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3 years ago

A race car travels 765 km around a circular sprint track of radius 1.263 km. How many times did it go around the track?

Physics

1 answer:

sladkih [1.3K]3 years ago

4 0

Answer:

It will go 96 times around the track.

Explanation:

Given that,

Distance covered by the race car, d = 765 km

Radius of the circular sprint track, r = 1.263 km

Let n times did it go around the track. It is given by :

$n=\dfrac{d}{C}$

C is the circumference of the circular path, $C=2\pi r$

$n=\dfrac{d}{2\pi r}$

$n=\dfrac{765}{2\pi \times 1.263}$

$n=96.4$

Approximately, n = 96

So, it will go 96 times around the track. Hence, this is the required solution.

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A thin, uniformly charged insulating rod has a linear charge density λ = 3 nC/m and lies along the x axis from x = 1m to x = 3m.

Contact [7]

Answer:

A) $V_A = 11.93~V$

B) The vector definition of E-field is

$\vec{E} = -1.13\^x + 2.41\^y$

where magnitude is E = 2.66 N/m.

Explanation:

The potential of a uniformly charged rod can be found by the method of integration. We will first choose an infinitesimal part on the rod. We will compute the potential of this part at point A. Then we will integrate this potential over the entire rod.

We will use the following formula for electric potential:

$V = \frac{1}{4\pi \epsilon_0}\frac{Q}{r}$

Let us choose the infinitesimal part a distance 'x' from the origin. Then the distance between this point and point A is

$r = \sqrt{x^2+4^2}$

The infinitesimal length is 'dx', and the potential of this length is dV. Let's apply the formula:

$dV = \frac{1}{4\pi\epsilon_0}\frac{\lambda dx}{\sqrt{x^2 + 4^2}}$

Here, the charge Q is equal to the charge density multiplied by the length. Q = λdx

Now we have to integrate this infinitesimal potential over the rod:

$V = \int\limits^3_1 {dV} \, dx = \frac{1}{4\pi \epsilon_0}\int\limits^3_1 {\frac{\lambda}{\sqrt{x^2 + 16}} \, dx$

By using an integral table, this can be calculated:

$V = \frac{3\times 10^{-9}}{4\pi\epsilon_0}\ln(|\sqrt{x^2+16}+x|)\left \{ {{x=3} \atop {x=1}} \right. \\V = 11.93~V$

B) The electric field can be found by a similar approach, but a different formula:

$\vec{E} = \frac{1}{4\pi \epsilon_0}\frac{Q}{r^2}\^r$

Let's apply this formula to the infinitesimal part we have chosen.

$dE_x = \frac{1}{4\pi\epsilon_0}\frac{\lambda dx}{x^2 + 4^2}\cos(\theta)\\dE_y = \frac{1}{4\pi\epsilon_0}\frac{\lambda dx}{x^2 + 4^2}\sin(\theta)$

By the geometry sine and cosine terms can be found:

$\sin(\theta) = \frac{4}{\sqrt{x^2+16}}\\\cos(\theta) = \frac{x}{\sqrt{x^2 + 16}}$

The x- and y-components of the E-field can be found separately by integrating the infinitesimal parts over the entire rod.

$E_x = \int\limits^3_1 {dE_x} \, dx = \frac{\lambda}{4\pi\epsilon_0}\int\limits^3_1 {\frac{x}{(x^2+16)^{3/2}}} \, dx = 1.13(-\^x)\\E_y = \int\limits^3_1 {dE_y} \, dx = \frac{4\lambda}{4\pi\epsilon_0}\int\limits^3_1 {\frac{1}{(x^2+16)^{3/2}}} \, dx = 2.41(\^y)$

So, the final E-field is

$\vec{E} = -1.13\^x + 2.41\^y$

The magnitude of the E-field is

E = 2.66 N/m

6 0

3 years ago

A Cassegrain telescope has a hole in the main mirror. This reduces the mirror area and thus the light gathering power, but how m

balu736 [363]

Answer:

Explanation: A cassegrain telescope is a kind of telescope which is made up of the curved mirrors one of the mirrors is a concave mirror is called the primary mirror and the second mirror called the secondary mirror which is a convex mirror, when light Penetrate the cassegrain telescope, it first hits the primary concave mirror and it's then reflected by the secondary convex mirror.

5 0

3 years ago

The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below 9 K. However,

Andreyy89

Answer:

note:

find the attached solution

4 0

3 years ago

Given a force of 56N and an acceleration of 7m/s2, what is the mass?

bearhunter [10]

F = ma
You need to rearrange this equation to find mass so you would have the equation :
M = f/a
Input the numbers into the equation :
M = 56/7
M = 8

8 0

3 years ago

Read 2 more answers

if a mass on a spring bobs up nad down completing 2 full cycles every section. WHat are the periouds and frequency of the mass

Alika [10]

Answer:

This question is incomplete

Explanation:

This question is incomplete because of the absence of the time taken to complete one full cycle.

Frequency (f) will be calculated first as

f = N ÷ t

where N is the number of cycles and t is the time taken to complete one full cycle. The unit for frequency is Hertz (Hz).

To calculate the period, T, the formula below will be used

T = 1 ÷ f

The unit for period is secs

4 0

3 years ago