Answer:
9.1m/s
Explanation:
Nate throws a straight ball to Kayla who is standing at a balcony 3.8m above Nate
When she catches the ball, it is still moving upward with a speed of 2.8m/s
v = 2.8m/s
u = ?
s = 3.8m
a= -9.8(The acceleration has a negative sign because the speed of the ball is declining)
Therefore the initial speed at which Nate threw the ball can be calculated as follows
v^2= u^2 + 2as
2.8^2= u^2 + 2(-9.8)(3.8)
7.84= u^2 + (-74.48)
7.84= u^2 - 74.48
u^2= 7.84 + 74.48
u^2= 82.32
u= √82.32
u = 9.1m/s
Hence the initial speed at which Nate threw the ball is 9.1m/s
Hello How to obtain the voltage and current for the resistors? I don't care about what the result is, I care about HOW Thanks
Answer:
its right the way it is
Explanation:
if there is a multiple choice then pick 20 v
The density of water is about 1 gram per milliliter. A milliliter is a cubic centimeter (i.e., cm3 ). A red blood cell has a density similar to water and is shaped like a one micrometer thick disk with a diameter of about 10 micrometers. About what is the mass in grams of a red blood
Answer:
The mass in grams of a red blood cell is about 7.85 × 10⁻¹¹ grams
Explanation:
To find the mass in grams of a red blood cell,
From,
[tex]Density = \frac{Mass}{Volume}[/tex]
Then,
[tex]Mass = Density \times Volume[/tex]
From the question,
Density of a red blood cell is similar to that of water
Density of water = 1 g/mL = 1 g/ cm³
Then, Density of a red blood cell = 1 g/cm³
Now, we will find the volume a red blood cell.
From the question,
A red blood cell is shaped like a one micrometer thick disk with a diameter of about 10 micrometersSince the shape is like that of a thick disc, we can determine the volume by using the formula for volume of a cylinder.
Hence,
Volume of a red blood cell = [tex]\pi r^{2}h[/tex]
Where [tex]\pi[/tex] Is a constant (Take [tex]\pi[/tex] = 3.14)
[tex]r[/tex] is the radius
and [tex]h[/tex] is the thickness
Diameter of a red blood cell = 10 micrometers
Then, radius of a red blood cell = 10/2 micrometers = 5 micrometers
[tex]r[/tex] = 5 micrometers = 5 × 10⁻⁶ meters
and [tex]h[/tex] = 1 micrometer = 1 × 10⁻⁶ meters
Hence,
Volume of a red blood cell = 3.14 × (5 × 10⁻⁶)² × 1 × 10⁻⁶
∴ Volume of a red blood cell = 7.85 × 10⁻¹⁷ cubic meter (m³)
Convert this to cubic centimeter
(NOTE: 1 cubic meter = 1000000 cubic centimeter)
Hence,
Volume of a red blood cell = 7.85 × 10⁻¹¹ cubic centimeter (cm³)
Now, for the mass
[tex]Mass = Density \times Volume[/tex]
Density of a red blood cell = 1 g/cm³
Volume of a red blood cell = 7.85 × 10⁻¹¹ cubic centimeter (cm³)
Then,
Mass = 1 g/cm³ × 7.85 × 10⁻¹¹ cm³
Mass = 7.85 × 10⁻¹¹ g
Hence, the mass in grams of a red blood cell is about 7.85 × 10⁻¹¹ grams
What is impossible for a machine to do?
A. do a greater amount of work than the amount of work done on the machine
B. apply a force in a direction that is different than the direction of the force applied to the machine
C. move an object a greater distance than the distance that part of the machine was moved
D. apply a force that is less than the force that is applied to the machine
Answer:
Choice A. Without energy storage, the total work output of a machine will not exceed the total work input.
Explanation:
Choice AWork is the product of force and the distance travelled in the direction of that force.
