Answers
Answer:
The tension in [tex]T_1[/tex] is 0.1024 Newtons.
The tension in [tex]T_2[/tex] is 0.1157 Newtons.
Explanation:
Lets create a free body diagram showing all of the forces; we need to show the vertical and horizontal components of the tension.
I will attach a picture of my free body diagram. Notice I created 2 new triangles with the adjacent angles of angle A and C from the original picture.
Lets make a list of all the variables we have now. Also lets write down the information we are given.
[tex]A=27\\C=38\\m=12\\g=9.81\\W\\T_{1} \\T_{1x} \\T_{1y}\\T_{2} \\T_{2x} \\T_{2y} \\[/tex]
In this situation the sum of of the vertical tension components must support the weight. To find the vertical components we can use the SIN function.
[tex]sin(x)=\frac{O}{H} \\O=Hsin(x)[/tex]
Therefore we can write that the sum of the forces in the y direction is
[tex]\sum F_y=T_1sin(A)+T_2sin(C)=W[/tex]
This system is in equilibrium; the object should not move along the x-axis. Therefore, the horizontal components of [tex]T_1[/tex] and [tex]T_2[/tex] must then equal each other. To find the horizontal components we can use the COS function.
[tex]cos(x)=\frac{A}{H} \\A=Hcos(x)[/tex]
Therefore we can write that the sum of the forces in the x direction is
[tex]\sum F_x=T_1cos(A)=T_2cos(C)[/tex]
Now we have to equations to help us solve the problem.
[tex]T_1cos(A)=T_2cos(C)[/tex]
[tex]T_1sin(A)+T_2sin(C)=W[/tex]
We do not know the numerical values of [tex]T_1[/tex] and [tex]T_2[/tex] so we will have to manipulate algebraically to solve them.
In the first equation lets solve for [tex]T_1[/tex].
[tex]T_1cos(A)=T_2cos(C)[/tex]
Divide both sides by [tex]cos(A)[/tex].
[tex]T_1=\frac{T_2cos(C)}{cos(A)}[/tex]
Separate the right side into two fractions.
[tex]T_1=\frac{T_2}{1} *\frac{cos(C)}{cos(A)}[/tex]
Use the reciprocal trig identity for cosine.
[tex]sec(x)=\frac{1}{cos(x)}[/tex]
[tex]T_1=\frac{T_2}{1} *cos(C)}*sec(A)[/tex]
[tex]T_1=T_2*cos(C)}*sec(A)[/tex]
Now insert our answer for [tex]T_1[/tex] into the second equation.
[tex]T_2*cos(C)}*sec(A)*sin(A)+T_2*sin(C)=W[/tex]
Solve for [tex]T_2[/tex]. Lets replace each trig function with its own variable to make this easier.
[tex]T_2*cos(C)}*sec(A)*sin(A)+T_2*sin(C)=W[/tex]
[tex]cos(C)=x\\sec(A)=y\\sin(A)=z\\sin(C)=u[/tex]
[tex]T_2*x*y*z+T_2*u=W\\T_2xyz+T_2u=W[/tex]
Now lets solve for [tex]T_2[/tex].
Factor [tex]T_2[/tex] out of each term.
[tex]T_2(xyz)+T_2(u)=W[/tex]
Factor [tex]T_2[/tex] out of each term.
[tex]T_2(xyz+u)=W[/tex]
Divide each side by [tex]xyz+u[/tex].
[tex]T_2=\frac{W}{xyz+u}[/tex]
Lets substitute the trig functions back in for the variables
[tex]T_2=\frac{W}{cos(C)*sec(A)*sin(A)+sin(C)}[/tex]
[tex]W[/tex] is the weight.
The formula for weight is [tex]W=mg[/tex]. Where [tex]m[/tex] is the mass in kilograms.
12 grams is 0.012 kilograms.
[tex]W=0.012*9.81[/tex]
[tex]W=0.11772[/tex]
Numerical Evaluation
Lets evaluate [tex]T_2[/tex].
[tex]T_2=\frac{0.11772}{cos(38)*sec(27)*sin(27)+sin(38)}[/tex]
[tex]T_2=0.11573[/tex]
Lets evaluate [tex]T_1[/tex].
[tex]T_1cos(A)=T_2cos(C)[/tex]
[tex]T_1*cos(27)=0.11573*cos(38)\\T_1=0.10235443[/tex]
A rating/review would be much appreciated.
