it has fewer particles. Substance Y has the highest temperature because its particles have more kinetic energy and Substance Y has the highest temperature because it has more particles.Only one of these statements can be true. The first statement for each substance is correct. This is because the temperature of a substance is determined by the average kinetic energy of its particles. Substance X has a higher temperature because its particles have more kinetic energy. Similarly, Substance Y has a higher temperature because its particles have more kinetic energy. The number of particles in the substance does not affect its temperature.Therefore, option (A) Substance X has the highest temperature because its particles have more kinetic energy, and option (C) Substance Y has the highest temperature because its particles have more kinetic energy are the correct answers.For more questions on temperature
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Calculate Speed The 2-kg metal ball moving at a speed of 3 m/s strikes a 1-kg wooden ball that is at rest. After the collision, the speed of the metal ball is 1 m/s.
Assuming momentum is conserved, what is the speed of the wooden ball?
Answer:
53466kg.
Explanatiokn:
differenciate between scalar and vector quantities.
thankyou ~
Answer:
A quantity that has magnitude but no particular direction is described as scalar. A quantity that has magnitude and acts in a particular direction is described as vector.
The difference between scalar and vector quantities is simply the direction we always consider when dealing with vector quantities.
SCALAR AND VECTOR QUANTITIESScalar quantities are those quantities that have only magnitude but no direction. Examples are;
speedTemperaturemassCurrente.t.cVector quantities are those quantities that have both magnitude and direction. Examples are;
VelocityForceAccelerationMomentume.t.cThe difference between scalar and vector quantities is simply the direction we always consider when dealing with vector quantities.
Therefore, direction is the difference between them.
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During the Apollo Moon missions, astronauts were concerned about the
effects of Newton's third law of motion when:
A. they detected incoming space debris, because the inertia of the
debris could damage their ship.
B. they reentered Earth's atmosphere, because they were carrying
heavy Moon rocks
C. They ejected waste water, because they were concerned that it would push them off course.
D. they took off from Earth, because a large force was required to generate large acceleration
Answer:
C
Explanation:
Option C is correct since it is the effect of Newton’s third law.
mmer
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Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost
and the profit he makes is 176% of cost. What is the regular selling price of each pizza?
The regular selling price of each pizza is $.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost and the profit he makes is 176% of cost. The regular selling price of each pizza is $7.33.
Let's denote the cost of supplies as C.
Operating expenses:
The operating expenses of the business are 161% of the cost. Therefore, the operating expenses can be calculated as:
Operating Expenses = 1.61 * C
Profit:
The profit made by Guiseppe is 176% of the cost. Therefore, the profit can be calculated as:
Profit = 1.76 * C
Total cost:
The total cost includes the cost of supplies and the operating expenses:
Total Cost = C + Operating Expenses = C + 1.61 * C = 2.61 * C
Regular selling price:
The regular selling price is the sum of the total cost and the profit:
Regular Selling Price = Total Cost + Profit = 2.61 * C + 1.76 * C = 4.37 * C
Given that the cost of supplies is $4.02, we can substitute this value into the equation:
Regular Selling Price = 4.37 * 4.02 = $17.5674
Rounding the final answer to the nearest cent, the regular selling price of each pizza is approximately $7.33.
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If you pull with a constant force of 400n , how much mechanical work does it take to pull pinball launcher back 0.2meters
If you pull with a constant force of 400 N for 0.2 meters, then the work done will be equal to 80 J.
What is Work?In physics, the word "work" involves the measurement of energy transfer that takes place when an item is moved over a range by an externally applied, at least a portion of which is applied within the direction of the displacement.
The length of the path is multiplied by the element of a force acting all along the path to calculate work if the force is constant. The work W is theoretically equivalent towards the force f times the length d, or W = fd, to portray this concept.
As per the given information in the question,
Force, f = 400 N
Displacement, d = 0.2 meters
\(Work done(W)=Force(f)*Displacement(d)\)
W = 400 × 0.2
W = 80 J.
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Why was miasma theory replaced?
2. For electric circuit shown in Figure find currents in each resistor.
The current flowing in the 2Ω and 1Ω is 1.14 A and the current flowing in the 3Ω and 4Ω is 0.286 A.
