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Ilia_Sergeevich [38]
2 years ago
8

A(n) 0.95-kg bucket is tied to a rope of negligible mass that is wrapped around a pole mounted horizontally on frictionless bear

ings. The cylindrical pole has a diameter of 0.340 m and a mass of 2.60 kg. When the bucket is released from rest, how long will it take to fall to the bottom of the 20.0 m well?
Physics
1 answer:
faust18 [17]2 years ago
8 0
<span>The difficulty is to find the acceleration with which the bucket will fall. It will not fall with "g" because of the tension in the rope.

</span><span>On pole torque ,τ = Tr = Iα where I is moment of inertia of pole =Mr^2/2 and r is the radius of the pole

α = Tr/I ..........................................(1)

Applying newtons law on bucket,

ma = mg-T a=g-T/m .................................................(2)
 
If the rope does not slip

a=αr

g-T/m = Tr^2/I

Putting I = Mr^2/2 ,we get

g-T/m = 2T/M T = g/(1/m+2/M)
 
Putting this value of T in eqn (2), we will get the value of "a" the downward accelration of bucket.

(Please find a by putting the values of m and M yourself).

Now that we know the value of "a", find time taken to travel 20m is very easy.
 
Apply the equation of motion s=ut+1/2at^2
 
u=0

s=20m
</span>
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
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The change in mean drift velocity for electrons as they pass from one end of the wire to the other is 3.506 x 10⁻⁷ m/s and average acceleration of the electrons is 4.38 x 10⁻¹⁵ m/s².

The given parameters;

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  • <em>Initial diameter of the wire, d₁ = 4 mm = 0.004 m</em>
  • <em>Final diameter of the wire, d₂ = 1 mm = 0.001 m</em>
  • <em>Length of wire, L = 2.00 m</em>
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The initial area of the copper wire;

A_1 = \frac{\pi d^2}{4} = \frac{\pi \times (0.004)^2}{4} =1.257\times 10^{-5} \ m^2

The final area of the copper wire;

A_2 = \frac{\pi d^2}{4} = \frac{\pi (0.001)^2}{4} = 7.86\times 10^{-7} \ m^2

The initial drift velocity of the electrons is calculated as;

v_d_1 = \frac{I}{nqA_1} \\\\v_d_1 = \frac{4\times 10^{-3} }{8.5\times 10^{28} \times 1.6\times 10^{-19} \times 1.257\times 10^{-5}} \\\\v_d_1 = 2.34 \times 10^{-8} \ m/s

The final drift velocity of the electrons is calculated as;

v_d_2 = \frac{I}{nqA_2} \\\\v_d_2 = \frac{4\times 10^{-3} }{8.5\times 10^{28} \times 1.6\times 10^{-19} \times 7.86\times 10^{-7}} \\\\v_d_2 = 3.74\times 10^{-7}  \ m/s

The change in the mean drift velocity is calculated as;

\Delta v = v_d_2 -v_d_1\\\\\Delta v = 3.74\times 10^{-7} \ m/s \ -\ 2.34 \times 10^{-8} \ m/s = 3.506\times 10^{-7} \ m/s

The time of motion of electrons for the initial wire diameter is calculated as;

t_1 = \frac{L}{v_d_1} \\\\t_1 = \frac{2}{2.34\times 10^{-8}} \\\\t_1 = 8.547\times 10^{7} \ s

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t_2 = \frac{L}{v_d_1} \\\\t_2= \frac{2}{3.74 \times 10^{-7}} \\\\t_2 = 5.348 \times 10^{6} \ s

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a = \frac{\Delta v}{\Delta t} \\\\a = \frac{3.506 \times 10^{-7} }{(8.547\times 10^7)- (5.348\times 10^6)} \\\\a = 4.38\times 10^{-15} \ m/s^2

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