Indeed, simple machines can alter the size or direction of a force. However, their work output can't exceed the work input to that machine (unless the machine stores some energy- by bending, for example.) Because of frictions and other forms of energy loss, the useful work output of a real machine can even be smaller than the work input to that machine.
The force output of some machines can certainly exceed their force input. However, at the same time, the input part of those machine needs to move a distance that is (more than) proportionally longer compared to the output part of the machine. As a result, the useful work output would be equal to or even smaller than the total work input.
Choice BA fixed pulley is an example of a machine that applies a force in a direction different from the direction of the force applied to the machine. Pulling the string down will lift up the weight on the other side. A seesaw (a first-class lever) is another real-world example of this kind of machines.
Choice C and DTongs are examples of machines where: the distance traveled by the output exceeds that of the input. However, that comes at a price: delivering the same amount of force with a pair of tongs requires more force than without a pair of tongs. That corresponds to choice D: the work output of some machines can be less than the force input to these machines.
At the same time, some extra force input might be required to overcome the friction between parts of the machine. That's another reason why the machine applies less force than the input even if it was designed to apply the same amount of force.
Answer:
A.) Do a greater amount of work than the amount of work done on the machine.
Explanation:
I took the quiz on Edge!
Hope this helped!
What constant acceleration in si units must a car have to go from zero to 60 mph in 10s. what fraction of g is this? How far has the car traveled when it reaches 60 mph?
A gnat takes off from one end of a pencil and flies around erratically for 26.1 s before landing on the other end of the same pencil. If the gnat flew a total distance of 2.15 m, and the pencil is 0.0463 m long, find the gnat's average speed and the magnitude of the gnat's average velocity.
Answer:
2.15m/26.1s is = average speed
0.08 m/s
When the bells are charged up, the left bell acquires a positive charge, the right bell a negative charge. When this occurs, the nut that is suspended between the two bells experiences a torque (it lines itself up with a line between the two bells) but it doesn't experience a net force. What does this tell us about the charge on the nut
Answer:
Thus simply tells us that The nut has no net charge and so therefore, There will be a negative charge on the left side, and an equal positive charge on the right side
This basically means that the nut has no net charge and thus will have a negative charge on the left side and an equal positive charge on the right side.
What is net charge?When an object has more protons than electrons, its net charge is positive.
If there are more electrons than protons in an object, the net charge is negative. If the object has an equal number of protons and electrons, it is electrically neutral.
The total charge on a body is the algebraic sum of all the charges on it. Every atom is electrically neutral because it contains the same number of electrons as protons.
This basically means that the nut has no net charge and thus has a negative charge on one side and an equal positive charge on the other.
Thus, this can be implied as per the given scenario.
For more details regarding net charge, visit:
https://brainly.com/question/8233653
#SPJ2
When the Voyager 2 spacecraft sent back pictures of Neptune during its flyby of that planet in 1989, the spacecraft’s radio signals traveled for 4 hours at the speed of light to reach the Earth. How far away was the spacecraft? Give your answer in astronomical units (AU). (2 points) When Mars and Earth are at their minimum separation from each other, they are 0.36 AU apart. How long would it take a radio signal sent from Earth to reach Mars? Give your answer in minutes.
Answer:
a) 28877 AU
b) 1.795 sec
Explanation:
Time it took the radio signal to reach earth = 4 hours = 4 x 3600 = 14400 s
speed of radio signal = speed of vacuum speed of light = 3 x 10^8 m/s
Distance traveled by this signal = speed x time
distance = 3 x 10^8 x 14400 = 4.32 x 10^12 m
One Astronomic unit AU is the distance between the Earth and the sun and it is approximately equal to 1.496 x 10^8 m
The distance traveled by the signal in AU = (4.32 x 10^12)/(1.496 x 10^8) = 28877 AU
b) The minimum separation between Earth and Mars = 0.36 AU
This distance = 0.36 x 1.496 x 10^8 = 538560000 m
Time that will be taken for a radio signal to travel this distance = distance/speed
==> 538560000/(3 x 10^8) = 1.795 sec
what are two things needed for acceleration
Answer:
Velocity and Time
Explanation:
I googled it-
A ball thrown vertically is caught by the thrower after 5.1s. Find the maximum height the ball reaches.
