When electrons are transferred from one atom to another, the atom that gained an electron becomes negatively charged, and the one that has lost an electron becomes positively charged. Atoms like these are called ions.
These 2 ions are held together by an ion bond.
Answer: Ionic Bond
An infinitely long line of charge has linear charge density 5.00×10−12 C/m5.00×10−12 C/m. A proton (mass 1.67×10−27 kg1.67×10−27 kg, charge +1.60×10−19 C+1.60×10−19 C) is 18.0 cm from the line and moving directly toward the line at 3.50×103 m/s.3.50×103 m/s. (a) Calculate the proton’s initial kinetic energy. (b) How close does the proton get to the line of charge?
(a) The initial kinetic energy of the proton is 1.023 x 10⁻²⁰ J.
(b) The position of the proton from the line of charge depends on the time of motion of the proton.
What is the initial kinetic energy of the proton?The initial kinetic energy of the proton is the energy of the proton due to its motion.
Mathematically, the initial kinetic energy of the proton is given by the following formula,
K.E = ¹/₂mv²
where;
m is the mass of the protonv is the initial velocity of the protonK.E = ¹/₂(1.67 x 10⁻²⁷)(3.5 x 10³)²
K.E = 1.023 x 10⁻²⁰ J
The position of the line is calculated as follows;
x = Q/σ
where;
Q is the charge of the protonσ is the linear charge densityx = (1.6 x 10⁻¹⁹ C) / (5 x 10⁻¹² C/m)
x = 3.2 x 10⁻⁸ m
We can determine the how close the proton get to the line of charge, if we know the time of motion of the proton. Unfortunately, more information is needed to determine the time of motion of the proton.
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Can somone please explain difference between potential and potential energy?
Answer:
Potential basically tells us the ability of an object to do some work . And Potential energy is the amount of energy it acquires due to that Potential difference.
Explanation:
I hope it will be helpful ror you.
At a baseball game, a ball of m = 0.15 Kg moving at a speed of v = 30m/s is caught by a fan.
a. Show that the impulse supplied to bring the ball to rest is 4.5 N x s. Remember to use the correct units (0.25pts)
b. Show that if the ball is stopped in 0.02 s, then the average force of the ball on the catcher’s hand is 225 N. Remember to use the correct units. (0.25pts)
A. The impulse supplied to bring the ball to rest 4.5 Ns. Details below
B The average force of the ball is 225 N. Details below
What is impulse?This is defined as the change in momentum of an object.
Impulse = change in momentum
Impulse = final momentum – Initial momentum
Impule = m(v - u)
Where
m is the massu is the initial velocityv is the final velocityAlso,
Impulse = force × time
Therefore
Force × time = final moment – Initial momentum
A. How to determine the impulse
The impulse can be obtainedas illustrated below
Mass (m) = 0.15 KgInitial velocity = 30 m/sFinal velocity = 0 m/sImpulse =?Impulse = m(v + u) since the came to rest
Impulse = 0.15 × (0 + 30)
Impulse = 0.15 × 30
Impulse = 4.5 Ns
Thus, the impulse is 4.5 Ns
B. How to determine the average force
The average force can be obtained as follow:
Impulse = 4.5 NsTime = 0.02Average force = ?Impulse = force × time
4.5 = average force × 0.02
Divide both sides by 0.02
Average force = 4.5 / 0.02
Average force = 225 N
Thus, the average force is 225 N
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What would cause the AMA of a machine to decrease?How could you increase the AMA of a machine?
The AMA is the quotient between the input and output forces and is given by:
[tex]AMA=\frac{F_o}{F_I}[/tex]Where:
[tex]\begin{gathered} F_o=\text{ output force} \\ F_I=\text{ input force} \end{gathered}[/tex]Therefore, the AMA is decreased if the input force is increased. If in a machine the friction force increases due to low maintenance then the required input force would increase and therefore, the AMA would decrease.
