Collin can use stoichiometry chemistry to determine the mass of the s'more using this information.
The study of quantitative ratios or relationships between two or more substances undergoing a physical change or a chemical change is known as stoichiometry (chemical reaction). The word is derived from the Greek words "element" and "metron" in the Greek language (meaning "to measure"). Calculations involving stoichiometry typically involve the mass or volume of products and reactants.
The law of conservation of mass, which holds that matter cannot be generated or destroyed but can only be changed from one form to another, is explained by the basic mathematical principle of stoichiometry. A chemical reaction needs a balanced stoichiometry in order to start and proceed to completion.
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A car accelerated from rest for 12 s, at which time it
had traveled 480 m. What were its average and final
velocities?
The initial velocity will be zero since the car started from rest, and final velocity is 40 m/s.
acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. The car began at zero miles per hour, or at rest. It then continued to speed quickly. A vector measurement of the rate and direction of motion is what is meant by the term "velocity." Simply said, velocity is the rate of movement in a single direction. Velocity may be used to gauge both the speed of a rocket launching into space and the speed of a car traveling north o6n a busy freeway.
T= 12s
D=480 m
velocity= 480/12
velocity=40 m/s.
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a toy train moves around a circular track, of radius 0.55 m, 10 complete times over 3 minutes. what is the train’s average speed?
The toy train that moves around a circular track, of radius 0.55 m, 10 complete times over 3 minutes has a speed of: 0.1919 m/s
To solve this problem the formulas and the procedures we will use are:
v = (2*π * r * n)/ t
Where:
v = tangential velocityπ = mathematical constantr = radiusn = number of lapst = timeInformation about the problem:
r = 0.55 mn = 10t = 3 minπ = 3.1416v=?By converting the time unit from (min) to (s) we have:
t = 3 min * 60 s/1 min
t = 180 s
Applying the tangential velocity formula we get:
v = (2*π * r * n)/ t
v = (2* 3.1416 * 0.55 m * 10)/ 180 s
v = 0.1919 m/s
What is tangential velocity?In physics is the length of arc traveled in each unit of time in uniform circular motion. It is expressed in units of distance per time (m/s), (km/h).
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A golf ball with a speed of 45 m/s travels straight for a distance of 128 meters. How long was the golf ball traveling for?
Answer: First multiply the numbers you have! 45 x 128 = 5760 miles ! Hope this helps!~
A boy throws a ball straight up into the air. It reaches the highest point of its flight after 4 seconds-How fast was the ball going when it left the boy's hand?
Answer:
Answer is
[tex]4g \: m {s}^{ - 1} [/tex]
Explanation:
We have to find the initial velocity, u.
Final velocity is v = 0. And acceleration is due to gravity.
Now,
[tex]v = u + at[/tex]
[tex]0 = u + ( - g)m {s}^{ - 2} \times 4s[/tex]
[tex]u = 4g \: m {s}^{ - 1} [/tex]
Therefore, the final answer depends on the value of g.
Trucks carrying garbage to the town dump form a nearly steady procession on a country road, all traveling at 19.7 m/s in the same direction. Two trucks arrive at the dump every 3 min. A bicyclist is also traveling toward the dump, at 4.47 m/s.(b) What If? A hill does not slow down the trucks, but makes the out-of-shape cyclist's speed drop to 1.56 m/s . How often do the trucks whiz past the cyclist now?
According to the question, the truck will pass now with a frequency of 10.2×10⁻³Hz.
What is the frequency?The number of waves that pass a fixed point in a unit of time is known as the frequency in physics. It is also the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. When a body in periodic motion moves through a series of events or locations before returning to its initial state, it is said to have experienced one cycle or one vibration.
Explanation:
To find the frequency of the cyclist being passed by the truck,
f' = {(19.7+(-1.56))/19.7}×1/90
= 10.2×10⁻³Hz.
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the specific brain mass is the brain mass divided by the body mass. if body mass increases, does the specific brain mass increase or decrease?
The specific brain mass: decreases if body mass increases.