Answer:
T₁ = 102.25 N (2 d.p.)
T₂ = 115.61 N (2 d.p.)
Explanation:
The diagram shows a body of mass 12 kg (weight = 12g N) held in equilibrium by two light, inextensible strings. One string makes an angle of 27° with the positive horizontal and the other string makes an angle of 38° with the negative horizontal.
The body is in equilibrium, so both the horizontal and vertical components of the forces must sum to zero.
Resolving horizontally, taking (→) as positive:
[tex]\implies -T_1 \cos (27^{\circ})+T_2 \cos (38^{\circ})=0[/tex]
[tex]\implies T_1 \cos (27^{\circ})=T_2 \cos (38^{\circ})[/tex]
[tex]\implies T_1=\dfrac{T_2 \cos (38^{\circ})}{ \cos (27^{\circ})}[/tex]
Resolving vertically, taking (↑) as positive:
[tex]\implies T_1 \sin(27^{\circ})+T_2 \sin(38^{\circ})-12\text{g}=0[/tex]
[tex]\implies T_1 \sin(27^{\circ})+T_2 \sin(38^{\circ})=12\text{g}[/tex]
Substitute the found expression for T₁ into the second equation and take g = 9.8 ms⁻²:
[tex]\implies \left(\dfrac{T_2 \cos (38^{\circ})}{ \cos (27^{\circ})}\right) \sin(27^{\circ})+T_2 \sin(38^{\circ})=12\text{g}[/tex]
[tex]\implies T_2 \cos (38^{\circ})\tan(27^{\circ})+T_2 \sin(38^{\circ})=12\text{g}[/tex]
[tex]\implies T_2 \left(\cos (38^{\circ})\tan(27^{\circ})+ \sin(38^{\circ})\right)=12\text{g}[/tex]
[tex]\implies T_2 =\dfrac{12\text{g}}{\cos (38^{\circ})\tan(27^{\circ})+ \sin(38^{\circ})}[/tex]
[tex]\implies T_2=115.614550...\:\text{N}[/tex]
Substitute the found value of T₂ into the equation for T₁ and take g = 9.8 ms⁻²:
[tex]\implies T_1=\dfrac{\left(\dfrac{12\text{g}}{\cos (38^{\circ})\tan(27^{\circ})+ \sin(38^{\circ})}\right) \cos (38^{\circ})}{ \cos (27^{\circ})}[/tex]
[tex]\implies T_1=102.250103...\text{N}[/tex]
Therefore, the value of T₁ and T₂ in the given diagram is:
T₁ = 102.25 N (2 d.p.)T₂ = 115.61 N (2 d.p.)
Related Questions
A small toy car of mass 3.00kg runs into another toy car of mass 2.00kg at rest. They stick together and slide 2.0 meters along the rough floor m = 0.25. how fast was the first car going when it hit the ground car? Is this collision elastic or inelastic?
Answers
Answer:
Explanation:To determine the speed of the first car when it hit the second car, we can use the conservation of momentum. The momentum of the first car before the collision is equal to its mass multiplied by its velocity, and the momentum of the two cars after the collision is also equal to their combined mass multiplied by their combined velocity.
The momentum of the first car before the collision is 3.00kg * v1 = m1 * v1
The momentum of the two cars after the collision is (3.00kg + 2.00kg) * v2 = (m1 + m2) * v2
From the conservation of momentum, we can set these two equations equal to each other and solve for v1:
m1 * v1 = (m1 + m2) * v2
v1 = (m1 + m2) * v2 / m1
v1 = (3.00kg + 2.00kg) * v2 / 3.00kg
v1 = 5.00kg * v2 / 3.00kg
v1 = (5/3) * v2
The combined velocity of the two cars after collision is v2 = 2.0m / (2.0s) = 1.0m/s
Therefore, the first car was going at (5/3) * 1.0m/s = 1.67m/s.
To determine if this collision is elastic or inelastic, we need to calculate the coefficient of restitution (e).
e = (initial velocity of first car - final velocity of first car) / (initial velocity of first car)
The initial velocity of the first car was 1.67m/s and final velocity of the first car is 0 m/s (since it stops after the collision).
e = (1.67m/s - 0m/s ) / (1.67m/s)
e = 1.0
The coefficient of restitution is 1.0, which means the collision is perfectly elastic. This means that the kinetic energy is conserved in the collision.
Which statement is true about the theory of plate tectonics and the theory of continental drift?