Answer:
h = 31.9 m
Explanation:
Since, the ball took 5.1 s in the air. Hence, the time to reach maximum height will be equal to the half of this value:
t = 5.1 s /2 = 2.55 s
Now, we use 1st equation of motion between the time of throwing and the time of reaching maximum height:
Vf = Vi + gt
where,
Vf = Final Velocity = 0 m/s (since, ball momentarily stops at highest point)
Vi = Initial Velocity = ?
g = - 9.8 m/s² (negative sign for upward motion)
Therefore,
0 m/s = Vi + (-9.8 m/s²)(2.55 s)
Vi = 24.99 m/s
Now, we use second equation of motion for height (h):
h = Vi t + (0.5)gt²
h = (24.99 m/s)(2.55 s) + (0.5)(-9.8 m/s²)(2.55 s)²
h = 63.7 m - 31.8 m
h = 31.9 m
Three tiny charged metal balls are arranged on a straight line. The middle ball is positively charged and the two outside balls are negatively charged. The two outside balls are separated by 20 cm and the middle ball is exactly halfway in between. (HINT: Draw a picture; in your picture, the distance between the two outermost balls should be 20 cm.) The absolute value of the charge on each ball is the same, 1.45 μCoulombs (the meaning of μ, which is read as "micro", is 10-6). Give your answers in newtons.
a) What is the magnitude of the attractive force on either outside ball due ONLY to the positively-charged middle ball?
(b) What is the magnitude of the repulsive force on either outside ball due ONLY to the other outside ball?
(c) What is the magnitude of the net force on the outside of the ball
Answer:
[tex](a) 189.23 N[/tex], [tex](b) 47.31 N[/tex] and [tex](c) 141.92 N[/tex].
Explanation:
Three balls are shown in figure having charge [tex]q=1.45 \mu C[/tex]. The middle ball, [tex]B[/tex], is positively charged having charge [tex]+q[/tex], and the remaining two outside balls, [tex]A[/tex] and [tex]C[/tex], are negatively charged having charged [tex]-q[/tex] as shown.
[tex]AC=20 cm[/tex] and [tex]AB=BC=10[/tex] cm as B is the mid-point of AC.
Let [tex]d_1=AC=20\times 10^{-3}m[/tex] and [tex]d_2=AB=BC=10\times 10^{-3}m[/tex]
From Coulomb's law, the magnitude of the force, [tex]F[/tex], between two point charges having magnitudes [tex]q_1 \& q_2[/tex], separated by distance, [tex]d[/tex], is
[tex]F=\frac {1}{4\pi\epsilon_0}\frac {q_1q_2}{d^2}\;\cdots (i)[/tex]
where, [tex]\epsilon_0[/tex] is the permittivity of free space and
[tex]\frac {1}{4\pi\epsilon_0}=9\times 10^9[/tex] in SI units.
This force is repulsive for the same nature of charges and attractive for the different nature of charges.
Now, Using equations(i),
(a) The magnitude of attraction force between balls A and B is
[tex]F_{AB}=F_{BC}= \frac {1}{4\pi\epsilon_0}\frac {qq}{(d_2)^2}[/tex]
[tex]\Rightarrow F_{AB}= 9\times 10^9}\frac {1.45\times 10^{-6}\times1.45\times 10^{-6}}{\left(10\times 10^{-3}\right)^2}[/tex]
[tex]\Rightarrow F_{AB}=189.23 N[/tex]
(a) The magnitude of the repulsive force between balls A and C is
[tex]F_{AC}= \frac {1}{4\pi\epsilon_0}\frac {qq}{(d_1)^2}[/tex]
[tex]\Rightarrow F_{AC}= 9\times 10^9}\frac {1.45\times 10^{-6}\times1.45\times 10^{-6}}{\left(20\times 10^{-3}\right)^2}[/tex]
[tex]\Rightarrow F_{AC}=47.31 N[/tex]
(c) The magnitude of the net force, [tex]F_{net}[/tex], on the outside of the ball is,
[tex]F_{net}=189.23-47.31 N[/tex]
[tex]\Rightarrow F_{net}=141.92 N[/tex]
language uses_ to quickly express concepts and ideas
a. emotions
b. letters
c. strings
d. symbols
Answer:
i try B
Explanation:
what describes a feature of the physical properties of all substances
Physical properties of matter tells us what a substance is or what a substance can do when it is not undergoing a chemical change.