Due to the specific brain mass is the ratio of brain mass to body mass is inversely proportional when the body mass increases, the specific brain mass decreases.
If we calculate the specific brain mass of a person with a brain mass of 2 kg and a body mass of 50 kg and then with a body mass of 60 kg we have:
specific brain mass (50 kg) = 2 kg/50 kg = 0.04
specific brain mass (60 kg) = 2 kg/60 kg = 0.03
We can state that the specific brain mass decreases if the body mass increases.
What is body mass?It is the amount of mass associated with a person's body
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are two quantities considered to be “directly proportional” and “indirectly
proportional” to each other?
brainliest for answer
Yes, two quantities are considered to be “directly proportional” and “indirectly proportional” to each other.
What are “directly proportional” and “indirectly proportional”?The term “directly proportional” refers to the relationship between two quantities when one factor increases the other factor or quantity is also increases while on the other hand, “indirectly proportional” refers to the relationship between two quantities when one factor increases the other factor or quantity is decreases. Indirectly proportional is also known as inversely proportion because one increases and the other increases.
So we can conclude that Yes, two quantities are considered to be “directly proportional” and “indirectly proportional” to each other.
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a force of 22,000 n will cause a 1 cm x 1 cm bar of magnesium to stretch from 10 cm to 10.07 cm. calculate the modulus of elasticity, both in gpa and ksi.
The elastic modulus of magnesium bar is 3.14 GPa.
We need to know about the modulus of elasticity to solve this problem. The elastic modulus of material can be measured by strain and stress. It can be determined as
B = σ / e
B = (F/A) / (ΔV/V)
where B is modulus of elasticity, σ is stress, e is strain, F is force, A is area, V is initial volume, ΔV is volume stretched.
From the question above, we know that:
F = 22000 N
A = 1cm x 1cm = 1 cm²
V = A x 10cm = 10 cm³
ΔV = (10.07-10) x A =0.07 cm³
Convert to SI unit
A = 1 x 10¯⁴ m²
V = 10¯⁵ m³
ΔV = 7 x 10¯⁴ m³
By substituting the following parameters, we get
B = (F/A) / (ΔV/V)
B = (22000 / (1 x 10¯⁴) / (7 x 10¯⁴ / 10¯⁵)
B = 3.14 x 10⁶ Pa
B = 3.14 GPa
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A straight wire carrying a 3.00-A current is placed in a uniform magnetic field of magnitude 0.280 T directed perpendicular to the wire. (a) Find the magnitude of the magnetic force on a section of the wire having a length of 14.0cm.
The magnitude of the magnetic force on a section of the wire having a length of 14.0cm is 0.1176 N.
What is a magnetic field?The magnetic field is defined as the field the magnetic materials generate or when an electric charge moves in a field region that generates the magnetic field.
It is given that:
A straight wire carrying a 3.00-A current is placed in a uniform magnetic field of magnitude 0.280 T directed perpendicular to the wire.
As we know,
F = i L B sin θ
i = 3 A
L = 14 cm = 0.14 meters
B = 0.280 T
θ = 90 degrees
F = 3(0.14)(0.280)sin 90
F = 0.1176 N
Thus, the magnitude of the magnetic force on a section of the wire having a length of 14.0cm is 0.1176 N.
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A tie fighter is traveling around Naboo with a velocity of 607 m/s. The tie fighter slows down at a rate of -7.5 m/s^2 for 14.6 s. How far did the tie fighter travel while slowing.
The distance the fighter travels is 8062.85 m
What is distance?This is the length between two points.
To calculate the distance the fighter travel, we use the formula below.
Formula:
s = ut+at²/2.......... Eqution 1Where:
s = Distancet = timea = Accelerationu = Initial velocityFrom the question,
u = 607 m/st = 14.6 sa = -7.5 m/s²Substitute these values into equation 1
s = 607×14.6+(-7.5×14.6²)/2s = 8862.2-799.35s = 8062.85 mHence, the distance the fighter travels is 8062.85 m
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS Two friends are discussing physical and chemical changes Isabela says that when you eat, it is a physical change because when you chew, the food is only changed into smaller pieces Mirabel says that when you eat , it is a chemical change because your body digests the food as the chemicals in your body break down the food into energy Who is right?