A) The theory of plate tectonics proves the theory of continental drift completely wrong.
B) The theory of plate tectonics tells exactly where the continents were before Pangaea divided.
C) The theory of plate tectonics gives the method by which continents can move as part of plates.
D) The theory of plate tectonics does not explain how continental movements could occur.
Answers
The statement that is true about the theory of plate tectonics and the theory of continental drift C. The theory of plate tectonics gives the method by which continents can move as part of plates .
What is theory of plate tectonics and the theory of continental drift ?According to the scientific hypothesis of plate tectonics, the underground movements of the Earth create the primary landforms. By explaining a wide range of phenomena, including as mountain-building events, volcanoes, and earthquakes, the theory, which became firmly established in the 1960s, revolutionized the earth sciences.
The scientist Alfred Wegener is most closely connected with the concept of continental drift. Wegener wrote a paper outlining his notion that the continents were "drifting" across the Earth, occasionally crashing through oceans and into one another, in the early 20th century.
According to tectonic theory, the Earth's surface is dynamic and can move up to 1-2 inches every year. The numerous tectonic plates constantly move and interact. The outer layer of the Earth is altered by this motion. The result is earthquakes, volcanoes, and mountains.
Therefore, option C is correct.
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Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring, with spring constant k = 95.0 N/m, is compressed 5.00 m from its equilibrium position, and a glass sits 19.8 m from her outstretched foot. WWW Assuming that Albertine's mass is 60.0 kg , for what value of th, the coefficient of kinetic friction between the chair and the waxed floor, does she just reach the glass without knocking it over? Use g = 9.80 m/s for the magnitude of the acceleration due to gravity.
Answers
The coefficient of kinetic friction between the chair and the waxed floor, does she just reach the glass without knocking it over is,
[tex]\mu_k[/tex]= Coefficient of kinetic friction = 0.102
What is kinetic friction?The friction coefficient is the ratio of the normal force pressing two surfaces together to the frictional force preventing motion between the two surfaces.
Greek letter mu (μ) is typically used to represent it. In mathematics, is equal to F/N, where F is the frictional force and N is the normal force.
The coefficient of friction is dimensionless because both F and N are expressed in units of force (such as newtons or pounds).
For both static and kinetic friction, the coefficient of friction has different values. When an object experiences static friction, the frictional force resists any applied force, and the object stays at rest until the static frictional force is removed.
Using Energy conservation:
KEi + PEi + Wf = KEf + PEf
KEi = 0, since initially Albertine was at rest
KEf = 0, since finally Albertine need to be at rest to just reach the glass
PEi = (1/2)*k*x^2 = Initial Potential energy due to compression of spring
PEf = 0 (since at final position compression in spring is zero)
Wf = Work-done by friction = Ff×d = -μκ*m*g*d
So,
0 + (1/2)*k*x^2 -[tex]\mu_k[/tex]*m*g*d = 0 + 0
[tex]\mu_k[/tex]= k*x^2/(2*m*g*d)
Using given values:
[tex]\mu_k[/tex] = 95.0*5.00^2/(2*60.0*9.80*19.8)
[tex]\mu_k[/tex]= Coefficient of kinetic friction = 0.102
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A net force always result in a ________
Answers
Answer:
Explanation:
______?
Net forces always result in an acceleration. Newton's Second Law of Motion states that a net force (the sum of all forces acting on an object) will cause an object to accelerate in the same direction as the net force. The acceleration is proportional to the magnitude of the net force and inversely proportional to the mass of the object.
Answer:
A net force always result in a acceleration
If you were Jean’s physician, how would you explain to her the changes that might be occurring in her aging mother?
Answers
The changes that occur in old age include decrease in bone density that can affect the normal physiological functioning of her aging mother.
What is aging process?Aging process is the changes and stages of life that an individual naturally undergoes as they advance in age and these experiences are individualized according to lifestyle.
The various changes that occur include but not the least the following:
hearing loss, cataracts and refractive errors, back and neck pain and osteoarthritis, chronic obstructive pulmonary disease, diabetes, depression and dementia. Osteoporosis.The onset of these changes depends on the mother's lifestyle, that is, intake of adequate nutrition, exercise and proper hydration.
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A car accelerates uniformly from rest and
reaches a speed of 28.7 m/s in 6 s. The
diameter of a tire is 58 cm.
Find the number of revolutions the tire
makes during this motion, assuming no slipping.