In a first-class lever we have the following:
We can calculate the ratio between input and output forces by adding the torque around the fulcrum:
[tex]F_oR_o-F_iR_i=0[/tex]Adding the product of the input force and input distance:
[tex]F_oR_o=F_iR_i[/tex]Now, we divide both sides by the input force:
[tex]\frac{F_oR_o}{F_i}=R_i[/tex]Now, we divide both sides by the output distance:
[tex]\frac{F_o}{F_i}=\frac{R_i}{R_o}[/tex]Therefore, the AMA is:
[tex]AMA=\frac{R_i}{R_o}[/tex]Therefore, if in the lever we increase the input distance or decrease the output distance we would increase the AMA.
Speed (m/s) vs. Time (s) Graph
30
*K
8
10
E-F
A-B
30
43
Car's Speed vs Time
E
50
Teets
LL
70
In the speed vs Time Graph, which time interval(s) show pricitive (+) acceleration?
Calculate the car's acceleration between the following points
(Acceleration (Speed-Speed,
F-G
In the speed vs Time Graph, which time interval(s) show negative (-) acouleration?
30
In the speed vs Time Graph, which lime interval(s) show constant speed?
92
100
Time, Time,) or Acceleration Aspeed/ Alime
B-C
C-D
G-H
D-E
H-I
Considering the acceleration concept and the speed vs time graph, it is found that:
The acceleration is positive in intervals CD and EF.The acceleration is negative in intervals BC, GH and HI.The acceleration is constant in intervals AB and FG.For each interval, the acceleration is given as follows:
AB: 0 m/s².BC: -1 m/s².CD: 1 m/s².DE: -1 m/s².EF: 3 m/s².FG: 0 m/s².GH: -3 m/s².HI: -1 m/s².How to calculate acceleration?Acceleration is given by the change in velocity divided by the change in time, according to the following formula:
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
Considering a graph of velocity x time, the acceleration is:
Positive when the graph is increasing, hence in intervals CD and EF.Negative when the graph is decreasing, hence in intervals BC, GH and HI.Constant when the graph is constant, hence in intervals AB and FG.Considering that each point has a time interval of 10s, and the numeric values of the velocity, the acceleration for the intervals is found as follows:
AB: 0 m/s². (constant velocity).BC: (10 - 20)/20 = -1 m/s².CD: (20 - 10)/10 = 1 m/s².DE: (10 - 20)/10 = -1 m/s².EF: (40 - 10)/10 = 3 m/s².FG: 0 m/s². (constant velocity).GH: (10 - 40)/10 = -3 m/s².HI: (0 - 10)/10 = -1 m/s².More can be learned about acceleration at https://brainly.com/question/14344386
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If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). what is theminimum speed required to take 84 meter radius banked at 17 degree so that you don't slide inward.
For the car to stay on the road without sliding in or sliding out, all the forces on the x-axis must equal each other. Thus by equating all the forces on the x-axis, we can find the coefficient of the friction.
In order to determine the minimum speed of the car, use the following expression:
[tex]v=\sqrt[]{R\cdot g\cdot\tan \theta}[/tex]where,
R: radius of the road = 84m
g: gravtitational acceleration constant = 9.8m/s^2
θ: angle of banking of the road = 17 degrees
Replace the previous values of the parameters into the formula for v:
[tex]\begin{gathered} v=\sqrt[]{(84m)(9.8\frac{m}{s^2})(\tan 17)} \\ v\approx15.86\frac{m}{s} \end{gathered}[/tex]Hence, the minimum speed requierd is approximately 15.86m/s
In order to determine the value of the minimum coefficient friction required, use the following formula:
[tex]\mu=\frac{v^2-Rg\tan \theta}{v^2\tan \theta+Rg}[/tex]by replacing, you get:
[tex]undefined[/tex]A ball is projected horizontally from the edge of a
table that is 1.00 m high, and it strikes the floor at a
point 1.20 m from the base of the table.
a. How high is the ball above the floor when its
velocity vector makes a 45.0° angle with the
ad horizontal?
The height of the ball at the given angle is 0.18 m.
What is the time of motion of the ball?