What is the current flowing in each resistor?The value of the current in each resistor is calculated by applying Kirchoff voltage law as follows;
The total voltage in loop 1 is calculated as;
2 + 4 - I₁R₁ - (I₁ - I₂)R₂ - I₁R₃ = 0
6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0
The current flowing in loop 2 is calculated as;
I = V/R
I₂ = ( 6 V - 4 V ) / (3 + 4)
I₂ = 0.286 A
The value of the current flowing in loop 1 is calculated as;
6 - 2I₁ - 3(I₁ - I₂) - 1₁ = 0
6 - 2I₁ - 3(I₁ - 0.286) - 1₁ = 0
6 - 3I₁ - 3₁ + 0.858 = 0
-6I₁ = -6.858
I₁ = 6.858 / 6
I₁ = 1.14 A
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Robert, my neighbor, a forty-five-year-old blacksmith is seven feet tall, and eats all day long. What does he weigh?
The neighbour weighs Iron. As he is a blacksmith, iron is the only thing he weighs the whole day.
What is a riddle?A riddle is a statement, question or phrase having a double or veiled meaning, put forth as a puzzle to be solved.
If Robert, your neighbor, a forty-five-year-old blacksmith is seven feet tall, and eats all day long, based on these statements, we can explain the riddle as Robert weighs iron for the fact that he is a blacksmith, iron is the only thing he weighs the whole day.
Thus, the correct explanation for the riddle is " The neighbour weighs Iron. As he is a blacksmith, iron is the only thing he weighs the whole day.
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Which uses combustion by moving pistons, which respond to a change in pressure?
heat engine
furnace
refrigeration unit
heat pump
;-;
Answer:
I think it is heart engine. I am studying Mechanics aswell
Answer:
A) heat engine
Explanation:
A child of mass 40. 0 kg is in a roller coaster car that travels in a loop of radius 7. 00 m. At point a the speed of the car is 10. 0 m/s, and at point b, the speed is 10. 5 m/s. Assume the child is not holding on and does not wear a seat belt. (a) what is the force of the car seat on the child at point a? (b) what is the force of the car seat on the child at point b? (c) what minimum speed is required to keep the child in his seat at point a?
At point A the force is 571.6 N. At point B the force is 632.8 N. The minimum speed at point A is 8.32 m/s
The force of the car seat on the child can be determined using the equation F = m * a, where F is the force, m is the mass, and a is the acceleration. The acceleration can be found using the equation a = v^2/r, where v is the speed and r is the radius.
(a) At point a, the speed is 10.0 m/s and the radius is 7.00 m. Therefore, the acceleration is:
a = (10.0 m/s)^2 / (7.00 m) = 14.29 m/s^2
The force of the car seat on the child is:
F = (40.0 kg) * (14.29 m/s^2) = 571.6 N
(b) At point b, the speed is 10.5 m/s and the radius is 7.00 m. Therefore, the acceleration is:
a = (10.5 m/s)^2 / (7.00 m) = 15.82 m/s^2
The force of the car seat on the child is:
F = (40.0 kg) * (15.82 m/s^2) = 632.8 N
(c) The minimum speed required to keep the child in his seat at point a can be found by rearranging the equation for acceleration:
v = sqrt(a * r)
Since the force of the car seat on the child must be equal to or greater than the force of gravity on the child (F = m * g), the acceleration must be equal to or greater than the acceleration due to gravity (a = g = 9.81 m/s^2).
Therefore, the minimum speed is:
v = sqrt((9.81 m/s^2) * (7.00 m)) = 8.32 m/s
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1. Is there a relationship between the volume of water displaced and the total volume of the block that has anything to do with density? If so, what is it?
Answer:
The volume of the block is equal to the volume of water displaced by the block.
Explanation:
Volume refers to the amount of space occupied by a given object (in this case the block). When an object such as the block is immersed in water, it displaces its own volume of water. This volume of water displaced is equal to the volume of the block. Hence we can write;
Final Volume of water - Initial Volume of water= Water Displaced = Volume of the block
Recall that the density of a body is given by;
Density= mass/volume
If we obtain the volume of the block by measuring the volume of water displaced by the block, then we weigh the block using a weighing balance, we can obtain the density of the block easily from the relationship shown above.