Answer in units of rev
Answers
The number of revolutions the tire makes in 6 s is
N = (58π)/(12π) = 4.83 rev.
What is revolutions?
Revolutions min physics is the study of the physical aspects of revolutions, including the forces and motions that cause them, the structures and systems that are produced in their wake, and the physical processes that lead to their initiation and termination. It has roots in the study of revolutions in the social sciences, but has developed its own principles and techniques to study physical phenomena related to revolutions. These techniques include the use of mathematical models, experiments, numerical simulations, and computer visualizations.
The linear velocity of a point on the tire's circumference is given by
v = (dπ)/t
where d is the diameter of the tire and t is the time.
Substituting d = 58 cm and t = 6 s, the linear velocity of a point on the tire's circumference is
v = (58π)/6 m/s.
The number of revolutions the tire makes in 6 s is given by
N = (v/2π)
Substituting v = (58π)/6 m/s, the number of revolutions the tire makes in 6 s is
N = (58π)/(12π) = 4.83 rev.
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A fish tank is 20 inches by 12 inches by 12 inches. What is its volume in m * m ^ 3
Answers
As the fish tank is 20 inches by 12 inches by 12 inches, its volume is 47194744.32 mm³.
What is volume?The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
1 inch = 0.0254 meters.
20 inches = 20 × 0.0254 meters = 0.508 meters = 508 mm.
12 inches = 12 × 0.0254 meters = 0.3048 meters = 304.8 mm.
Hence, The volume of the fish tank = length × width × height
= 508 mm × 304.8 mm × 304.8 mm.
= 47194744.32 mm³
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1. Helium gas is cooled from 20 °C to 10 °C by expanding from 40 atm to 1 atm. If there is 1.4 mol of helium,
(a) What is the final volume of helium?
(b) What is the change in internal energy?
Answers
By expanding from 40 atm to 1 atm, helium gas is cooled from 20 °C to 10 °C. If there is 1.4 mol of helium;(a) The final volume of helium is 28.7 L.(b) The change in internal energy is -453.8 kJ.
What is the volume?Volume is a measure of the amount of three-dimensional space an object takes up. It is measured in units of cubic units, such as cubic meters, cubic centimeters, or cubic inches. Volume is often used to measure the size of liquids, solids, and other substances. It is also used to calculate the amount of space an object occupies, such as a room, box, or container. Volume is a useful tool to calculate the amount of an ingredient in a recipe or mixture, or to measure the capacity of a storage container.
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Frici the cat has excellent hearing. He hears the tapping of his favorite treat from afar
in his plate in front of the door.
His owner dropped the treat into his plate from a height of 125 cm, the door is 30 meters from the garden gate, Frici
and he was wandering at the edge of the forest 300 meters from the garden entrance. Its reaction time is 0.1 seconds and 6.6
is speeding home at a speed of m/s.
How long after dropping the reward snack does Frici arrive if the speed of sound is 330 m/s?
Help:
Sub-question 1: How long will the reward wall fall if the difficulty acceleration is set to 10 m/s²
shall we round?
Sub-question 2: How long does it take for the voice to reach Frici?
Sub-question 3: How long does it take Frici The cat to reach her plate?
Answers
The time spent after dropping the reward snack is
0.5 seconds1 second4.55 secondsWhat are Frici's resolves?Generally, To determine how long it takes Frici to arrive at his plate after the treat is dropped, we need to calculate the time it takes for the sound of the treat hitting the plate to reach Frici, and then add the time it takes for Frici to run back home.
Sub-question 1: The time it takes for the treat to fall from a height of 125 cm can be calculated using the formula:
t = √(2h/g)
where
h is the height (125 cm) and g is the acceleration due to gravity (10 m/s²). The height must be converted to meters first. So,t = √(2*1.25/10)
= 0.5 seconds
Sub-question 2: The time it takes for the sound to reach Frici can be calculated using the formula:
t = d/s where d is the distance
30 meters + 300 meters = 330 meters
and s is the speed of sound (330 m/s).
So, t = 330/330
= 1 second
Sub-question 3: Frici's reaction time is 0.1 seconds and he runs at a speed of 6.6 m/s, so the time it takes for him to reach his plate can be calculated using the formula:
t = d/s
where
d is the distance (30 meters) and s is his running speed (6.6 m/s).
