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ale4655 [162]
3 years ago
6

If A=3i +2j+3k ,find the magnitude of A+B and A-B​

Physics
1 answer:
omeli [17]3 years ago
4 0

<u>Since vector B was not specified, I'll assume one at random. You can later answer your own question.</u>

Answer:

\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}

\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}

Explanation:

Given:

\vec A=3\hat i +2\hat j+3\hat k

And (assumed):

\vec B=-5\hat i +8\hat j-4\hat k

Find the magnitude of

\vec A+\vec B

\vec A-\vec B

Given a vector

\vec P=x\hat i +y\hat j+z\hat k

The magnitude of the vector is:

\mid\mid \vec P\mid \mid=\sqrt{x^2+y^2+z^2}

  • First part:

\vec A+\vec B =3\hat i +2\hat j+3\hat k-5\hat i +8\hat j-4\hat k

\vec A+\vec B =-2\hat i +10\hat j-\hat k

The magnitude of the sum is:

\mid\mid \vec A+\vec B \mid \mid=\sqrt{(-2)^2+10^2+(-1)^2}=\sqrt{4+100+1}

\mathbf{\mid\mid \vec A+\vec B \mid \mid=\sqrt{105}}

  • Second part:

\vec A-\vec B =3\hat i +2\hat j+3\hat k-(-5\hat i +8\hat j-4\hat k)

\vec A-\vec B =3\hat i +2\hat j+3\hat k+5\hat i -8\hat j+4\hat k

\vec A-\vec B =8\hat i -6\hat j+7\hat k

The magnitude of the difference is:

\mid\mid \vec A-\vec B \mid \mid=\sqrt{8^2+(-6)^2+7^2}=\sqrt{64+36+49}

\mathbf{\mid\mid \vec A-\vec B \mid \mid=\sqrt{149}}

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ExtremeBDS [4]

Answer:

α = 2,857 10⁻⁵ ºC⁻¹

Explanation:

The thermal expansion of materials is described by the expression

          ΔL = α Lo ΔT

          α = \frac{\Delta L}{L_o \ \Delta T}

in the case of the bar the expansion is

         ΔL = L_f - L₀

         ΔL=   1.002 -1

         ΔL = 0.002 m

the temperature variation is

         ΔT = 100 - 30

         ΔT = 70º C

we calculate

         α = 0.002 / 1 70

         α = 2,857 10⁻⁵ ºC⁻¹

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3 years ago
Which statement accurately describes a relationship between parts of the
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<u>Answer:</u>

C. There are trillions of galaxies in the universe.

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Which of the following layers in the earth has the highest density?
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4 years ago
A 50 Kg box sits at rest on a 30 degree ramp where the coef of static friction is 0.5773. If your push was directed at an angle
emmasim [6.3K]

<u>Given data:</u>

m= 50 Kg,

W= m×g = 50 × 9.81 = 490.5 N

ramp angle (α) = 30 degrees,

coefficient of friction (μs) = 0.5773,

Push at an angle (Θ) = 40 degrees,

Determine: Push to get box move up (P)=?

From the figure,

Resolving the forces along the plane

W sinα + μs.R = P cos Θ       --------------------- (i)

Resolving the forces perpendicular to the inclined plane

W cosα = R+Psin Θ  =>  R= W cosα - Psin Θ -------------- (ii)

Solving (i) and (ii) and keeping <em>μs = tan Φ, Φ = Θ </em>

<em>Pmin = W sin( α +Θ  )</em>

<em>          = W[ sin α.Cos Θ + cos α.sin Θ]</em>

<em>           = 490.5 [ (sin 30.cos40) + (cos30.sin 40)]</em>

<em>           = 460.9 N</em>

<em>Minimum push required to move the box up the ramp is 460.9 N</em>


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