Answer:
Explanation:
Length, l = 35.5 cm = 0.355 m
y = 2 x
Slope, y / x = 2
tan θ = 2
θ = 63.4°
i = 22.5 A
B = 0.318 i Tesla
[tex]\overrightarrow{l}=0.355\widehat{k}+0.355 Cos63.4\widehat{i}+0.355 Sin63.4\widehat{j}[/tex]
[tex]\overrightarrow{l}=0.16\widehat{i} + 0.32\widehat{j}+0.355\widehat{k}[/tex]
[tex]\overrightarrow{B}=0.318\widehat{i}[/tex]
The magnetic force is given by
[tex]\overrightarrow{F}=i(\overrightarrow{l}\times \overrightarrow{B})[/tex]
[tex]\overrightarrow{F}=22.5\left ( 0.16\widehat{i}+0.32\widehat{j}+0.355\widehat{k} \right )\times 0.318\widehat{i}[/tex]
[tex]\overrightarrow{F}=2.54\widehat{j}-2.29\widehat{k}[/tex]
Magnitude of force
[tex]F=\sqrt{2.54^{2}+2.29^{2}}[/tex]
F = 3.42 N
The angle is Ф
tanФ = -2.29/2.54
Ф = 42° below y axis
The total force experienced by the wire in the magnetic field has a magnitude of 145 N and is directed -30 degrees relative to the z-axis, according to the right-hand rule and Lorentz force law.
Explanation:In order to determine the direction of the total force on the wire, you would need to use the right-hand rule. First, you know the current is flowing down the z-axis and out along the y=2x line in the xy-plane. You also know that the magnetic field, B, is given by (.318 i)T which lies along the x-axis.
According to the Lorentz force law, the force exerted on a current-carrying conductor in a magnetic field is given by F = I * (L x B), where I represents the current, L is the length vector of the wire, and x is the cross product. Because the wire is bent at a right angle, the force will have two components: one for each section of the wire.
The force along the z-axis is given by F = I*LB*sin(theta), where theta is the angle between L and B. Here, L = 35.5/2 = 17.75 cm, B = 0.318 T, I = 22.5 A, and theta = 90 degrees (since B is along x-axis and L is along z-axis). Calculating gives Fz = 22.5 A * 17.75 cm * 0.318 T * sin(90) = 126.6 N.
The force along the y-axis is similar, but with the length vector along y=2x in the xy plane and B still along the x-axis, so theta = 180 degrees - arctan(2). Substituting the values we get Fy = - 22.5 A * 17.75 cm * 0.318 T * sin(180 - arctan(2)) = -73.8 N.
Therefore, the total force is given by the vector sum of Fz and Fy, which has magnitude sqrt(Fz^2 + Fy^2) = 145 N, in the direction of atan2(Fy, Fz) = -30 degrees relative to the z-axis.
Learn more about Lorentz force on a current-carrying wire here:https://brainly.com/question/15552911
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A student sees her physical science professor approaching on the sidewalk that runs by her dorm. She gets a water balloon and waits. When the professor is 2.0s from being directly under the window about 11m from the sidewalk, she drops the balloon. Finish the story.
Answer:
The balloon falls to the ground before the professor gets there. The student is DEFINITELY in for some TROUBLE!
Explanation:
The balloon picks up speed due to gravity and we can calculate the time taken for it to fall to the ground as follows:
Gravity (g) = 9.81 m/s^2
Height or distance (s) = 11 meters
Initial Speed (u) = 0 m/s
[tex]s = u*t + 0.5 * (a*t^2)[/tex]
[tex]11 = 0*t + 0.5 (9.81*t^2)[/tex]
[tex]t= 1.4975 s[/tex]
So we can see that the balloon takes 1.4975 seconds to fall to the ground, and since the professor takes 2 seconds to get to that place, the balloon hits the ground right before the professor gets there.
What is the measure of the ability of a force to rotate or accelerate an object around an axis?
A. Centripetal Force
B. Level Arm
C. Axis of Rotation
D. Torque
D. Torque
Explanation:
Torque is a pattern of the force that can make a victim to revolve on an axis. The torque's direction vector based on the force's direction on the axis. The SI unit for torque is the Newton-meter. Torque can be both static or dynamic.