The time of motion of the ball from the given height is calculated as follows;
h = ut + ¹/₂gt²
where;
u is the initial vertical velocity of the ball = 0t is time of motionh = ¹/₂gt²
t = √(2h/g)
t = √(2 x 1 / 9.8)
t = 0.45 s
The horizontal speed of the ball is calculated as follows;
X = vt
where;
X is the horizontal distancev = X/t
v = (1.2 m) / (0.45 s)
v = 2.67 m/s
The height of the ball at the given angle is calculated as follows;
(vsinθ)² = (usinθ) + 2gh
where;
u is the initial vertical velocity = 0(vsinθ)² = (0) + 2gh
(vsinθ)² = 2gh
h = (vsinθ)²/2g
h = (2.67 sin45)²/(2 x 9.8)
h = 0.18 m
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The height achieved by the ball will be 0.18 m above the floor when its velocity vector makes a 45° angle with the horizontal.
What is Velocity?The velocity of a vector represents the rate and direction of motion. Anything's velocity is the rate at which it moves in a single direction.
The SI unit is meter per second (m/s) and the dimension formula is M⁰L¹T⁻¹.
According to the question,
The given values are :
Initial Speed, u = 0 m/s
Height, h = 1.00 m
The horizontal distance, X = 1.2 m.
Use the equation of time of motion,
h = ut + 1/2gt²
put the values in the equation,
1 = 0 + 1/2(9.8)t²
t² = [tex]\sqrt{2/9.8}[/tex]
t = 0.45 seconds.
The ball will move horizontally at a speed of :
X = v × t
v = X/t
v = 1.2 / 0.45
v =2.67 m/s.
Now, calculate the height of the ball at a given angle,
(v sinθ)² = (u sinθ) + 2gh
(v sinθ)² = 0 + 2gh
h = (v sinθ)²/2g
h = (2.56 sin 45°)² / (2 × 9.8)
h = 0.18 m.
Hence, the height of the ball above the floor is 0.18 meters.
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A person stands at a point 245 m in front of the face of a sheer cliff. 1f the person shouts, how much time will elapse before an echo is heard? (Assume the speed of sound is 344 m/s.)
Answer: time = 1.42 seconds
Explanation:
The formula for calculating time is expressed as
time = distance/speed
From the information given,
distance of person from cliff = 245
total distance travelled by echo in returning = 245 x 2 = 490
speed of sound = 344 m/s
Thus,
time = 490/344
time = 1.42 seconds
Find the answer to the problem
Acceleration of box is 2.82m/s.
How does acceleration work?acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is constantly changing, even motion on a circle accelerates at a constant pace.
Acceleration is measured in what ways?Meters per second per second (m/s2) is a unit of measurement for acceleration.
Formula,
F_NET = ∑ F1 + F2 , and F_NET = m . a
F_NET = 18N + 6N = 24N
Then,
F_NET = m . a , a = F_NET/m
a = 24N / 8.5kg
a = 2.82m/s.
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What did Piaget believe about his stages of cognitive development?
A. It is not required to complete one stage to move on to the next one.
B. All children go through the stages in the exact same order.
C. A child’s age is the main factor to determine when they enter a stage.
D. All adults complete all four stages of development by the age of 25.
All adults complete all four stages of development by the age of 25. Option D.
For Piaget cognitive development was the gradual reorganization of mental processes as a result of biological maturation and environmental experience. Children make sense of the world around them and experience discrepancies between what they already know and what they discover around them.
Fundamentally Piaget believed that man could make sense of the world on his own. From a theological point of view, he was a psychological constructivist believing that learning is caused by a mixture of two processes for him assimilation and adaptation. Piaget supported the idea that children think differently than adults and his research identified several important milestones in children's intellectual development.
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If the limits of human hearing are 20 Hz to 20,000 Hz, what are the sound wavelengths thatare associated with both of these two extremes, assuming the speed of sound is 345 m/s.Frequency = 20 Hz: Wavelength = 1.725 10 m
Given data:
* The value of the frequency of wave is 20,000 Hz.