Answer: Both are correct.
Explanation: When eating, food undergoes both physical and chemical changes.
Answer: Both girls are correct.
Explanation: Your body system undergoes both physical and chemical change when you eat.
A marble is released from rest at the top of a ramp and it rolls down the ramp for 5 seconds. The position of the marble is shown once every second. The angle of the ramp allows the force due to gravity to accelerate the marble at 4.5 m/s^2. How far does the marble travel from the top of the ramp after 5 seconds?
The marble travel from the top of the ramp is 56.25 m.
Ramp is can be understand in physics, such as the inclined planes, also referred to as ramps . That means,ramp is a type of simple machine which manipulate the direction and magnitude of a force. It is very useful machine by which we can understand the problems in mechenics .
We are given that,
The marble rolls down from the ramp in time = t = 5s
Acceleration of the marble due to gravity = a = 4.5 m/s²
Therefore , for getting the distance (s) of the marble which travelled from the top of the ramp by using the equation of motion i.e. given as,
s = ut + (1/2) at²
Here the marble released from thew rest at the top of the ramp so that initial velocity u = 0 , therefore after putting the value above equation can be written as,
s = (1/2)× 4.5 m/s²×5s × 5s
s = 56.25 m
Hence, the marble travel from the top of the ramp 56.25 m after 5 seconds.
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at what distance is an object if its parallax, as measured from either end of a 1000 km baseline, is 1''(arcsec)?
distance of object = (½ baseline)/(tanθ/2)
= (½ × 1000)/(tan0.5")
= 500/0.000000242 km
distance of object = 206248306 km
Definition of parallax?
Particularly: the angular difference in direction of a celestial body as measured from two places on the earth's orbit. The apparent displacement or the difference in apparent direction of an object as seen from two separate points that are not on a straight line with the object
The apparent movement of objects when observed from various angles is referred to as "parallax." An illustration of this can be noticed while traveling on the highway; when you glance out the window, electricity poles close to the road seem to fly by, while distant trees seem to drift by slowly.
The angle here between Earth at one time of year and the Earth 6 months later, as measured from a nearby star, is defined as the parallax angle.
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a pushes a block weighing 5.0 n against a vertical wall (fig. 6-26). the coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. assume that the block is no
(a) The block does not move a bit.
(b) The force on the block from the wall is −(12N)i+(5.0N)j
How can we calculate the force?(a)
To know that the block is going to move or not we are using the formula,
We compare f and μF₁
If
f<μF₁,
the block does not slide on the wall
but if
f>μF₁,
the block does slide.
We are given,
F= This is the applied force
F₁= This is the normal force of the wall on the block.
f=This is the force of friction.
mg= This is the force of gravity.
The horizontal component of Newton’s second law is,
F-F₁=0
So, F= F₁ = 12N
and
μ F₁ =(0.60)(12N)=7.2N.
The vertical component is,
f-mg=0
so, f=mg=5.0N.
From the above calculation we can get that,
f<μF₁,
So The block does not move a bit
(b)Since the block does not move,
f=5.0N.
F₁ = 12N
So, The force of the wall on the block is
F(wall) =−F₁ i + f j=−(12N)i+(5.0N)j
Therefore from the above calculation we can conclude that, The force on the block from the wall is −(12N)i+(5.0N)j
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Disclaimer: The question is incomplete in the portal here is the total question.
Question:
A 12N horizontal force pushes a block weighing 5.0 N against a vertical wall (Fig.). The coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. Assume that the block is not moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?
In the accompanying diagram of right triangle ABC, AB= 8, BC= 15, AC= 17, and m/ABC = 90.
What is tan C?
The correct answer is tan C = 8/15.
