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ale4655 [162]
2 years ago
6

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

Physics
1 answer:
omeli [17]2 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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PSYCHO15rus [73]

Answer:

|\Delta v |=\sqrt{\frac{4Gm}{d} }

Explanation:

Consider two particles are initially at rest.

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now, since both the masses have mass m

therefore,

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The final K.E. of the particles is

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By law of conservation of energy we have

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Now plugging the values we get

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2 years ago
For a damped simple harmonic oscillator, the block has a mass of 1.2 kg and the spring constant is 9.8 N/m. The damping force is
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Answer:

a) t=24s

b) number of oscillations= 11

Explanation:

In case of a damped simple harmonic oscillator the equation of motion is

m(d²x/dt²)+b(dx/dt)+kx=0

Therefore on solving the above differential equation we get,

x(t)=A₀e^{\frac{-bt}{2m}}cos(w't+\phi)=A(t)cos(w't+\phi)

where A(t)=A₀e^{\frac{-bt}{2m}}

 A₀ is the amplitude at t=0 and

w' is the angular frequency of damped SHM, which is given by,

w'=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}} }

Now coming to the problem,

Given: m=1.2 kg

           k=9.8 N/m

           b=210 g/s= 0.21 kg/s

           A₀=13 cm

a) A(t)=A₀/8

⇒A₀e^{\frac{-bt}{2m}} =A₀/8

⇒e^{\frac{bt}{2m}}=8

applying logarithm on both sides

⇒\frac{bt}{2m}=ln(8)

⇒t=\frac{2m*ln(8)}{b}

substituting the values

t=\frac{2*1.2*ln(8)}{0.21}=24s(approx)

b) w'=\sqrt{\frac{k}{m}-\frac{b^{2}}{4m^{2}} }

w'=\sqrt{\frac{9.8}{1.2}-\frac{0.21^{2}}{4*1.2^{2}}}=2.86s^{-1}

T'=\frac{2\pi}{w'}, where T' is time period of damped SHM

⇒T'=\frac{2\pi}{2.86}=2.2s

let n be number of oscillations made

then, nT'=t

⇒n=\frac{24}{2.2}=11(approx)

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Plugging this into the energy equation you obtain the equation for the total energy stored in the magnetic field of the solenoid, given by,

U = u_{0} *N^{2}*A*I^{2}/(2*L)

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