* The value of wavelength of sound wave is,
[tex]undefined[/tex]What planet is more similar in size to earth
Answer: Venus
Explanation:
Please help me solving these questions :(
A block is at rest on an inclined on the plane.
(a) The forces acting on the object shows in the picture.
(b) The component of gravitational force on the slope is (Fsinθ)=50N
(c) The amount of friction is (f)=25N
(d) The force perpendicular to the plane is (Fcosθ)=86.60N
What is force?Force is a physical quantity when it is applied on a object which is at rest start moving and a moving object change its velocity. It can be measured in Newton and Dyne.
How can we calculate the force?(b) To calculate the component of gravitational force on the slope we are using the formula, r=Fsinθ
Here we are given,
F= The amount of force acting on the object. = 100N
θ= The angle which was made by the plane. =30°
We have to calculate the values of the component of gravitational force on the slope = r
Now we put the values in the equation,
r=Fsinθ
Or, r=100*cos(30)
Or, r=50N
From the calculation we can say, The component of gravitational force on the slope is (Fsinθ)=50N
(c) To calculate friction we are using the formula,
f= μₙr
Here we given,
μₙ= coefficient of dynamic friction = 0.5
r= The component of gravitational force on the slope = 50N
Now we put the values in above equation we get,
f= μₙr
Or, f= 0.5*50
Or, f=25N
So we can say, The amount of friction is (f)=25N
(d) To calculate the force perpendicular to the plane we are using formula here is, N= Fcosθ
As we know both the values of F and θ.
Then we put the values in the equation we get,
N=Fcosθ
Or, N= 100* cos30
Or, N=86.60N
According to the calculation we can say that, The force perpendicular to the plane is (Fcosθ)=86.60N
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2. The gravitational force between the star and object X is equal to the forces between the
star and the two planets. From that information, what can you conclude about object X?
if the star's gravitational pull on object X is equivalent to the star's pull on the two planets.
The mass of the object X is equal to the mass of the two planets and the distance between the star and object X is equal to the distance between the star and two planets.
Simply put, the gravitational force is the force that pulls objects with mass together. It draws crowds together.
According to the information provided, the gravitational attraction between the star and planet A and planet B will be equal.
The gravitational attraction force grows together with the mass. This will result in decreased gravitational forces as the separation distance increases.
As the gravitational force is directly proportional to mass and inversely proportional to the square of the distance, therefore, the mass of object X is equal to the mass of the planets and the distance between the star and object X is equal to the distance between the star and the two planets.
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A frictionless pulley, which can be modeled as a 0.83 kg solid cylinder with a 0.33 m radius, has a rope going over it, as shown in (Figure 1). The tensions in the rope are 12 N and 10 N . What is the angular acceleration of the pulley?
A frictionless pulley, which can be modeled as a 0.83 kg solid cylinder with a 0.33 m radius, contains a rope going over it. The tensions in the rope exists 12 N and 10 N. The angular acceleration of the pulley will be 13.025 rad/s².
What is meant by angular acceleration?The temporal rate at which angular velocity changes is known as angular acceleration. The standard unit of measurement exists radians per second. Rotational acceleration is another name for angular acceleration.
Rotational acceleration is another name for angular acceleration. It has both magnitude and direction, making it a vector quantity.
We know that,
Torque = I α = r × Fnet
Iα = r × Fnet
0.5 × m × r² * α = 2 × r × sin 90
After solving, we get
α = 4/mr = 4/(0.83 × 0.37)
α = 13.025 rad/sec²
Therefore, the angular acceleration of the pulley exists 13.025 rad/sec².
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Logan pushes a box with a 400n of force with a direction angle of 30 degrees, while Andrew pushes the same box with a force of 250N with a direction angle of 290 degrees.Which of the following represents the component vectors of the force applied by Andrew?
Given:
The force applied by the logan is
[tex]F=400\text{ N}[/tex]The force applied by the Andrew is
[tex]F=250\text{ N}[/tex]Required: component of force applied by the andrew.