A static is one that does not generate an angular acceleration.The Torque's magnitude vector ζ for a torque generated by a given force F is
ζ = F .r sin(θ)
where,
r is the width of the moment arm
θ is the angle within the force vector and the moment arm.
In rotational kinematics, torque is measured as
ζ = Iα
Where,
α is the angular acceleration
I is the rotational inertia
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A diver goes under water and measures the pressure. At some point his instruments read a pressure of 50,000 Pa. How deep did the diver go in meters? The density of water is 1000 kg/m^3. (Write the number only with 1 significant figure)
Answer:
[tex]y\approx 5\ m[/tex]
Explanation:
The pressure of a Fluid
A fluid of density [tex]\rho[/tex] exerts pressure at a distance y (deep) given by
[tex]P=\rho\cdot y\cdot g[/tex]
Where g is the acceleration of gravity or [tex]g=9.8\ m/s^2[/tex]
This formula computes the pressure assuming the initial pressure is 0 at fluid (water in this case) level.
Knowing the measured pressure, we can know how deep the diver went by solving the equation for y
[tex]\displaystyle y=\frac{P}{\rho\cdot g}[/tex]
Let's plug in the given values
[tex]P=50,000\ Pa= 50,000\ N/m^2[/tex]
[tex]\rho=1,000\ kg/m^3[/tex]
[tex]g=9.8\ m/s^2[/tex]
Thus
[tex]\displaystyle y=\frac{50,000\ N/m^2}{1,000\ kg/m^3\cdot 9.8\ m/s^2}[/tex]
[tex]y\approx 5\ m[/tex]
The electric field of a sinusoidal electromagnetic wave obeys the equation E = (360V/m) sin[ (6.00×1015rad/s)t + (1.96×107rad/m)x ]. What is the amplitude of the magnetic field of this wave? A) 0.06 μT B) 0.23 μT C) 1.10 μT D) 1.20 μT
Answer:
Option D is correct.
Explanation:
Bmax = Emax / c
The general form for electromagnetic wave equation is
E = jEmax ×cos(kx-wt)
We were given
(360V/m) sin[ (6.00×1015rad/s)t + (1.96×107rad/m)x ].
So from the equation above
Emax = 360V/m
Bmax = 360/(3×10⁸) = 1.2 ×10‐⁶ T.
Answer
Option D
Amplitude of Magnetic field = B = 1.2×10⁻⁶ T
Explanation:
The relationship between electric field and magnetic field of an electromagnetic wave is given by
B = E/c
Where B is the amplitude of magnetic field and E is the amplitude of electric field and c is the speed of light
The amplitude of electric field is given as 360 V/m
B = (360 V/m)/(3×10⁸ m/s)
B = 1.2×10⁻⁶ V.s/m²
Since 1 Tesla is equal to 1 V.s/m²
B = 1.2×10⁻⁶ T
Therefore, option D is correct
A current I = 20 A is directed along the positive x-axis and perpendicular to a magnetic field. A magnetic force per unit length of 0.16 N/m acts on the conductor in the negative y-direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes. magnitude T direction
Answer:
the magnitude and direction of the magnetic field in the region through which the current passes is 0.008 T and +z direction.
Explanation:
given information:
current, I = 20 A
magnetic force per unit length, F/L = 0.16 N/m
the conductor in the negative y-direction
θ = 90° (perpendicular)
as we know the formula to calculate magnetic force is
F = B I L sin θ
B = F/(I L sin θ)
= (F/L) (1/I sin θ)
= 0.16 (1/15 sin 90)
= 0.008 T
since F is in the negative y direction, based of the right hand rule the magnetic field is in positive z direction
Answer:
Explanation:
Given:
current, I = 20 A
Magnetic force per unit length, F/L
= 0.16 N/m
Conductor in the negative y-direction, therefore θ = 90° (perpendicular)
For a magnetic field,
F = B I L sin θ
B = F/(I L sin θ)
= 0.16 × (1/15 sin 90)
= 0.008 T
The field is in the +ve z - direction.
According to the Ideal Gas Law, , where P is pressure, V is volume, T is temperature (in Kelvins), and k is a constant of proportionality. A tank contains 2500 cubic inches of nitrogen at a pressure of 36 pounds per square inch and a temperature of 700 K. Write P as a function of V and T after evaluating k.
