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natali 33 [55]
3 years ago
12

A 1.50 m cylinder of radius 1.10 cm is made of a complicated mixture of materials. Its resistivity depends on the distance x fro

m the left end and obeys the formula rho( x ) = a + bx^2, where a and b are constants. At the left end, the resistivity is 2.25 10^-8 Omega*m, while at the right end it is 8.50 x 10^-8 Omega*m.
What is the resistance of this rod?

What is the electric field at its midpoint if it carries a 1.75 A current?

If we cut the rod into two 75.0 cm halves, what is the resistance of each half?
Physics
1 answer:
Semenov [28]3 years ago
8 0
I have solved parts A and B by doing the following:
A) R = ρL/A First I found the constants a and b by solving for them, which I found to be: a = 2.25x10^-8 Ωm b = 2.78x10^-8 Ωm A = πr^2 A = 3.8013x10-4 m2 Taking the integral of the Resistance equation gave me: 1/A*(ax + bx3/3) I then took the integral from 0 to 1.50m, thereby giving me: (1/3.801299x10-4)*3.38x10-8*1.50 + 2.78x10-8*1.53/3 = 1.71x10-4 This I know to be correct.
B) ∫E.dl = V dV/dx = d/dx(IR) 1.75/A*(a + bx2) Plugging in 0.75 for x gave me E = 1.76x10^-4 V/m This is also correct
C) This is where I'm stuck. I had thought that if I used the integral in part A to find the integral from 0 to 0.75 then that would be my resistance in the left hand side. Then I thought that I could subtract the left hand value from the value I found in part A to give me the right hand value, but this hasn't worked. My workings are as follow: R = ρL/A A = 3.8x10^-4 m2 Rleft hand1/A*(2.25x10^-8)(0.75) + (2.78x10^-8)(0.75^3/3) = 4.43966x10^-5 Then Rright hand = 1.71x10^-4 - 4.43966x10^-5 = 1.266x10^-4 
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VashaNatasha [74]

A) In the case of the Boundary Thickness Layer we use the given formula,

\delta = \frac{4.91x}{\sqrt{Re}}

We know as well that,

Re = Número de Reynolds = \frac{U*x}{\upsilon}

Where,

U = velocity

\upsilon = kinematic viscosity

For water, kinematic viscosity, \upsilon = 1.21*10^{-5} ft^2 /s

So, 500,000 = \frac{ 17x}{(1.21*10^{-5})}

x = 0.355 ft

d = \frac{4.91*0.355}{\sqrt {500000}}

d = 0.002465 ft = 0.029in

B) For flat plate boundary layer. Given the Critical Reynolds Number.= 5*10^5 we know that is equal to Re above.

Thus, x = 0.355 ft

C. Wall shear stress,

\tau = \mu*\sqrt{ U^3 / (2*\nu*x) }

For water, dynamic viscosity, \nu = 2.344*10^-5 lbf-s/ft^2

\tau = 2.344*10^-5 \sqrt {17^3 / (2*1.21*10^{-5}*0.355)}

\tau = 0.5605 lbf/ft^2

4 0
3 years ago
1 ) Starting from rest, a toy rocket accelerates at 12 m/sec/sec for exactly 4.0 seconds. It reaches 48 m/sec. Find the distance
dusya [7]
Displacement equals (Velocity times Time) plus half times the (acceleration times time squared). =. (48 * 4) + 1/2 * (12 *12^2) = 288meters
3 0
3 years ago
Instantaneous speed is measured
VMariaS [17]

Answer:

C. At a particular instant

Explanation:

Speed is the defined as the ratio between the distance covered by an object and the time taken:

v=\frac{d}{t}

where d is the distance and t the time.

However, there are two possible measurements of speed:

- Average speed: this is the speed measured over a non-zero time interval (for example: a car moving 100 metres in 5 seconds; its average speed is

v=\frac{100 m}{5 s}=20 m/s

- Instantaneous speed: this is the speed of an object measured at a particular instant in time, so for a time interval that tends to zero. So, in the previous example, the average speed is 20 m/s but the instantaneous speed of the car at various instants of time can be different from that value.

7 0
3 years ago
What will happen if you rub two different materials together?
Dafna1 [17]
It will cause heat from friction
6 0
3 years ago
Read 2 more answers
A 16.2 kg person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The
S_A_V [24]

To solve this problem we will apply the concepts related to the balance of forces. We will decompose the forces in the vertical and horizontal sense, and at the same time, we will perform summation of torques to eliminate some variables and obtain a system of equations that allow us to obtain the angle.

The forces in the vertical direction would be,

\sum F_x = 0

f-N_w = 0

N_w = f

The forces in the horizontal direction would be,

\sum F_y = 0

N_f -W =0

N_f = W

The sum of Torques at equilibrium,

\sum \tau = 0

Wdcos\theta - N_wLsin\theta = 0

WdCos\theta = fLSin\theta

f = \frac{Wd}{Ltan\theta}

The maximum friction force would be equivalent to the coefficient of friction by the person, but at the same time to the expression previously found, therefore

f_{max} = \mu W=\frac{Wd}{Ltan\theta}

\theta = tan^{-1} (\frac{d}{\mu L})

Replacing,

\theta = tan^{-1} (\frac{0.9}{0.42*2})

\theta = 46.975\°

Therefore the minimum angle that the person can reach is 46.9°

8 0
3 years ago
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