These properties are observable with our senses or instruments or some pieces of apparatus.
Some of these properties are :
Color
Odor
hardness
texture
boiling point
Melting point
density
viscosity
They differ from chemical properties which are shown by the reaction of a substance with another.
A car is moving at 35 mph and comes to a stop in 5 seconds.
Find the acceleration of the car.
Answer:
-10.267
Explanation:
Initial speed > 35 miles per hour
Final speed > 0 miles per hour
Time > 5 seconds
you have to divide the velocity by the time which should be 35 / 5 = 7
so the answer should be 7 but I'm not sure
Which statement describes Redi’s experiment, which helped disprove spontaneous generation?
A. He examined covered and uncovered meat to determine that maggots came from eggs.
B. He heated milk to show that it could destroy bacteria.
C. He wrote a book on how cells come from other cells through reproduction.
D. He showed that the shape of a flask was important to the experiment.
Answer:
He examined covered and uncovered meat to determine that maggots came from eggs.
In other other words A
if a car is traveling 30 m/s slows to a stop in 20 seconds it has a acceleration of ____m/s^2
Answer:
[tex]a=-1.5\ m/s^2[/tex]
Explanation:
Given that,
Initial velocity, u = 30 m/s
Final velocity, v = 0
Time, t = 20 s
We need to find the acceleration of the car. The rate of change of velocity is equal to acceleration. So,
[tex]a=\dfrac{v-u}{t}\\\\a=\dfrac{-30}{20}\\\\a=-1.5\ m/s^2[/tex]
So, the magnitude of the acceleration of the car is [tex]1.5\ m/s^2[/tex] and it is decelerating.
A man on a road trip drives a car at different constant speeds over several legs of the trip. He drives for 55.0 min at 60.0 km/h, 18.0 min at 80.0 km/h, and 60.0 min at 60.0 km/h and spends
25.0 min eating lunch and buying gas.
Complete Question
A man on a road trip drives a car at different constant speeds over several legs of the trip. He drives for 55.0 min at 60.0 km/h, 18.0 min at 80.0 km/h, and 60.0 min at 60.0 km/h and spends
25.0 min eating lunch and buying gas
What is the total distance traveled over the entire trip (in km)
Answer:
The value is [tex]D = 139.02 \ km[/tex]
Explanation:
From the question we are told that
For [tex] t_1 = 55 min = \frac{55}{60} = 0.917 \ h[/tex] the speed is [tex]v_1 = 60 \ km/h[/tex]
For [tex] t_2 = 18 min = \frac{18}{60} = 0.3 \ h[/tex] the speed is [tex]v_2 = 80 \ km/h[/tex]
For [tex] t_3 = 60 min = \frac{60}{60} = 1 \ h[/tex] the speed is [tex]v_3 = 60\ km/h[/tex]
The time taken to have lunch is [tex]t _l = 25 \ min = \frac{25}{60} = 0.42 \ h[/tex]
Generally the total distance traveled over the entire trip (in km) is mathematically represented as
[tex]D = t_1 * v_1 + t_2 * v_2 + t_3 * v_3[/tex]
=> [tex]D = 0.917 * 60 + 0.3 * 80 + 1 * 60[/tex]
=> [tex]D = 55.02 + 24 + 60[/tex]
=> [tex]D = 139.02 \ km[/tex]
An automobile travels at a displacement of 75km 45 degrees north of east. How many kilometers north does it travel?