So,
t = 30/6.6
= 4.55 seconds
Therefore, the total time it takes for Frici to arrive at his plate is: 0.11 seconds (time for treat to fall) + 1 second (time for sound to reach Frici) + 4.55 seconds (time for Frici to run back) = 5.66 seconds
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Explain how a person who weighs 500 N and is wearing high heels can exert a force of 45,000 N on the floor.
Answers
Pressure on ground is inversely proportional to the surface area in contact, more the surface area in contact, less will be the exrted pressure and vice versa.
even if small force of 500N is applied, due to extremely less surface area, the force acts as 45000 N.
A tuning fork is vibrating the air around it. What best describes the waves produced by the tuning fork?
Answers
The waves produced by a vibrating tuning fork are longitudinal waves, also known as compression waves.
What are Longitudinal Waves?Longitudinal waves are waves that oscillate along the direction of propagation, meaning they create alternating regions of compression and rarefaction in the medium through which they travel.
In the case of a vibrating tuning fork, the tines of the fork move back and forth, causing the surrounding air to alternately compress and expand. These pressure changes propagate through the air as longitudinal waves.
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A student lifts a 4.10-kg box of books vertically from rest with an upward force of 52.7 N. The distance of the lift is 1.60 m. Find: (a) the work done by the student. (b) the work done by gravity. (c) the final speed of the box
Answers
The work done in each case is;
a) 84.32 J done by the student.
b) 64.3 J done by gravity as described.
c)2.77 m/s is the final speed of the box.
What is the work done?We know that the work that is done is the product of the mass and the acceleration of the object. The work that is done by gravity would depend on the depend on the height of the object that is in question.
Now we know that;
a) Work done by the student = Force * distance
= 52.7 N * 1.60 m
= 84.32 J
b) Work done by gravity = mass * acceleration due to gravity * height
= 4.1 Kg * 9.8 m/s^2 * 1.6 m
= 64.3 J
c) The speed of the box;
64.3 J = 1/2mv^2
v = √2 * 64.3/4.1
v = 2.77 m/s
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A car of mass 800 kg initially at rest is accelerated at the rate of 4ms^-2. The kinetic energy of the car after 5 seconds is ?
Answers
Answer:
Explanation:
velocity after 5 seconds is 4 x 5 = 20 m/s
KE formula = 0.5mv²
= 0.5 x 800 x 400
= 400²
= 160000 J
or, 160kJ
What are non-examples of inertia?
Answers
Answer:
A TURNING CAR WITH CONSTANT SPEED......NON-EX OF INERTIA
Explanation:
An object is dropped off a cliff . Assume there is no air resistance, so it accelerates at -9.8m/sec/sec what is the velocity at the end of 2 seconds?
Answers
The velocity of an object dropped off a cliff can be calculated using the equation:
v = v0 + at
Given:
v0 = 0 m/s (initial velocity)
a = -9.8 m/s^2 (acceleration due to gravity)
At the end of 2 seconds:
t = 2 s
v = v0 + at = 0 m/s + (-9.8 m/s^2) * 2 s = -19.6 m/s
The velocity of the object at the end of 2 seconds is -19.6 m/s, downward.
At the end of 5 seconds:
t = 5 s
v = v0 + at = 0 m/s + (-9.8 m/s^2) * 5 s = -49 m/s
The velocity of the object at the end of 5 seconds is -49 m/s, downward.
At the end of 12 seconds:
t = 12 s
v = v0 + at = 0 m/s + (-9.8 m/s^2) * 12 s = -117.6 m/s
The velocity of the object at the end of 12 seconds is -117.6 m/s, downward.
It's worth mentioning that in the case of an object falling freely under the influence of gravity alone, the velocity will continue to increase
Who came up with a law that forces on the behavior of molecules
Answers
Answer: I hope this helps
Explanation:
The law is named after Amedeo Avogadro who, in 1812, hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of molecules.n 1811 Avogadro put forward a hypothesis that was neglected by his contemporaries for years. Eventually proven correct, this hypothesis became known as Avogadro's law, a fundamental law of gases.On this day in 1776, Amedeo Avogadro, an Italian scientist known as one of the founders of physical chemistry, was born. Avogadro studied the properties of electricity and liquids, but his best known work was with gases. It was known by 1809 that all gases, when heated equally, expand by the same amount.
The United States is heading for its biggest political and constitutional crisis since the Civil War, and in the next three or four years there is a high risk of mass violence, the collapse of federal authority, and the division of the country into Republican and Democratic enclaves.