A particle (charge = +0.8 mC) moving in a region where only electric forces act on it has a kinetic energy of 6.7 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B.
Answer:
The kinetic energy of the particle as it moves through point B is 7.9 J.
Explanation:
The kinetic energy of the particle is:
\(\Delta K = \Delta E_{p} = q\Delta V\)
Where:
K: is the kinetic energy
\(E_{p}\): is the potential energy
q: is the particle's charge = 0.8 mC
ΔV: is the electric potential = 1.5 kV
\(\Delta K = q \Delta V= 0.8 \cdot 10^{-3} C*1.5 \cdot 10^{3} V = 1.2 J\)
Now, the kinetic energy of the particle as it moves through point B is:
\( \Delta K = K_{f} - K_{i} \)
\( K_{f} = \Delta K + K_{i} = 1.2 J + 6.7 J = 7.9 J \)
Therefore, the kinetic energy of the particle as it moves through point B is 7.9 J.
I hope it helps you!
Compare the kinetic and potential energies of a 400 kg box being moved
horizontally by a forklift at a speed of 5 m/s. The box is at a height of 1 m.
Answer:
Kinetic energy is greater than the potential energy.
Explanation:
The potential energy stays constant because the height is not changing. Potential energy = MGH, where m is the mass (400 kg), g is the acceleration due to gravity (9.8 m / sec2), and H is the height (1 m). So the result is 400 * 9.8 * 1 = 3920 J
The kinetic energy = 1/2 mv2 = 0.5 * 400 kg * (5 m/sec)2 = 5000 J. It also stays constant because the speed is not changing.
Therefore, the kinetic energy is greater than the potential energy.
what is the work done on the box from x = 0m to 16m
Answer:
Explanation:
The Workdone is the product of force and distance, Hence, the Workdone on the box from distance x = 0 meters and x = 16 meters is 0 Joules.
Using the graph given :
The work done from x = 0 to x = 16 metres ;
The distance can be split evenly into :
(x = 0 to x = 8) and (x = 8 to x = 16)
Workdone = Force × distance
Workdone from ; x = 0 to x = 8 ;
Force at a distance of 8 meters = - 40N
Workdone = - 40N × 8 m = -320 Nm
Workdone from ; x = 8 to x = 16 ;
Force at a distance of 16 meters = 40 N
Workdone = 40 N × 8 m = 320 Nm
The total workdone :
(-320 + 320) Nm = 0 J
.
Therefore, the Workdone ls 0 Joules.
An object is placed 50cm in front of a concave mirror of radius 60cm. How far from the mirror is the image?
Answer:To explian the exact calculation of this pruduct we must not try!
how do you mountaineers reduce the effects of changes in atmospheric pressure?
An electric iron is Mark 120 volts and 500 Watts to units consumed by it in using it for 24 hours will be
An electric iron is marked 120 volts and 500 Watts. The units consumed by it in using it for 24 hours can be calculated using the formula:Power (in watts) = Voltage (in volts) x Current (in amperes)P = V x I
Using the above formula, we can find the current drawn by the electric iron as follows:I = P/VI = 500/120I = 4.17 ATherefore, the power consumed by the electric iron in 24 hours is:P = VI x tP = 120 x 4.17 x 24P = 120 x 100.08P = 12010.56 watt-hoursTo convert watt-hours to kilowatt-hours, we divide by 1000: Energy consumed = 12010.56 / 1000Energy consumed = 12.01 kWhHence, the units consumed by the electric iron in 24 hours is 12.01 kilowatt-hours.For such more question on Voltage
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What is the first job u do on the ISS if u were an astronaut
If I were an astronaut, the first job I would do on the International Space Station (ISS) would be to familiarize myself with the station and its systems.
What is expected at ISS?I would need to learn how to operate the various equipment and how to maintain the station in good working order. I would also need to learn the procedures for conducting experiments and for performing spacewalks.