Explanation:
first, draw the free body diagram,
from the free body diagram we can write resolve the force into two components
one along the y axis and one along the x axis
Along x axis
[tex]F\sin(290^{\circ})[/tex]Plugging the values, we get
[tex]\begin{gathered} =250\times\sin(290) \\ =250\times-0.939 \\ =-234.92\text{ N} \end{gathered}[/tex]Along y axis
[tex]\begin{gathered} F\cos(290^{\circ}) \\ =250\times\cos(290^{\circ}) \\ =250\times0.342 \\ =85.50\text{ N} \end{gathered}[/tex]Thus, the component of forces are
[tex]85.50\text{ N, }-234.92\text{ N}[/tex]and option first is correct.
A mechanic changing the spark plugs in a car notes that the instruction manual calls for a torque with a magnitude of 22 N · m. If the mechanic grasps the wrench as shown in the figure below, determine the magnitude (in N) of the force she must exert on the wrench.
Given,
The magnitude of the torque is
[tex]T=22\text{ N.m}[/tex]The angle is
[tex]\theta=60\text{ }[/tex]The distance d is
[tex]d=0.30\text{ m}[/tex]Solution:
The torque is calculated by the formula,
[tex]T=dFsin\theta[/tex]Calculate the magnitude of the force.
[tex]\begin{gathered} F=\frac{T}{dsin\theta} \\ F=\frac{22\text{ N.m}}{0.30\text{ m}\times sin(60)} \\ F=\frac{22\text{ N.m}}{0.30\times\frac{\sqrt{3}}{2}} \\ F=157.8\text{ N} \end{gathered}[/tex]Thus, the magnitude of the force is 157.8 N.
Not yet answered Marked out of 1.00
Which of the following statements about gravitational force, Fe, is not
correct?
Oa. The gravitational force between two objects depends on their separation.
Ob. Gravitational force is the strongest of the fundamental forces.
Oc. Gravitational forces always exist in pairs of equal magnitude.
Od. Gravitational force is an attractive force only; it is never repulsive.
a. The distance between two objects affects the gravitational force between them.
All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is by far the most insignificant natural force.
The gravitational attraction, an attractive force whose magnitude is directly proportional to the masses of the two objects and inversely proportional to the square of their distance from one another, attracts all objects with mass toward one another.
According to Newtonian mechanics, the "pull" of gravity is caused by mass. There is only a pull between any two masses and every other mass. However, the fact that the magma is so hot is what causes the gravitational pull, not the magma itself.
The gravitational pull between two objects is proportional to their masses and becomes weaker as their distance from one another grows. Both things are attracted to one another equally; for example, a falling object is attracted to the Earth with a force equal to that of the Earth's attraction.
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Calculate the net force.
A book of mass 0.5 kg is dropped from a height of 2.8 m. How much mechanical energy does it have right before it hits the ground? (Assume there is no air resistance.) Acceleration due to gravity is g = 9.8 m/s2.
The mechanical energy the book has right before it hits the ground is equal to 13.72 J.
What is mechanical energy?Mechanical energy can be described as the sum of potential energy and kinetic energy. The law of conservation of mechanical energy states that for an isolated system is only subjected to the conservative forces then its mechanical energy is constant.
The mechanical energy of the object is conserved during the fall in absence of air resistance. When the book is just about to hit the ground, the initial gravitational potential energy at the beginning of the fall will be completely converted into kinetic energy.
Therefore, the mechanical energy at the beginning of the fall will be equal to the mechanical energy just before the book hits the ground.
The mechanical energy in starting is all gravitational potential energy:
U = mgh
where m = 0.5 kg is the mass of the book, g = 9.8 m/s² is the acceleration of gravity, h = 2.8 m is the height above the ground.
U = 0.5× 9.8×2.8
U = 13.72 J
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Please select the word from the list that best fits the definition
Situation in which a mother holds most of the authority.
family
nuclear family
patriarchy
matriarchy
Answer:
Explanation:
Situation in which a mother holds most of the authority:
Matriarchy
An object has a mass 60 kg on the Earth's surface. The object is taken to a point 4 times the Earth's radius from the Earth's center. What is the object's mass at this point?
