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dedylja [7]
3 years ago
6

A square coil ℓ = 2cm on a side with 30 turns rotates in a uniform magnetic field, B~ = B0zˆ = 0.1Tˆz, such that the normal of t

he coil is aligned with the field once per rotation. The coil rotates once every T = 5s and starts with its normal parallel to the field. (a)Write the magnetic flux as a function of time symbolically. Report the numeric values for any constants you introduce separately. (b)Compute the induced emf at t = 12.5s. Report both a symbolic and numeric value.
Physics
1 answer:
kow [346]3 years ago
5 0

Answer:

a) 1.2*10^{-3}cos(1.25t)

b) 0.49mV

Explanation:

a) The coil rotates periodically with period T. Hence, we can write the variation of the magnetic flux with a sinusoidal function, and with max flux NAB. Thus, we have that:

\Phi_B(t)=NABcos(\omega t)\\\\\omega=\frac{2\pi}{T}=1.25\frac{rad}{s}\\\\A=l^2=(0.02m)^2=4*10^{-4}m^2\\\\B=0.1T\\\\\Phi_B(t)=1.2*10^{-3}cos(1.25 t) W

where we have used the values given by the information of the problem for N B and A.

b)

the emf is given by:

emf=-\frac{d\Phi_B}{dt}=-NBA\omega sin(\omega t)\\\\emf(t=12.5s)=-(30)(0.1T)(4*10^{-4})(1.25\frac{rad}{s})sin(1.25*12.5)=1.49*10^{-4}V=0.49mV

hope this helps!!

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A 1600kg cannon fires a 5kg cannonball horizontally. The exit velocity of the cannonball is 80m/s and the barrel length is 2m. W
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Explanation:

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Assume: The bullet penetrates into the block and stops due to its friction with the block. The compound system of the block plus
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Answer:

1)4.7334J

2)225.4m/s

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v= the Velocity of both the bullet and the block after collision=?

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g= acceleration due to gravity= 9.81m/s^2

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v = √2gh

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= √2 x 9.81 x 0.1 = 1.40m/s

1) We can now calculate the total energy of the system after collision as

KE = 1/2(m+M)v^2

= 1/2 x (0.03+4.8) x (1.40)^2

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Hence, the total energy of the composite system at any time after the collision is 4.7334J

2)to determine the initial velocity of the bullet.

From law of momentum conservation, which can be expressed as

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0.03u1=6.762

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