Answers
In the statement above. i believe that the United States is heading for its biggest political and constitutional crisis since the Civil War, and in the next three or four years there is a high risk of mass violence is a false statement.
What is the Civil War about?The American Civil War, also known as the War Between the States, was a conflict that lasted from 1861 to 1865 and resulted in the deaths of an estimated 620,000 soldiers and civilians.
The war was fought primarily in the Southern United States and pitted the Confederate States of America, made up of 11 southern states that had seceded from the United States, against the United States of America (the Union). The main cause of the war was the disagreement over the institution of slavery and states' rights.
Therefore, It is important for individuals and leaders to engage in peaceful and democratic processes to address any issues or conflicts that may arise. It is not productive to speculate on potential crises or violence.
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See full question below
The United States is heading for its biggest political and constitutional crisis since the Civil War, and in the next three or four years there is a high risk of mass violence, the collapse of federal authority, and the division of the country into Republican and Democratic enclaves. Explain
A 75-kg base runner begins his slide into second base when he is moving at a speed of 5.0 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.
a) How much mechanical energy is lost due to friction acting on the runner? how many J?
b) How far does he slide? how many m?
Answers
(a) The mechanical energy lost due to friction force acting on the runner is 936.4 J.
(b) The distance travelled by the runner as he slides is 1.82 m.
What is the acceleration of the runner?The acceleration of the runner is calculated by applying Newton's second law of motion as shown below.
ma = μmg
a = μg
where;
μ is the coefficient of frictiong is acceleration due to gravitya = ( 0.7 x 9.8 m/s² )
a = 6.86 m/s²
The distance travelled by the runner is calculated as;
v² = u² - 2as
where;
v is the final velocity of the runner = 0u is the initial velocity of the runners is the distance travelled by the runnera is the acceleration of the runner0 = u² - 2as
s = u² / 2a
s = ( 5² ) / ( 2 x 6.86 )
s = 1.82 m
The mechanical energy lost due to friction force is calculated as;
W = Fs
W = mas
W = ( 75 kg x 6.86 m/s² x 1.82 m )
W = 936.4 J
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A hiker walks 27.0 km from her base camp at 35° south of east. The next day, she walks 41.0 km in a direction 65° north of east and discovers a forest ranger's tower. Find the magnitude and direction of her resultant displacement between the base camp and the tower.
Answers
The magnitude and direction of the hiker's resultant displacement is 42.7 km, 64.6° north of east.
How to find the magnitude and direction?To find the magnitude and direction of the hiker's resultant displacement, we can use vector addition.
First, we need to convert the given magnitudes and directions into x and y components. We can use trigonometry to do this:
x component of the first displacement = 27.0 km * cos(35°) = 21.5 km
y component of the first displacement = 27.0 km * sin(35°) = 15.5 km
x component of the second displacement = 41.0 km * cos(65°) = 17.6 km
y component of the second displacement = 41.0 km * sin(65°) = 30.6 km
Now we can add the x and y components of each displacement to find the x and y components of the resultant displacement:
x component of the resultant displacement = 21.5 km + 17.6 km = 39.1 km
y component of the resultant displacement = 15.5 km + 30.6 km = 46.1 km
To find the magnitude of the resultant displacement, we can use the Pythagorean theorem:
magnitude of the resultant displacement = sqrt(39.1 km^2 + 46.1 km^2) = sqrt(1820.81 km^2) = 42.7 km
Finally, we can use the arctangent function to find the direction of the displacement:
direction = arctan(46.1 km / 39.1 km) = 64.6° north of east.
So the magnitude and direction of the hiker's resultant displacement is 42.7 km, 64.6° north of east.
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Match the correct numbers and letters together please.
Answers
A wave in physics is a moving disturbance in the energy level of a field.
A transmitter is an electronic device that generates and amplifies a carrier wave, modulates it with a meaningful signal derived from speech, music, TV or other sources, and broadcasts the resulting signal from an antenna.
The antenna is an apparatus to receive or transmit electromagnetic waves and convert respectively to or from an electrical signal.
Receiver is one of the several electronic devices that receive electromagnetic waves, or signals transmitted as such.
Therefore, the correct description of a transmitter, a receiver and an antenna is given above.
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1. At what displacement the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm?
Answers
The displacement at which the kinetic energy and potential energy of a particle executing SHM will be equal when the amplitude is 3cm is 1.5cm.