Given that the mass of the object, m = 60 kg, and the distance from the earth's surface is, h = 4R.
We have to find mass at this height.
The mass of the object is 60 kg as mass is constant irrespective of height.
Suppose you need average speed of 100 km/h to arrive at a certain destination on time. However, trafficlimits your average speed to only 60 km/h during the first half of the trip's distance. What must youraverage speed be in the second half of the trip to be on time?
Answer:
140 km/h
Explanation:
If you have a speed of v1 the first half of the trip and a speed of v2, the second half of the speed, the average speed will be
[tex]v_{\text{avg}}=\frac{v_1+v_2}{2}[/tex]Solving for v2, we get:
[tex]\begin{gathered} 2v_{\text{avg}}=v_1+v_2 \\ 2v_{\text{avg}}-v_1=v_2 \\ v_2=2v_{\text{avg}}-v_1 \end{gathered}[/tex]Then, we can replace the average speed Vavg = 100 km/h and the speed of the first half v by 60 km/h
[tex]\begin{gathered} v_2=2(100\operatorname{km}/h)-60\operatorname{km}/h \\ v_2=200\operatorname{km}/h-60\operatorname{km}/h \\ v_2=140\operatorname{km}/h \end{gathered}[/tex]Therefore, the speed in the second half of the trip must be 140 km/h
A pool cue strikes a 0.25 kg billiard ball with a force of 22 N. If the felt on the pool table supplies
a force of 7 N what is the acceleration of the billiard ball.
Answer:
Approximately [tex]0.06\; {\rm m \cdot s^{-2}}[/tex], assuming that the force from the pool cue is horizontal.
Explanation:
As the billiard ball moves forward, the pool table will exert friction on the ball. In this question, it is given that the magnitude of this friction is [tex]7\; {\rm N}[/tex]. If the ball is moving forward, this friction will point backward.
The cue exerts a forward force of magnitude [tex]22\; {\rm N}[/tex] on the billiard ball. The [tex]22\; {\rm N}[/tex] forward force from the cue and the [tex]7\; {\rm N}[/tex] backward force from the table interact with each other. The resultant force on the ball will be [tex](22\; {\rm N} - 7\; {\rm N}) = 15\; {\rm N}[/tex], forward.
When an object of mass [tex]m[/tex] experiences a net force of [tex]F[/tex], the acceleration [tex]a[/tex] of that object will be [tex]a = (F / m)[/tex].
Apply unit conversion and ensure that the mass of the billiard ball is in standard units (grams): [tex]m = 0.25\; {\rm kg} = 250\; {\rm g}[/tex].
In this question, the net force on this billiard ball is [tex]F = 15\; {\rm N}[/tex]. With a mass of [tex]m = 250\; {\rm g}[/tex], the acceleration [tex]a[/tex] of this billiard ball will be:
[tex]\begin{aligned}a &= \frac{F}{m} \\ &= \frac{15\; {\rm N}}{250\; {\rm g}} = 0.06\; {\rm m\cdot s^{-2}}\end{aligned}[/tex].
The pilot of an airplane traveling 180 km/h wants to drop supplies to flood victims isolated on a patch of land 160 m below. The supplies should be dropped how many seconds before the plane is directly overhead?
Given speed of airplane is 18km/h, then the supplies should be dropped 5.71 sec before the plane is directly overhead.
Motion of an object thrown into the air is called projectile motion. When the initial force launches the object, it experiences only the force of gravity. The object is called a projectile and path is its trajectory. Throwing the ball straight upward, or kicking a ball or just dropping things and make them free fall are examples of projectile motion.
Given, y = -160 m
As we know, g = 9.8 m/s
y = Vt - ½ gt^2
=1/2gt^2
t = (-2y/g)^0.5
t =[-2(-160m)/9.8m/s]^0.5
= 5.71 sec
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A brick dropped from rest falls for 4 seconds. How far does the brick fall?
