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;
- <em>Current flowing in the wire, I = 4.00 mA</em>
- <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>
- <em>Density of electron in the copper, n = 8.5 x 10²⁸ /m³</em>
<em />
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](https://tex.z-dn.net/?f=A_1%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7D%20%3D%20%5Cfrac%7B%5Cpi%20%5Ctimes%20%280.004%29%5E2%7D%7B4%7D%20%3D1.257%5Ctimes%2010%5E%7B-5%7D%20%5C%20m%5E2)
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](https://tex.z-dn.net/?f=A_2%20%3D%20%5Cfrac%7B%5Cpi%20d%5E2%7D%7B4%7D%20%3D%20%5Cfrac%7B%5Cpi%20%280.001%29%5E2%7D%7B4%7D%20%3D%207.86%5Ctimes%2010%5E%7B-7%7D%20%5C%20m%5E2)
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](https://tex.z-dn.net/?f=v_d_1%20%3D%20%5Cfrac%7BI%7D%7BnqA_1%7D%20%5C%5C%5C%5Cv_d_1%20%3D%20%5Cfrac%7B4%5Ctimes%2010%5E%7B-3%7D%20%7D%7B8.5%5Ctimes%2010%5E%7B28%7D%20%5Ctimes%201.6%5Ctimes%2010%5E%7B-19%7D%20%5Ctimes%201.257%5Ctimes%2010%5E%7B-5%7D%7D%20%5C%5C%5C%5Cv_d_1%20%3D%202.34%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20m%2Fs)
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](https://tex.z-dn.net/?f=v_d_2%20%3D%20%5Cfrac%7BI%7D%7BnqA_2%7D%20%5C%5C%5C%5Cv_d_2%20%3D%20%5Cfrac%7B4%5Ctimes%2010%5E%7B-3%7D%20%7D%7B8.5%5Ctimes%2010%5E%7B28%7D%20%5Ctimes%201.6%5Ctimes%2010%5E%7B-19%7D%20%5Ctimes%207.86%5Ctimes%2010%5E%7B-7%7D%7D%20%5C%5C%5C%5Cv_d_2%20%3D%203.74%5Ctimes%2010%5E%7B-7%7D%20%20%5C%20m%2Fs)
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](https://tex.z-dn.net/?f=%5CDelta%20v%20%3D%20v_d_2%20-v_d_1%5C%5C%5C%5C%5CDelta%20v%20%3D%203.74%5Ctimes%2010%5E%7B-7%7D%20%5C%20m%2Fs%20%5C%20-%5C%202.34%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20m%2Fs%20%3D%203.506%5Ctimes%2010%5E%7B-7%7D%20%5C%20m%2Fs)
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](https://tex.z-dn.net/?f=t_1%20%3D%20%5Cfrac%7BL%7D%7Bv_d_1%7D%20%5C%5C%5C%5Ct_1%20%3D%20%5Cfrac%7B2%7D%7B2.34%5Ctimes%2010%5E%7B-8%7D%7D%20%5C%5C%5C%5Ct_1%20%3D%208.547%5Ctimes%2010%5E%7B7%7D%20%5C%20s)
The time of motion of electrons for the final wire diameter is calculated as;
![t_2 = \frac{L}{v_d_1} \\\\t_2= \frac{2}{3.74 \times 10^{-7}} \\\\t_2 = 5.348 \times 10^{6} \ s](https://tex.z-dn.net/?f=t_2%20%3D%20%5Cfrac%7BL%7D%7Bv_d_1%7D%20%5C%5C%5C%5Ct_2%3D%20%5Cfrac%7B2%7D%7B3.74%20%5Ctimes%2010%5E%7B-7%7D%7D%20%5C%5C%5C%5Ct_2%20%3D%205.348%20%5Ctimes%2010%5E%7B6%7D%20%5C%20s)
The average acceleration of the electrons is calculated as;
![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](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B%5CDelta%20v%7D%7B%5CDelta%20t%7D%20%5C%5C%5C%5Ca%20%3D%20%5Cfrac%7B3.506%20%5Ctimes%2010%5E%7B-7%7D%20%7D%7B%288.547%5Ctimes%2010%5E7%29-%20%285.348%5Ctimes%2010%5E6%29%7D%20%5C%5C%5C%5Ca%20%3D%204.38%5Ctimes%2010%5E%7B-15%7D%20%5C%20m%2Fs%5E2)
Thus, 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.
Learn more here: brainly.com/question/22406248
Answer:
-34.3m/s
Explanation:
first lets find the time befor it hit the ground by using free fall equation and we know we use that in one condition which is a constant acceleration in this case its a gravitational acceleration which is -9.8
![h = \frac{1}{2} g {t}^{2}](https://tex.z-dn.net/?f=h%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20g%20%7Bt%7D%5E%7B2%7D%20)
![t = \sqrt{ \frac{2 \times 60}{9.8 } } = 3.5s](https://tex.z-dn.net/?f=t%20%3D%20%20%20%5Csqrt%7B%20%5Cfrac%7B2%20%5Ctimes%2060%7D%7B9.8%20%7D%20%7D%20%20%20%3D%203.5s)
now we know that the initial velocity its zero :
so applu the another kinematic equation which is
![v = u - gt](https://tex.z-dn.net/?f=v%20%3D%20u%20-%20gt)
v is final velocity and u is the initial velocity and its equal zero.
v = - 9.8 × 3.5 = - 34.3
The Pony Express
Chapter 1
At A Nation's Crisis
The Pony Express was the first rapid transit and the first fost mail line across the continent from the Missouri River to the Pacific Coast. It was a system
by means of which messages were carried swiftly on horseback across the plains and deserts, and over the mountains of the far West It brought the
Adontic coost and the Pacific slope ten days nearer to each other.
It had a brief existence of only sixteen months and was supplanted by the transcontinental telegraph. Yet it was of the greatest importance in
binding the East and West together at a time when overland travel was slow and cumbersome, and when a great national crisis made the rapid
communication of news between these sections an imperative necessity.
The Pony Express marked the highest development in overland travel prior to the coming of the Pacific railroad, which it preceded nine years.
It, in fact, proved the feasibility of a transcontinental road and demonstrated that such a line could be built and operated continuously the year
around-a feat that had always been regarded as impossible.
The operation of the Pony Express was a supreme achievement of physical endurance on the part of man and his ever faithful companion, the
horse. The history of this organization should be a lasting monument to the physical sacrifice of man and beast in an effort to accomplish
something worthwhile. Its history should be an enduring tribute to American courage and American organizing genius.
Read this line from the Pony Express excerpt
It hod a brief existence of only sixteen months and was supplanted by the transcontinental telegraph.
Based on the corres, what does the word "supplanted" mean? (5 points)
Defeated
Joined
Replaced
Os
Oo
Unearthed
The radial force on the particle is given by the Lorentz force. They don't give you the velocity so you have to solve for it in terms of the radius and get them to cancel.