Six trigonometric ratios, namely Sine, Cosecant, Tangent, Cosecant, and Secant, are defined for right triangles in mathematics. These trigonometric ratios are actual functions that connect a right-angled triangle's angle to the ratios of its two side lengths. Basic trigonometric functions like Sin and Cos can be used to determine how a right triangle is shaped. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are the six trigonometric ratios; they are sometimes known as Sin, Cos, Tan, Csc, Sec, and Cot. These can be represented in terms of the sides of a right-angled triangle given a particular angle, which is why they are known as ratios.
From the figure
[tex]$\tan A=\frac{\text { leg opposite } \angle A}{\text { leg adjacent to } \angle A}: \tan (\angle A C B)=\frac{\overline{A B}}{\overline{B C}}$[/tex]
Substitute [tex]$\overline{A B}=8, \overline{B C}=15$[/tex] into [tex]$\tan (\angle A C B)=\frac{\overline{A B}}{\overline{B C}}: \tan (\angle A C B)=\frac{8}{15}$[/tex]
Hence tan C = 8/15.
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6. A technician examines different electrical devices to determine the one that is the most
energy efficient. While conducting a test, he notes that one of these devices consumes
550 000 J of energy and loses 315 000 J at the same time. What is the energy efficiency
of this device?
A)
42.7%
B) 57.2%
D) 174.6%
C) 68.1%
A) 42.7% is the energy efficiency of the device.
Energy efficiency is a measure of how much energy is wasted. There are several ways to save energy, especially thermal energy, and the rate at which it is lost needs to be slowed down. Energy efficiency is defined as requiring less energy to complete an activity or reach a goal. Homes, structures, and production facilities that use less energy to create their products also consume less energy to heat, cool, and run gadgets and appliances.
Energy efficiency is one of the most straightforward and cost-effective ways to halt global warming, reduce consumer energy costs, and increase the competitiveness of American businesses. Energy efficiency is also a key component in the decarbonization process to attain net-zero emissions of carbon dioxide.
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Answer please answer
Check the correctness of the formula, . Where, t is the time period, m is the mass and k is the force per unit displacement. [2]
T=2ᴫ√(m/k) , T be the time period, m be the mass and k be the force per unit displacement.
To check the correctness of the above equation we are using DIMENSIONAL ANALYSIS THEOREM. After using the theorem we can say that the formula is dimensionally correct.
What is dimension?The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity. . Dimensions are physical quantities that can be measured. A dimension is a combination of length, breadth and height as [M], [L] and [T] respectively.
How can we conclude that the formula is dimensionally correct or not?We shall use DIMENSIONAL ANALYSIS to check the correctness of the above equation. In this analysis , we shall try to check the dimensions on the LHS and RHS :
LHS:
{T}≡{time}
RHS:
{2π√(m/k)}≡{√(m/k)}
Or,{2π√(m/k)}≡{√(m/(force/x))}
Or,{2π√(m/k)}≡{√(M/(MLT⁻²/L))}
Or,{2π√(m/k)}≡{√(1/T⁻²)}
Or,{2π√(m/k)}≡{√T²}
Or,{2π√(m/k)}≡{T}≡{time}
So, LHS = RHS .
Hence, from the above prove we can conclude that, the equation is dimensionally correct.
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Check the correctness of formula, T=2ᴫ√m/k , T be the time period, m be the mass and k be the force per unit displacement.
two trains each having a speed of 20km/h, are headed towards each other on the same straight track. a bird
The calculated distance is 20 km.
Speed indicates how quickly something, or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. For instance, if a car drives 120 miles in 2 hours, we may calculate the speed as 120 x 2 = 60 miles per hour. The units for speed are determined by the units of distance and time.
Recognizing that the gap between the trains is closing at a constant rate of 20 km/h,
the total time that elapses before they crash is
t=(20km)/(20km/h)
=1.0h.
During this time, the bird travels a distance of
x=vt
=(20km/1.0h)
=20km.
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find an expression for the electric field e⃗ at the center of the semicircle. hint: a small piece of arc length δs spans a small angle δθ
Rxpression for the electric field E at the center of the semicircle is
Q/[tex]\frac{}{}[/tex](2π² ∈₀ R²) (-j) , where j is the unit vector.