Answer:53.03
Explanation:
A parallel-plate air capacitor with a capacitance of 240pF has a charge of magnitude 0.146uC on each plate. The plates have a separation of 0.367 mm.
A) What is the potential difference between the plates?
B) What is the area of each plate?
C) What is the electric field magnitude between the plates?
D) What is the magnitude of the surface charge density on each plate?
Answer:
A. The potential difference is given as
V =q/C=0.146uC/240pF
608.33 V
B) The area of each plate is
A =Cd/eo =9.9525*10^-3m ²
C) the electric field magnitude between the plates=V/d
608.33/0.367mm
=1.657x 10^6 N/C
D) The surface-charge density on each plate=q/A
0.146uC/9.9525 x 10^-3m ²
=1.466 x 10^-5 C/m²
PLEASE HELP!!!! You are given the initial velocity, Vox, and initial displacement, xo, of an object. Assume that
over a specified period of time, t, the object undergoes constant acceleration. Which equation
can be used to find the total displacement of the object by time t ? Use V, and az to represent
the final velocity and the final acceleration, if necessary.
Ox-Xo =
vox tuxt
2
Ox - Xo = vaxt + Laxe?
O v2 = vox² + 2ax (x - Xo)
1 X-X0
+-axt =
2
O vox
t
Answer:
[tex]v^2 = v_{ox}^2 + 2a(x - o_x)[/tex]
Explanation:
The options are not well presented; However, the questions can still be solved
Given
[tex]Initial\ Velocity= V_{ox}[/tex]
[tex]Initial\ Displacement = X_{o}[/tex]
[tex]Time = t[/tex]
Required
Determine the final displacement
This question will be answered using the following equation of motion
[tex]v^2 = u^2 + 2as[/tex]
Where s represent the total distance
s is the distance between the initial and final displacements and is calculated as thus;
[tex]s = x - o_x[/tex]
Where x represents the final displacement
Substitute [tex]V_{ox}[/tex] for [tex]u[/tex] ---- The initial velocity
[tex]v^2 = v_{ox}^2 + 2as[/tex]
Substitute [tex]x - o_x[/tex] for s
[tex]v^2 = v_{ox}^2 + 2a(x - o_x)[/tex]
Hence, the above equation can be used to determine the final displacement by solving for x
What equation describes conservation of charge?
Answer:
The equation which describes conservation of charge is [tex]Q_{initial} - Q_{final } = 0[/tex]
Explanation:
The law of conservation charge states that for an isolated system that sum of initial charges is equal to sum of final charges, that is the total charge is conserved.
let the sum of initial charges = [tex]Q_{initial}[/tex]
let the sum of the final charges = [tex]Q_{final}[/tex]
[tex]Q_{initial } = Q_{final}\\\\Q_{initial } - Q_{final} = 0[/tex]
Therefore, the equation which describes conservation of charge is [tex]Q_{initial} - Q_{final } = 0[/tex]
Answer:
[tex]Q_{initial}-Q_{final}=0[/tex]
Explanation:
According to the conservation of charge "Charge can neither be created nor destoryed". This line means the net amount of charges remain conserved, no matter what happens.
Equation will be of the form:
Initial Charge =Final Charge
It can also be written as:
Initial Charge- Final Charge=0
Let Q be the charge:
[tex]Q_{initial}-Q_{final}=0[/tex]
The above equation describes conservation of charge.
Urgent
The following picture is an example of which type of energy?
Electromagnetic Energy
Nuclear Energy
Electric Energy
Answer:
I think its n u c l e a r e n e r g y.
define rolling friction
Answer:
Definition - The friction that occurs when an object rolls across a rolling friction is easier to overcome than sliding friction.
Ex - Anything with wheels (cars, bicycle,etc) or ball rolling.