Free fall acceleration of any object at any time is 10 m/s^2
distance = 1/2 a t ^2 = 1/2 * 10m/s^2 * (4s )^2= 80 m
1. What is the acceleration of a car that takes 8.5 seconds to change its velocity from 35 m/s to 5 m/s?
Knowns:
Unknowns:
Formula:
Solve:
Answer:
Final velocity(v)= 25m/s^2
Initial velocity(u)=10m/s^2
Acceleration(a)=5m/s^2
let time taken be t sec
From first eq of motion
v=u+at
v-u=at
25–10=5t
15=5t
t=3s.
Note: specific heat capacity of water C= 4184 J/kg 0 CWith 31,840 Joules, a water was heated raising its temperature from 22.0 °C to 28.5 °C. Find the mass of the water, in grams. Q =m=ΔT=C=Solution:
We are given the following information
Specific heat capacity of water = 4184 J/kg.°C
Amount of heat = 31,840 Joules
Change in Temperature = 22.0 °C to 28.5 °C
We are asked to find the mass of the water in grams.
Recall the specific heat capacity formula is given by
[tex]Q=m\cdot c\cdot\Delta T[/tex]Let us substitute the given values and solve for mass (m)
[tex]\begin{gathered} Q=m\cdot c\cdot\Delta T \\ 31,840=m\cdot4184\cdot(28.5-22.0) \\ 31,840=m\cdot4184\cdot6.5 \\ 31,840=m\cdot27,196 \\ m=\frac{31,840}{27,196} \\ m=1.1708\; kg \end{gathered}[/tex]Multiply the mass in kg by 1000 to convert into grams.
[tex]m=1.1708\times1000=1170.8\; g[/tex]Therefore, the mass of the water is 1170.8 grams.
Question 6 of 25What does the labeled point in the diagram represent?АА2A. A crestB. A troughO C. The frequency
By definition, the trough of a wave is the lowest point on a wave, since the labelled is on such a point we conclude that the point is representing a trough and the answer is B.
An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector A which has a magnitude of 220km and points in a direction 32 degree north of west. The displacement from the control tower to plane 2 is given by the vector B, which has a magnitude of 140km and points 65 degree east of North. (a) sketch the vectors A, B and D = A -B. Notice that D is the displacement from plane 2 to plane 1. (b) Find the magnitude and direction of the vector D
Given,
The magnitude of vector A, A=220 km
The direction of vector A, θ₁=32° north of west
The magnitude of vector B, B=140 Km
The direction of vector B, θ₂=65° east of north
(a)
(b)
The vector A is given by,
[tex]\vec{A}=Acos\theta_1(-\hat{i})+A\sin \theta_1\hat{j}[/tex]That is,
[tex]\begin{gathered} \vec{A}=-220\cos 32^{\circ}\hat{i}+220\sin 32^{\circ}\hat{j} \\ =-186.57\hat{i}+116.52\hat{j} \end{gathered}[/tex]And vector B is given by,
[tex]\begin{gathered} \vec{B}=B\sin \theta_2\hat{i}+B\cos \theta_2\hat{j} \\ =140\sin 65^{\circ}\hat{i}+140\cos 65^{\circ}\hat{j}_{} \\ =126.88\hat{i}+59.17\hat{j} \end{gathered}[/tex]Thus, vector D is given as
[tex]\begin{gathered} \vec{D}=\vec{A}-\vec{B} \\ =(-186.75-126.88)\hat{i}+(116.52-59.17)\hat{j} \\ =-313.63\hat{i}+57.35\hat{j} \end{gathered}[/tex]The magnitude of the vector D is given by,
[tex]\begin{gathered} D=\sqrt[]{(-313.63)^2+57.65^2} \\ =318.88\text{ km} \end{gathered}[/tex]The direction of vector D is given by,
[tex]\begin{gathered} \theta=\tan ^{-1}(\frac{57.65}{313.63}) \\ =10.41^{\circ} \end{gathered}[/tex]Therefore the magnitude of vector D is 318.88 km and the direction of the vector D is 10.41° north of the west.
The direction of the vector D is represented as,