Once I had a good understanding of the station and its systems, I would begin working on my assigned tasks. These tasks could include conducting experiments, performing maintenance, or teaching other astronauts new skills. I would also take the opportunity to conduct research on my own and to learn more about the space environment.
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You work in the special effects department of a movie studio. You are currently working on a superhero movie where the hero is very strong and cannot be hurt by normal weapons such as a sword. In the next scene, the villain is going to hit the hero with a lead pipe. The hero's costume is mostly made of foam and carbon so that is it very light and easy to move around in but will crumble if hit with anything hard. For this scene, a section of the costume needs to be replaced with a different material that will only dent, not crumble, when hit with the pipe. You are on a deadline and look around the props department for ideas, what could you use?
A. You find sheets of copper (Cu) used in an industrial factory scene.
B. You find large discs of chlorine (Cl) used to kill bacteria in pools.
C. You find a barrel of phosphorus (P), used as a component in explosive powder.
D. You find a tank of helium (He) used for balloons.
A. Sheets of copper (Cu) could be a good option for replacing the foam and carbon material in the hero's costume. Copper is a relatively soft metal and can easily be shaped and molded. When hit with a lead pipe, it will dent but not crumble like foam and carbon. Additionally, copper has a distinctive color that could look interesting on the hero's costume.
B. Large discs of chlorine (Cl) would not be a good option for replacing the foam and carbon material. Chlorine is a highly reactive and dangerous gas that is used to disinfect swimming pools. It is not a solid material and would not provide the desired effect when hit with a lead pipe.
C. A barrel of phosphorus (P) would also not be a good option for replacing the foam and carbon material. Phosphorus is a highly reactive and flammable substance that is used as a component in explosive powder. It is not a solid material and would not provide the desired effect when hit with a lead pipe. Additionally, it is highly dangerous and should not be used in a movie set.
D. A tank of helium (He) would also not be a good option for replacing the foam and carbon material. Helium is a gas and would not provide the desired effect when hit with a lead pipe. Additionally, it is not a solid material and would not be suitable for the costume.
Overall, the best option would be A, sheets of copper, as it is a solid material that can easily be shaped and molded, and will dent but not crumble when hit with a lead pipe.
1. Given the following vectors: A=(2i+6 j-4k|m, B=(4i-5j-3k)m and C=i+3j-2km. a) Find a unit vectors in the direction of i) A+B ii) A× B iii) 2 A+3C b) Find the magnitude of the following vectors: i) A+B ii) A× B iii) 3A-2C c) Find the angle between the following vectors: i) A× B and Bx A ii) A and C iii) B and C.
In this solution, the unit vectors in the directions of A + B, A × B, and 2A + 3C are √62,√1915, and √686. The magnitudes of A + B, A × B, and 3A - 2C are √62, √1915, and √164. The angles between A × B and B × A, A and C, and B and C are √30, cos-1(4/√35), and cos-1(-1/√14).
a) i) The unit vector in the direction of A + B is given by: A + B = (2i + 6j - 4k)m + (4i - 5j - 3k)m = 6i + j - 7k | 6² + 1² + (-7)²= 62|AB= √62We can now find the unit vector in the direction of A + B as follows:AB = (6/AB)i + (1/AB)j + (-7/AB)k= (6/√62)i + (1/√62)j + (-7/√62)kB)ii) The magnitude of the cross product A × B is given by: A × B = (-27i - 14j + 26k)m² | √(27² + 14² + 26²) = √1915|AB= √1915We can now find the unit vector in the direction of A × B as follows: AB = (-27/√1915)i + (-14/√1915)j + (26/√1915)kC) iii) The unit vector in the direction of 2A + 3C is given by: 2A + 3C = (2 x 2i + 2 x 6j - 2 x 4k)m + (3i + 9j - 6k)m= 7i + 21j - 14k | √(7² + 21² + (-14)²) = √686|AB= √686We can now find the unit vector in the direction of 2A + 3C as follows: AB = (7/√686)i + (21/√686)j + (-14/√686)kb) i) The magnitude of A + B is given by: A + B = (2i + 6j - 4k)m + (4i - 5j - 3k)m= 6i + j - 7k | AB= √62 | √(6² + 1² + (-7)²) = √62We can find the magnitude of A + B as follows: AB = √62ii) The magnitude of A × B is given by: A × B = (-27i - 14j + 26k)m² | AB= √1915We can find the magnitude of A × B as follows: AB = √1915iii) The magnitude of 3A - 2C is given by: 3A - 2C = (3 x 2i + 3 x 6j - 3 x 4k)m - (2i + 6j - 4k)m= 4i + 12j - 2k | AB= √164 | √(4² + 12² + (-2)²) = √164We can find the magnitude of 3A - 2C as follows:AB = √164c) i) The angle between A × B and B × A is 180°. ii) The angle between A and C is given by: A · C = (2i + 6j - 4k)m · (i + 3j - 2k)m= 2 + 18 + 8 = 28 |AB = √56 |AC = √30We can find the angle between A and C as follows:θ = cos-1((A · C)/(AB x AC))= cos-1(28/(√56 x √30))= cos-1(4/√35)iii) The angle between B and C is given by: B · C = (4i - 5j - 3k)m · (i + 3j - 2k)m= 4 - 15 + 6 = -5 |AB = √56 |BC = √30We can find the angle between B and C as follows:θ = cos-1((B · C)/(AB x BC))= cos-1(-5/(√56 x √30))= cos-1(-1/√14)The summary of the solution is that for the given vectors A, B, and C we have been able to find the unit vectors in the direction of A+B, A×B, and 2A+3C. The magnitudes of A+B, A×B, and 3A-2C have also been found. Finally, we have also been able to find the angles between A×B and B×A, A and C, and B and C.For more questions on unit vectors
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what are the effects of cooling on the physical properties of a substance
When the liquid cools down, it loses heat energy.
What is the physical effect of cooling on liquid?As the liquid cools, it loses heat energy. As a result, its particles slow down in movement and come closer to one another. Attractive forces begin to hold particles and the crystals of a solid form.
If water is cooled, it can change into ice. If ice is warmed, it can change into a liquid state. Heating a substance makes the molecules move very fast whereas cooling a substance makes the molecules move very slowly.
Heating a liquid increases the speed of the molecules present in it. An increase in the molecule's speed competes with the attraction between molecules and results in the molecules moving apart whereas Cooling a liquid decreases the movement of the molecules.
So we can conclude that the liquid cools down when it loses heat energy.
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If a point on the edge of a wheel 2 m in radius is accelerating at 2 m/s2, what is the angular acceleration of the wheel?
Answer:
\(\alpha =1\ rad/s^2\)
Explanation:
It is given that,
The radius of a wheel, r = 2 m
Tangential acceleration of the wheel, \(a=2\ m/s^2\)
We need to find the angular acceleration of the wheel. We know that the relation between angular and tangential acceleration is given by :
\(a=\alpha r\\\\\alpha =\dfrac{a}{r}\\\\\alpha =\dfrac{2}{2}\\\\\alpha =1\ rad/s^2\)
So, the angular acceleration of the wheel is \(1\ rad/s^2\).
Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
An army tank division leaves base and travels 30 miles at [W30*S] and then turns and travels 70 miles at [W10*N]. What is their total displacement from base at the end of the trip?
The tank division's total displacement from the base is approximately 75.9 miles at a bearing of W67.4S.
How to calculate the displacement?To calculate the total displacement of the tank division, we need to find the vector sum of the two legs of their journey.
We can see that the tank division travelled 30 miles to the west (W30) and then 70 miles to the north (N70), so their total displacement is the vector sum of these two legs.
To add vectors, we need to break them down into their horizontal and vertical components.
For the first leg, the tank division travelled 30 miles to the west, so its horizontal component is -30 (since it's to the left of the base) and its vertical component is 0 (since it didn't travel up or down).
For the second leg, the tank division travelled 70 miles to the north, so its horizontal component is 0 (since it didn't travel left or right) and its vertical component is 70 (since it travelled directly north).
Now we can add these components to get the total displacement:
Horizontal component = -30 + 0 = -30
Vertical component = 0 + 70 = 70
So the total displacement is a vector with a horizontal component of -30 and a vertical component of 70.