How does the amplitude of simple harmonic motion affect the ratio of kinetic to potential energy at a specific displacement?The amplitude of simple harmonic motion affects the ratio of kinetic to potential energy at a specific displacement in the following way: as the amplitude increases, the ratio of kinetic to potential energy decreases. This is because the amplitude represents the maximum displacement from the equilibrium position, and as the amplitude increases, the potential energy of the particle increases, while the kinetic energy remains constant. Therefore, at a specific displacement, a particle with a larger amplitude will have a greater proportion of its energy in the form of potential energy, while a particle with a smaller amplitude will have a greater proportion of its energy in the form of kinetic energy.
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4.og of nacl is heated with mno2 in excess concentrated h2so4 the chlorine gas liberated is then passed through KI solution to liberate iodin. Calculate the mass of mno2
Answers
The mass of MnO₂ required by 4 g of NaCl in the chemical reaction is 1.487 g.
What is the balanced chemical reaction of NaCl, MnO₂ and H₂SO₄?
The balanced chemical reaction of NaCl, MnO₂ and H₂SO₄ is given as follows;
4NaCl + MnO₂ + 4H₂SO₄ → MnCl₂ + 4NaHSO₄ + Cl₂ + 2H₂O
From the chemical equation given above, we can calculate the mass of 4NaCl and MnO₂ as follows;
where;
Na is sodium, mass = 23 g/molCl is chlorine, mass = 35.5 g/molMn is manganese, mass = 55 g/molO is oxygen = 16 g/mol4NaCl = 4 ( 23 + 35.5 ) = 234 g
MnO₂ = ( 55 + 32 ) = 87 g
The mass of MnO₂ required by 4 g of NaCl in the chemical reaction is calculated as;
4NaCl + MnO₂ + 4H₂SO₄ → MnCl₂ + 4NaHSO₄ + Cl₂ + 2H₂O
in this equation, 234 g of NaCl ---------> 87 g of MnO₂
4 g of NaCl -------------> ? MnO₂
= ( 4 x 87 ) / ( 234 )
= 1.487 g
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Even though some things may be impossible such as raining cats and dogs, and humans turning into a different species, realistically, it can happen but at a very extremley low percent?
Answers
In the above case, It is not possible for it to rain cats and dogs as it is a figure of speech and not a literal occurrence. Similarly, humans cannot turn into a different species as it goes against the laws of science and biology.
While it may be possible for genetic mutations to occur, they are extremely rare and would not result in a change of species. Therefore, it is not realistic to expect these things to happen.
What is the species about?The statement above is not entirely accurate. Raining cats and dogs is a phrase used to describe heavy rain, it is not a real phenomenon. And humans cannot turn into a different species, it is a biological impossibility.
The concept of evolution over millions of years has led to the development of different species, but one species cannot turn into another within a short period of time or through any known scientific means.
Therefore, It is important to understand that some things are truly impossible, and it is not realistic to assume otherwise.
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Even though some things may be impossible such as raining cats and dogs, and humans turning into a different species, realistically, it can happen but at a very extremley low percent? explain
A radioactive substance of mass 800g has half life of 4 years, how many years those it have with only 8g undecayed
Answers
It will take approximately 8 years for a radioactive substance of mass 800g to have 8g undecayed.
What is the half-life of the radioactive substance in question?The half-life of the radioactive substance in question is 4 years. The half-life of a radioactive substance is the amount of time it takes for half of the original amount of the substance to decay. In this case, after 4 years, half of the initial 800g of the radioactive substance will have decayed, leaving 400g remaining. This means that the decay rate of the radioactive substance is 50% per 4 years. The half-life is a constant for a specific radioactive substance and it does not change, this means that if we wait another 4 years, half of the remaining 400g will decay leaving only 200g, and so on.
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At its closest distance from Earth, the moon experiences a gravitational force of 2.22 E 20 N. The mass of the Earth is 5.97 E24 kg. The mass of the moon is 7.35 E22 kg. What is the distance between the Earth and the moon at that point if G = 6.67 E−11 N*m2/kg2?
A. 1.32 E 4 km
B. 3.63 E 6 km
C. 3.63 E 8 km
D. 1.32 E 17 km
Answers
Answer:
Explanation:
Answer: B. 3.63 E 6 km
The equation for gravitational force is F = G*m1*m2/r2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. We can rearrange the equation to solve for r: r = (G*m1*m2/F)1/2.