Since the total charge on the semicircle is Q and the Radius of the semicircle is R.
if we consider that an elemental charge makes an angle theta with the horizontal on the semicircle and along the y axis the charge distribution is symmetrical, which means there is a symmetrical charge on the other side too.
So, the vertical component will get added and the horizontal component will cancel out each other .
No let consider due to elemental charge dE be the electric Field and λ be the charge per unit length .
So, we can write λ =Q/πR.
k = 1 /(4π∈₀)
Now the total Electric Field at the center is
= 2dE sinθ
= 2kλ/r [tex]\int\limits^_ {} \,[/tex] Sinθ dθ
After integrating the above term from 0 to π/2, we get
E= 2kλ / R (-j)
E=Q/(2π²∈₀R²) (-j)
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If a football player runs with an average speed of 7.76 m/s, then how much time ( in seconds ) would it take to run 58.6 m?
Average speed is the total distance travelled in total time taken. Here, the total distance covered by the football player is 58.6m ad the average speed is 7.76m/s therefore, the time taken will be 7.55 sec.
What is Average Speed?
Average Speed is the rate at which the total distance is covered by an individual. It can be calculated by the formula:
Average Speed = Total distance travelled by an object ÷ Total time taken
Average Speed = 7.76 m/s
Total distance travelled = 58.6 m
Hence, time taken to cover the distance can be calculated by dividing the distance covered by the object by Average Speed of the object:
Time taken = 58.6 m ÷ 7.76 m/s
Time taken = 7.55 sec
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Owen and Dina are at rest in frame S' , which is moving at 0.600 c with respect to frame S . They play a game of catch while Ed , at rest in frame S , watches the action (Fig. P39.75). Owen throws the ball to Dina at 0.800 c (according to Owen), and their separation (measured in S' ) is equal to 1.80 × 10¹²m .(d) how fast. is the ball moving.
0.385c m/s is the speed of the ball relative to Ed.
A frame of reference is a set of reference points—geometric points whose positions are known mathematically and physically—that define the origin, orientation, and scale of an abstract coordinate system.
If a body does not continuously adjust its position in relation to its environment throughout the course of time, it is said to be at rest.
In the frame S', Dina and Owen are at rest.
The speed of the ball with respect to Owen, u =0.800c
The speed of the frame S' with respect to frame S, v = 0.600c
Distance between Dina and Owen, L(p) = 1.8 × 10¹² m
Speed of light, c = 3 × 10⁸ m/s
Therefore, the velocity of the ball in relation to Ed is:
u' = (u-v) / 1-(uv/c²)
u' = (0.8c - 0.6c) / 1- [(0.8c)(0.6c)/c²]
u' = (0.8c - 0.6c) / 1- [(0.8)(0.6)]
u' = 0.3846c ≈ 0.385c
The speed of the ball with respect to Ed is 0.385c m/s.
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a 5m wide gate will be constructed in the dam. the lake is 6m deep. please find the average horizontal force applied on the gate from the lake water. use water density of 1000 kg/m3 , atmospheric pressure of 101 kpa, and g
The average horizontal force applied on the gate from the lake water. will be 882.9 kN
What is a force?Force is defined as the external agent applied to any object which tries to displace the body from one place to another or resist the body movement.
Given,
width of gate, W = 5 m
depth of the lake, h = 6 m
density of water = 1000 kg/m³
Atmospheric pressure = 101 kPa
Pressure at the bottom of the gate will be calculated as below:-
P = ρ g h
P = 1000 x 9.81 x 6
P = 58860 Pa
Now, Force acting on the plate is
F = ( 1 / 2)pwh
F = ( 1 / 2 ) x 58860 x 5 x 6
F = 882900 N
F = 882.9 k N
The average horizontal force applied on the gate from the lake water is equal to F = 882.9 kN
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When two waves interfere constructively or destructively, is there any gain or loss in energy in the system of the waves? Explain.
There is no gain or loss in energy as it remains constant in the system in case of interference.
When two waves interact, either positively or negatively, there is no gain or loss in the system's energy, according to the principle of conservation of energy.