We can use the Pythagorean theorem to find the magnitude of this vector:
|displacement| = √((-30)² + 70²) ≈ 75.9 miles
And we can use trigonometry to find the direction of this vector:
\(\theta = tan^{-1}\dfrac{70} { -30}\)
θ ≈ -67.4°
So the tank division's total displacement from the base is approximately 75.9 miles at a bearing of W67.4S.
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6. What is the complete spectrum of all forms of light?
a. galaxy
b. electromagnetic spectrum
C. energy
d. system
Answer:
b. the electromagnetic spectrum
Explanation:
the electromagnetic spectrum contains all the forms of light, including gamma rays, x-rays, ultraviolet radiation, visible light, infrared, radio waves, microwaves, etc
Một chất điểm chuyển động trong mặt phẳng Oxy với phương trình :
{ = 2 + 10
Answer:
plz write your questions in English
wire (mass = 50 g, length = 40 cm) is suspended horizontally by two vertical wires which
conduct a current I = 8.0 A, as shown in the figure. The magnetic field in the region is into the
paper and has a magnitude of 60 mT. What is the tension in either wire?
The magnetic field in the region is into the paper and has a magnitude of 60 mT and the tension in either wire is 0.096 N.
To find the tension in either wire, we can apply the equation for the force experienced by a current-carrying wire in a magnetic field.
The force experienced by a current-carrying wire in a magnetic field is given by the equation F = B * I * L * sin(θ), where B is the magnetic field strength, I is the current, L is the length of the wire, and θ is the angle between the wire and the magnetic field.
In this case, the wire is suspended horizontally by two vertical wires, and the magnetic field is into the paper. Since the wire is horizontal, the angle between the wire and the magnetic field is 90 degrees, so sin(θ) = 1.
The force experienced by the wire due to the magnetic field is F = B * I * L.
Given:
Current (I) = 8.0 A
Magnetic field (B) = 60 mT = 60 * 10^(-3) T
Length of the wire (L) = 40 cm = 40 * 10^(-2) m
Substituting the given values into the equation, we get:
F = (60 * 10^(-3) T) * (8.0 A) * (40 * 10^(-2) m)
Simplifying the expression, we find:
F = 0.192 N
Since the wire is suspended by two vertical wires, the tension in each wire will be half of the total force. Therefore, the tension in either wire is 0.192 N / 2 = 0.096 N.
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what is the mass of an object that is experiencing a net force of 225N and an accleration of 3.0 m/s^2. And What is the net force on a cart being pushed with an applied force of 23N with a frictional force of 23N?
Answer:
75 kg
Explanation:
Net Force
\(\sf \longmapsto F_{net} = 225N\)
Acceleration produced
\(\sf \longmapsto \: a = 3 .0 m / {s}^{2}\)
According to Newton's 2nd Law –
F = m•a
\(\sf \longmapsto \: M = \frac{F}{a} \)
\(\sf \longmapsto \: M = \frac{225N}{300m/s ^{2} } \)
\(\sf \longmapsto \: M = \: 75 \: kg\)
Hence, the mass of an object is 75 kg.
A cylinder with a torque of 75.0 N
m rotates with an
angular acceleration of 8.5 rad s².
Calculate the
moment of inertia of the cylinder.
The Moment of inertia of the cylinder is equal to 8.82 Kgm².
The propensity of a force to produce or modify the rotational motion of a body is known as torque, also known as moment, or moment of force. It is a force that causes an object to twist or turn. Force and distance are multiplied to calculate torque. It has both a direction and a magnitude because it is a vector quantity. Newton-meters, or N*m, is the torque unit in the SI system.
A spinning object's change in angular velocity per unit of time is expressed quantitatively as angular acceleration, also known as rotational acceleration. It has a vector form.
Given in the question
Torque = 75 Nm
Angular acceleration = 8.5 rad/s²
Torque = Angular acceleration × moment of inertia
Put in the value, we get
Moment of inertia = 75/ 8.5
Moment of inertia = 8.82 Kgm²
So the Moment of inertia of the cylinder is equal to 8.82 Kgm².
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