Answer:
P = 128.6 T / V
Explanation:
The ideal gas equation is
P V = n R T
Where the pressure is
P = 36 pounds / in²
V = 2500 in³
T = 700 K
PV = k T
k = PV / T
k = 36 2500/700
k = 128.6
P = 128.6 T / V
Find a unit vector in the direction in which f increases most rapidly at P and give the rate of chance of f in that direction; find a unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction.
Answer:
Check attachment for complete question
Question
Find a unit vector in the direction in which
f increases most rapidly at P and give the rate of change of f
in that direction; Find a unit vector in the direction in which f
decreases most rapidly at P and give the rate of change of f in
that direction.
f (x, y, z) = x²z e^y + xz²; P(1, ln 2, 2).
Explanation:
The function, z = f(x, y,z), increases most rapidly at (a, b,c) in the
direction of the gradient and decreases
most rapidly in the opposite direction
Given that
F=x²ze^y+xz² at P(1, In2, 2)
1. F increases most rapidly in the positive direction of ∇f
∇f= df/dx i + df/dy j +df/dz k
∇f=(2xze^y+z²)i + (x²ze^y) j + (x²e^y + 2xz)k
At the point P(1, In2, 2)
Then,
∇f= (2×1×2×e^In2+2²)i +(1²×2×e^In2)j +(1²e^In2+2×1×2)
∇f=12i + 4j + 6k
Then, unit vector
V= ∇f/|∇f|
Then, |∇f|= √ 12²+4²+6²
|∇f|= 14
Then,
Unit vector
V=(12i+4j+6k)/14
V=6/7 i + 2/7 j + 3/7 k
This is the increasing unit vector
The rate of change of f at point P is.
|∇f|= √ 12²+4²+6²
|∇f|= 14
2. F increases most rapidly in the positive direction of -∇f
∇f=- (df/dx i + df/dy j +df/dz k)
∇f=-(2xze^y+z²)i - (x²ze^y) j - (x²e^y + 2xz)k
At the point P(1, In2, 2)
Then,
∇f= -(2×1×2×e^In2+2²)i -(1²×2×e^In2)j -(1²e^In2+2×1×2)
∇f=-12i -4j - 6k
Then, unit vector
V= -∇f/|∇f|
Then, |∇f|= √ 12²+4²+6²
|∇f|= 14
Then,
Unit vector
V=-(12i+4j+6k)/14
V= - 6/7 i - 2/7 j - 3/7 k
This is the increasing unit vector
The rate of change of f at point P is.
|∇f|= √ 12²+4²+6²
|∇f|= 14
There's a part of the question missing and it is:
f(x, y) = 4{x(^3)}{y^(2)} ; P(-1,1)
Answer:
A) Unit vector = 4(3i - 2j)/ (√13)
B) The rate of change;
|Δf(1, - 1)|= 4/(√13)
Explanation:
First of all, f increases rapidly in the positive direction of Δf(x, y)
Now;
[differentiation of the x item alone] to get;
fx(x, y) = 12{x(^2)}{y^(2)}
So at (1,-1), fx(x, y) = 12
Similarly, [differentiation of the y item alone] to get; fy(x, y) =
8{x(^3)}{y}
At (1,-1), fy(x, y) = - 8
Therefore, Δf(1, - 1) = 12i - 8j
Simplifying this, vector along gradient = 4(3i - 2j)
Unit vector = 4(3i - 2j)/ (√(3^2) + (-2^2) = 4(3i - 2j)/ (√13)
Therefore, the rate of change;
|Δf(1, - 1)|= 4/(√13)
green light in the visible portion of the electromagnetic radiation sepectrum has a wave length around 550nm.Express this wavelength in meters using exponential notation
The wavelength of green light in meters using exponential notation is 5.5 × 10-7 m.
Explanation:The green light in the visible portion of the electromagnetic radiation spectrum has a wavelength of around 550 nm (nanometers).
To express this wavelength in meters using exponential notation, we can convert nanometers to meters by dividing by 109. So, the wavelength of green light is 5.5 × 10-7 m (meters).