Explanation:
I think this answer will help .... if so please follow me.
For each experiment involving nanotechnology, Gerry
and Lena will test a(n)
Gerry and Lena work in a modern physics laboratory
and study nanotechnology, which is a new type of
technology that allows control over individual particles as
small as molecules or atoms. Even though they work
with new technology, they still follow the scientific
method, so their experiments attempt to find
relationships between independent and dependent
variables.
Answer: Hypothesis
Explanation:
For each experiment involving nanotechnology, Gerry and Lena will test a hypothesis.
Gerry and Lana will use the Scientific method for their nanotechnology research and a key stage in the scientific method is to come up with a Hypothesis.
A hypothesis gives a researcher direction because it is a theory that they formulate that is meant to explain the phenomenon that they are researching.
They will then test this theory to either disprove or approve it and in so doing will be able to come up with conclusions to the research. Gerry and Lana will therefore have to test a hypothesis for each experiment in order to continue with their research.
Show that the force vector D=(2.0i-4.0j+k)N is orthogonal to the force vector G=(3.0i+4.0j+10k)N.
Answer:
Explanation:
For two vectors to be orthogonal (perpendicular) the product of both vectors must be zero. Given the vectors D=(2.0i-4.0j+k)N and G=(3.0i+4.0j+10k)N, to show that they are orthogonal, we will take their dot product as shown;
D.G = (2.0i-4.0j+k).(3.0i+4.0j+10k)
Note that i.1 = j.j = k.k = 1 and dot product of different component is zero.
D.G = 2.0(3.0) (i.i) + (-4.0)(4.0)j.j + 1(10)k.k
D.G = 6.0(1) -(16)(1)+10(1)
D.G = 6-16+10
D.G = -10+10
D.G = 0
Since the dot product of the two vectors is zero, this shows that force vector D is orthogonal to force vector G.
A projectile is shot in the air from ground level with an initial velocity of 560 m/sec at an angle of 30° with the horizontal. (Round your answers to two decimal places.) (a) At what time (in seconds) is the maximum range of the projectile attained? s (b) What is the maximum range (in meters)?
Answer:
a) t = 57.14 s
b) x = 27711.4 m
Explanation:
This is a missile throwing exercise
a) They ask us for the time to the maximum reach, this corresponds to when it reaches the ground y = 0, let's use
y = [tex]v_{oy}[/tex] t - ½ g t²
Let's use trigonometry to find the vertical initial velocity
sin θ = v_{oy} / v₀
v_{oy} = v₀ sin θ
we substitute
y = v₀ sin θ t - ½ g t²
since the height is zero
0 = t (v₀ sin θ - ½ g t)
This equation has two solutions
* t = 0 which corresponds to the moment of launch
*
v₀ sin 30 - ½ g t = 0
t = v₀ sin 30 2/g
let's calculate
t = 560 sin 30 2 / 9.8
t = 57.14 s
b) with this time we can calculate the distance traveled
x = v₀ₓ t
let's use trigonometry for velocity
cos θ = v₀ₓ / v₀
v₀ₓ = v₀ cos 30
we substitute
x = v₀ cos 30 t
let's calculate
x = 560 cos 30 57.14
x = 27711.4 m
A busy chipmunk runs back and forth along a straight line of acorns that has been set out between its burrow and a nearby tree. At some instant, it moves with a velocity of −1.09 m/s−1.09 m/s . Then, 2.99 s2.99 s later, it moves with a velocity of 1.75 m/s1.75 m/s . What is the chipmunk's average acceleration during the 2.99 s2.99 s time interval
Answer:
0.59 seconds
Explanation:
If Vx= 9.5 units and Vy= -6.4 units, determine the magnitude of V
Answer:
The magnitude of the velocity is approximately 11.45 units
Explanation:
Since they give us the x and y components of the vector velocity, we can find its magnitude via the Pythagorean theorem:
[tex]|v|=\sqrt{9.5^2+(-6.4)^2} \approx 11.45[/tex]
A sprinter accelerates from rest to 9.00 in 1.38 sec.What is his acceleration in a. m/s2b. m/h2
Answer:
a) The acceleration of the sprinter is 6.521 meters per square second, b) The acceleration of 84512.16 kilometers per square hour.