Using the given values, we can calculate the distance between the Earth and the moon at the closest point: r = (6.67 E−11 N*m2/kg2 * 5.97 E24 kg * 7.35 E22 kg / 2.22 E 20 N)1/2 = 3.63 E 6 km.
Therefore, the answer is B. 3.63 E 6 km.
If the potential across two parallel plates, separated by 4.0 cm, is 15.0 V, what is the electric field strength in volts per meter?
27 V
0.27 V
380 V
3.8 V
Answers
The electric field strength in volts per meter is 380 V. Option D is the correct answer.
What is electric field strength?This refers to the physical field that encloses electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It can also be called the physical field for a system of charged particles or ( E-field).
The electric field strength (E) can be calculated using the b the formula:
E = V / d,
where,
V = the potential difference (in volts)
d = the distance (in meters) between the plates.
Calculating the electric:
V = 15.0 V
d = 0.04 m (4.0 cm converted to meters).
Hence,
E = 15.0 V
0.04 m
= 375 V/m.
E ≈ 380 V
Hence The electric field strength (E) is 380 V.
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in a resonant vibration a body oscillates under the action of a force along a line such that maximum acceleration is equal to maximum velocity. Then frequency of applied force is
Answers
If the maximum acceleration is equal to maximum velocity, then frequency of applied force is equal to natural frequency of the vibrating body.
What is simple harmonic motion?
A simple harmonic motion is characterized by this changing acceleration that always is directed toward the equilibrium position and is proportional to the displacement from the equilibrium position.
Mathematically, the formula for the maximum acceleration of a simple harmonic motion is given as;
a ( max ) = ω²A
where;
ω is the angular speed of the oscillatorA is the amplitude of the oscillationResonance vibration is a type of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external applied force and the amplitude of forced vibration is maximum.
Thus, we can conclude that, the natural frequency of the vibrating body or object is equal to the frequency of the applied force, hence the term resonant vibration.
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Part A
Compute the x and y components of vector A.
Express your answers in meters to three siginificant figures. Enter your answers separated by
A comma
Answers
The component of vector A in the x direction will be -11.01 meters. and in the y direction will be 9.18 meters.
What is meant by vectors?A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are examples of vectors in nature.
What are examples of vectors?Vector quantities can also include things like movement, acceleration, force, momentum, weight, the speed of light, a gravitational field, current, and more.
component of vector A in x direction = A cos theta
= 12 cos(53)
= -11.01 meters
component of vector A in y direction = A sin theta
= 12 sin (53)
= 9.18 meters
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An observer in a truck observes a billboard appearing to move -21m/s to the east (east being in the +x direction), while a skater appears to be skating 24.94m/s 38 degrees north of west (north being in the +y direction, west in the −x direction). What is the velocity of the skater relative to the billboard?
Answers
The velocity of the skater relative to the billboard is 5.65 m/s east.
What is the velocity of the skater relative to the billboard?
The velocity of the skater relative to the billboard is the measure of the change in position of the skater with respect to the billboard. That is, how fast is the skater moving away from the billboard.
Considering the signs of east and west direction, the formula for the relative velocity of the Skater is given as;
Vs/B = Vs - VB
where;
Vs is the velocity of the skater with respect to the observerVB is the velocity of the billboard with respect to the observerThe magnitude of the velocity of the skater in west direction is given as;
Vs = V cos ( θ )
where;
V is the magnitude of the velocityθ is the angle of velocity of the skater with respect to x axisVs = 24.94 m/s x cos ( 90 - 38 )
Vs = 24.94 m/s x cos ( 52 )
Vs = 15.35 m/s
The velocity of the skater relative to the billboard is calculated as follows;
west = negative direction
east = positive direction
Vs/B = -15.35 m/s - ( -21 m/s )
Vs/B = 5.65 m/s
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The purpose of the chiller is to
A. remove heat from the air.
B. cool conditioned air.
C. distribute the refrigerant.
D. cool warmed water.
Answers
The purpose of the chiller is to remove heat from the air and is therefore denoted as option A.
What is a Chiller?This is a type of device which is referred to as type of a cooling system that removes heat by circulating heat-absorbing a refrigerant through a series of mechanisms through which the heat is released.
The result of this process is that the heat in the air is removed as a result of the refrigerant being adequately circulated and then the environment becomes cooler and is therefore the reason why it was chosen as the correct choice.
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