The distribution of energy in the system changes depending on the angle of superimposition during constructive interference, but the system's overall energy does not change and remains constant.
Although it may appear that waves are canceling each other out or losing energy in the event of destructive interference, energy is still present. There is no gain or loss of energy in the system even though the energy distribution may alter, the energy may be preserved, and the system's temperature may rise.
Hence Energy does neither gain nor lose in the presence of interference; it remains constant.
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Bailey is plagued with sleep problems at least a couple of times a week. She often feels tired at work and doesn't do her best work because she is "just so tired." According to the lesson, it can be said that __________ adults have some of the same problems with sleep that Bailey does. A. few B. many C. no D. all
Option (B) many
According to the lesson, it can be said that many adults have some of the same problems with sleep that Bailey does.
Sleeplessness is one of the most common issues, every second adult or a teenager is facing now a days. Due to a lot of responsibilities, we end up having little time for sleep and this in turn affects our body functions.
A sleep disorder can affect our overall health, safety and quality of life. Lack of sleep can affect your ability to drive safely and increase our risk of other health problems.Sleep plays a key role in thinking and learning. Lack of sleep impairs these cognitive processes in a number of ways.Good sleep hygiene is often recommended to improve sleep quality, which also helps in alleviating anxiety due to work load and responsibilities.
Answer is Option (B) many
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A grating with 250 grooves mm is used with an incandescent light source. Assume the visible spectrum to range in wavelength from 400nm to 700nm . In how many orders can one see (a) the entire visible speed
The number of orders that one can see the entire visible speed is 5 orders.
How to calculate the orders?From the information given, it should be noted that the grating with 250 grooves mm is used and the visible spectrum range in wavelength from 400nm to 700nm. Therefore, the grating spacing will be:
d = (1.00 × 10^-4) / 250
d = 4000nm
Therefore, the number of times that are needed to complete the order will be the same as the number of orders which the long wavelength time will be visible. This will be:
= (4000 × sin 90°)/700
= 5.71
Therefore, the maximum orders will be 5.
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earth has a mass of 5,970,000 how would scientists express this in a number scientific notation
Taking into account the definition of Scientific notation, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.
Definition of scientific notationScientific notation is a quick way to represent a number using powers of base 10.
The numbers are written as a product:
a×10ⁿ
where:
a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the point decimal is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.This caseIn this case, to write the number 5,970,000 in scientific notation, the following steps are performed:
The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number will be the value of a in the previous expression. Then a = 5.97The base 10 is written with the exponent equal to the number of spaces that the decimal point moves. This is a positive number because the decimal point is shifted to the left, and it will have a value of n = 6.Finally, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.
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a window washer does not want to change her position. what does she want the forces acting on her to be? large large small small balanced balanced unbalanced
When a window washer does not want to change her position but still her position got changes to range then the force acting on the window washer is an Unbalanced force because only an Unbalanced force can change the position.
What is Unbalanced Force?Unbalanced forces are those acting on a body when the net force acting on the body is greater than zero. The body alters its state of motion when unbalanced forces act on it. Or, In other words, the net force acting on an object is unbalanced when it is moving at a variable speed. For instance, when an apple falls from a tree, it experiences an imbalanced force equal to its weight. A toy vehicle being pushed is an example of an imbalanced force, and the toy car begins to move as a result of the unbalanced force.
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a ball of mass 2.0 kg is thrown vertically upward from the top of a building. the ball’s velocity v is given as a function of time t by the equation v(t)
The acceleration of the ball at t = 1.5 sec is -10 m/s².
The height of the building is 16 m.
The ball will reach maximum height after 0.2 seconds.
The mass of the ball is 2 kg.
The ball is thrown vertically from upwards top of the building.
Let the velocity of the ball is v and the total time taken by the ball be t.
Now, the velocity of the ball as a function of t is given as:
v(t) = 2 - 10t
The acceleration can be obtained by differentiating the velocity with respect to time.