Explanation:
Note: Statement is incomplete, complete description of the problem is: A sprinter accelerates from rest to [tex]9.00\,\frac{m}{s}[/tex] in 1.38 seconds. What is his acceleration in a. [tex]\frac{m}{s^{2}}[/tex] and b. [tex]\frac{km}{h^{2}}[/tex]?
a) We assume that sprinter accelerates uniformly, so that acceleration ([tex]a[/tex]), measured in meters per square second, can be obtained from this kinematic expression as function of initial and final velocities ([tex]v_{o}[/tex], [tex]v[/tex]), measured in meters per second, and time ([tex]t[/tex]), measured in seconds, as well.
[tex]v = v_{o} + a\cdot t[/tex]
[tex]a = \frac{v-v_{o}}{t}[/tex]
If we know that [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]v = 9\,\frac{m}{s}[/tex] and [tex]t = 1.38\,s[/tex], the acceleration experimented by the sprinter is:
[tex]a = \frac{9\,\frac{m}{s}-0\,\frac{m}{s} }{1.38\,s}[/tex]
[tex]a = 6.521\,\frac{m}{s^{2}}[/tex]
The acceleration of the sprinter is 6.521 meters per square second.
b) If we know that a hour is equivalent to 3600 seconds and a kilometer is equivalent to 1000 meters, the result of the previous item is converted by using two consecutive unit conversions:
[tex]a = \left(6.521\,\frac{m}{s^{2}} \right)\cdot \left(\frac{1}{1000}\,\frac{km}{m} \right)\cdot \left(3600^{2}\,\frac{s^{2}}{h^{2}} \right)[/tex]
[tex]a = 84512.16\,\frac{km}{h^{2}}[/tex]
The acceleration of 84512.16 kilometers per square hour.
A long straight conducting rod carries a current I with a non-uniform current density J = ar2, and has a radius R. The value of the constant is 28.5 A/mm4 and the radius of the rod is 5.20 mm. Determine the magnitude of the magnetic field at the following points.(a) r1 = R/2(b) r2 = 2R
The magnetic field is just a unit vector that explains the electromagnetic influence on electric currents, current flow, and magnetic fluids.
Magnetic field:Current density [tex]J = ar^2[/tex]
value of the constant is= [tex]28.5 \ \frac{A}{mm^4}[/tex]
radius = 5.20 mm
magnetic permeability [tex]\mu = 4\pi \times 10^7 \ \frac{N}{A^2}[/tex]
calculating the area element for the straight circular conduction rod
:
[tex]d_A=2\pi r dr[/tex]
Calculating the current, which is carried in the rod
[tex]dI = \int dA \vec{J}[/tex]
Calculating the above equation with the limit value that is 0 to r.
[tex]I^{1}=\int_{0}^{r} ar^2 \times 2 \pi \cdot r d_r[/tex]
[tex]=2\pi a\int_{0}^{r} r^3 d_r \\\\=\frac{\pi ar^4}{2}[/tex]
The calculated current value which is carried by the rod is [tex]\boxed{\frac{\pi ar^4}{2}}[/tex]
In option (a)
calculating the magnitude of the magnetic field at the point [tex]r_1= \frac{R}{2}[/tex]
[tex]\to B=\frac{\mu_{0} I^{1}}{2 \pi r}\\\\\to B \times 2\pi r= \mu_{0} (\frac{\pi a}{2}r^4)\\\\\to B \times 2\pi = \mu_{0} (\frac{\pi a}{2}r^3)\\\\\to B= \frac{\mu_{0}}{4}r^3 a\\\\[/tex]
Substituting the above value:[tex]\frac{R}{2} \ for \ r[/tex]
[tex]B= \frac{\mu_{0}}{4}(\frac{R}{2})^3 a[/tex]
[tex]B= \frac{4 \pi \times 10^{-7}}{4}(\frac{5.2 \times 10^{-3}}{2})^3 \frac{28.5}{10^{-12}}[/tex]
[tex]= \frac{4 \pi \times 10^{-7}}{4} \times \frac{140.608 \times 10^{-9}}{8} \times \frac{28.5}{10^{-12}}\\\\= \frac{ 3.14 \times 10^{-7}}{1} \times \frac{140.608 \times 10^{-9}}{8} \times \frac{28.5}{10^{-12}}\\\\=\frac{1572.87624 \times 10^{-16}}{ 10^{-12}}\\\\=0.157 \ \ T[/tex]
Thus, the magnitude of the magnetic field at the point [tex]r_1 =\frac{R}{2}[/tex] is [tex]\boxed{0.157 \ T}[/tex]
In option (b)
In this, we calculate the magnitude of the magnetic field at the point [tex]r_2= 2R[/tex]
[tex]\to B=\frac{\mu_{0} I^{1}}{2 \pi r} \\\\\to B \times 2\pi r= \mu_{0} (\frac{\pi a}{2}R^4)\\\\\to B \times 2\pi 2R = \mu_{0} (\frac{\pi a}{2}R^3)\\\\\to B= \frac{\mu_{0}}{8}R^3 a\\\\[/tex]
Substituting the values
[tex]B= \frac{4 \pi \times 10^{-7}}{8}(5.2 \times 10^{-3})^3(\frac{28.5}{10^{-12}})[/tex]
[tex]= \frac{4 \times 3.14 \times 10^{-7}}{8} \times (5.2)^3 \times (10^{-3})^3 \times\frac{28.5}{10^{-12}}\\\\= \frac{ 3.14 \times 10^{-7}}{2} \times 140.608 \times 10^{-9} \times\frac{28.5}{10^{-12}}\\\\= 6291.50495 \times 10^{-4}\\\\= 0.629 \ \ or \ \ 0.63\\[/tex]
Thus, the magnitude of the magnetic field at the point [tex]r_2 = 2R[/tex] is [tex]\boxed{0.63 \ \ T}[/tex]
Find out more about Magnetic fields here:
brainly.com/question/14848188
The density (mass divided by volume) of pure water is 1.00 g/cm^3 that of whole blood is 1.05 g/cm^3 and the density of seawater is 1.03 g/cm^3. Required:a. What is the mass of 5.00 L of pure water?b. What is the mass of 5.00 L of whole blood?c. What is the mass of 5.00 L of seawater?
Answer:
a) 5000 g
b) 5250 g
c) 5150 g
Explanation:
For easier calculations, the formulas will be converted from g/cm³ to kg/m³, and then back when we're done.
Density of pure water is 1 g/cm³
1 g/cm³ = 1 * 0.001/0.000001
1 g/cm³ = 1000 kg/m³, and thus,
Density of pure blood
1.05 g/cm³ = 1050 kg/m³
Density of seawater
1.03 g/cm³ = 1030 kg/m³
Recall that, Density = mass / volume, and as such, mass = density * volume.
Converting our volume from L to m³
1 m³ = 1000 L, and as such
1 L = 0.001 m³
5 L = 0.005 m³
Mass of pure water = 1000 * 0.005
Mass of pure water = 5 kg
Mass of pure blood = 1050 * 0.005
Mass of pure blood = 5.25 kg
Mass of seawater = 1030 * 0.005
Mass of seawater = 5.15 kg
Converting these masses back to g, we have
Mass of pure water = 5 kg * 1000 g
Mass of pure water = 5000 g
Mass of pure blood = 5.25 kg * 1000 g
Mass of pure blood = 5250 g
Mass of seawater = 5.15 kg * 1000 g
Mass of seawater = 5150 g