Therefore,
a = dv/dt
a = d/dt ( 2 - 10t )
a = - 10 m/s²
When t = 1.5 sec
The acceleration of the ball is - 10 m/s².
(b) The ball reaches the ground at t = 2.0 sec.
Now, velocity can be defined as the differentiation of velocity with respect to time.
v(t) = dx/dt
dx/dt = 2 - 10t
dx = 2 - 10t
Now integration the above equation for limits x = 0 to x and time t = 0 to t = 2sec as the balls reached the ground in 2 seconds.
Then,
∫dx = ₀∫² [ 2- 10t]dt
x = [2t]₀² - [10t²/2]₀²
x = 4 - 20
x = -16 m
Therefore, the height of the building is 16 m.
(c) The ball will reach the maximum height when the instantaneous velocity is zero.
v(t) = 2 - 10t
0 = 2 - 10t
t = 2/10 = 0.2 sec
The ball will reach maximum height after 0.2 seconds.
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The complete question is mentioned below:
A ball of mass 2.0kg is thrown vertically upward from the top of a building. the ball velocity v is given as a function of time t by the equation v(t)= 2-10t. the positive direction is upward. what is the ball acceleration at time t = 1.5 complete. (b) if the ball reaches the ground at t=2.0s what is the height of the building? (c) at what time does the ball reach a maximum height above the building?
Two long, parallel wires are attracted to each other by a force per unit length of 320μ N/m . One wire carries a current of 20.0 A to the right and is located along the line y= 0.500 m . The second wire lies along the x axis. Determine the value of y for the line in the plane of the two wires along which the total magnetic field is zero.
The value of y for the line in the plane of the two wires along which the total magnetic field is zero is 0.1667 m below the upper wire .
The force per unit length between two parallel thin current-carrying [tex]I_1[/tex] and [tex]I_2[/tex] wires at distance ' r ' is given by [tex]f=\frac{u_0I_1I_2}{2\pi r}[/tex] ....(1) The field between parallel wires will be zero only if the current is flowing in both wires in the same direction, and the force between them will be the attractive force.It is given that force per unit length is 320μ N/m and one wire carries a current [tex](I_1)[/tex] of 20.0 A and is located along the line y= 0.500 m .
Putting above values in equation (1) , we get
[tex]320\times10^{-6}=\frac{4\pi \times10^{-7}\times20.0\times I_2}{2\pi \times0.500}\\\ \\320\times10^{-6}=\frac{4 \times10^{-5}\times I_2}{5}\\\\I_2=\frac{320\times10^{-6}\times5}{4 \times10^{-5}} \\\\I_2=40A[/tex]
Now the magnitude of the magnetic field at a distance "a" due to long current carrying is given by
[tex]B=\frac{u_0I}{2\pi a}[/tex]
The direction of this magnetic field is given by the right-hand rule of thumb of holding the wire in the right hand, with the outstretched thumb pointing in the direction of current flow and the direction of curled fingers pointing in the direction of magnetic field circulation. of wire.
Hence, field due the wire has an outward direction from the top side of the wire to the bottom side of the wire. Thus, the field is added, above the upper wire comes out of the paper for two wires and enters the paper below the lower wire.
Between the two wires, due to top wire magnetic field is in the paper and due to the bottom wire magnetic field is outside so it is subtracted. The magnetic field is zero here.
Let the resultant magnetic field is zero at a distance x below the upper wire and then magnitude of the field at this distance due to both field must be equal and opposite and is given by
[tex]B=\frac{u_0I_1}{2\pi x} -\frac{u_0I_1}{2\pi (r-x)} \\\\0=\frac{u_0I_1}{2\pi x} -\frac{u_0I_1}{2\pi (r-x)} \\\\\frac{u_0I_1}{2\pi x} =\frac{u_0I_1}{2\pi (r-x)} \\\\\frac{I_1}{x} =\frac{I_2}{r-x} \\\\\frac{20}{x} =\frac{40}{0.500-x} \\\\20(0.500-x)=40x\\\\10-20x=40x\\\\10=60x\\\\\x=\frac{10}{60} \\\\x=0.1667m[/tex]
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