How long does it take a car traveling at 50 mph to travel 75 miles? Use one of the following to find the answer.

where would the spaceprobe experience the strongest net (or total) gravitional force exerted on it by Earth and Mars

Arte-miy333 [17]

Answer:

r = 41.1 10⁹ m

Explanation:

For this exercise we use the equilibrium condition, that is, we look for the point where the forces are equal

∑ F = 0

F (Earth- probe) - F (Mars- probe) = 0

F (Earth- probe) = F (Mars- probe)

Let's use the equation of universal grace, let's measure the distance from the earth, to have a reference system

the distance from Earth to the probe is R (Earth-probe) = r

the distance from Mars to the probe is R (Mars -probe) = D - r

where D is the distance between Earth and Mars

$G \ \frac{m \ M_{Earth}}{r^2} = G \ \frac{m \ M_{Mars}}{(D-r)^2}$

M_earth (D-r)² = M_Mars r²

(D-r) = $\sqrt{ \frac{M_{Mars}}{ M_{Earth}} }$ r

r ( $1 + \sqrt{ \frac{M_{Mars}}{M_{Earth}} }$ ) = D

r = $\frac{D}{ 1+ \sqrt{\frac{M_{Mars}}{ M_{Earth}} } }$

We look for the values in tables

D = 54.6 10⁹ m (minimum)

M_earth = 5.98 10²⁴ kg

M_Marte = 6.42 10²³ kg = 0.642 10²⁴ kg

let's calculate

r = 54.6 10⁹ / (1 + √(0.642/5.98) )

r = 41.1 10⁹ m

5 0

2 years ago

Which of the following are true about renewable resources?

Oksana_A [137]

Answer:

option A

Explanation:

renewable resources are replenishable that means they can't be depleted

6 0

2 years ago

How are different types of radiation arranged along the electromagnetic spectrum

Leona [35]

In order of increasing frequency: Radio, Microwaves, Infrared, Visible light, Ultra-violet, X-rays, Gamma rays. To remember this try:
Rabbits
Mates
In
Very
Unusual
e(X)pensive
Gardens

7 0

2 years ago

Two fully charged cylindrical capacitors are connected to two identical batteries. The capacitors are identical except that the

Leni [432]

Answer:

Part(a): The relative capacitance is $\dfrac{C_{A}}{C_{B}} = 0.33$

Part(b): The relative energy stored is $\dfrac{U_{A}}{U_{B}} = 0.33$

Part(c): The relative charge stored is $\dfrac{Q_{A}}{Q_{B}} = 0.33$

Explanation:

We know the capacitance ( $C$ ) of a capacitor having charge ( $Q$ ) and subjected to a potential difference of ( $V$ ) is given by

$C = \dfrac{Q}{V}$

Also, the energy ( $U$ ) stored by a capacitor can be written as

$U = \dfrac{1}{2}C~V^{2}$

Let us assume that the inner radius of the Capacitor B, as shown in the figure, be $\textbf{r_{i}^{B}}$ $\bf{r_{i}^{B}}$ , the outer radius be $\bf{r_{o}^{B}}$ , the inner radius of Capacitor A be $\bf{r_{i}^{A}}$ and the outer radius be $\bf{r_{o}^{B}}$ .

Given in the problem,

$&& r_{o}^{B} = 2~r_{B}^{i}\\&& r_{o}^{A} = 4~r_{B}^{i}\\&& and~r_{i}^{B} = 4~r_{o}^{B} = 8~r_{B}^{i}$

Now, the capacitance ( $C$ ) of a cylindrical capacitor is given by,

$\bf{C = \dfrac{2~\pi~\epsilon_{0}~L}{ln(\dfrac{r_{o}}{r_{i}})}}$

where $\epsilon_{o}$ is the permittivity of the free space, $L$ is the length of the cylindrical capacitor.

Part(a):

The capacitance of capacitor A,

$C_{A} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{r_{o}^{A}}{r_{i}^{A}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{8~r_{i}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(8)}$

and the capacitance of capacitor B,

$C_{B} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{r_{o}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(\dfrac{2~r_{i}^{B}}{r_{i}^{B}})} = \dfrac{2~\pi~\epsilon_{0}L}{ln(2)}$

giving the relative capacitance of each capacitor to be

$\dfrac{C_{A}}{C_{B}} = \dfrac{ln(2)}{ln(8)} = \dfrac{ln(2)}{3~\ln(2)} = \dfrac{1}{3} = 0.33$

Part(b):

Energy stored by capacitor A,

$U_{A} = \dfrac{1}{2}~C_{A}~V^{2}$

Energy stored by capacitor B,

$U_{B} = \dfrac{1}{2}~C_{B}~V^{2}$

giving the relative energy stored by each capacitor to be

$\dfrac{U_{A}}{U_{B}} = \dfrac{C_{A}}{C_{B}} = 0.33$

Part(c):

The charge stored by capacitor A,

$Q_{A} = C_{A}~V$

The charge stored by capacitor B,

$Q_{B} = C_{B}~V$

giving the relative charge stored by each capacitor to be

$\dfrac{Q_{A}}{Q_{B}} = \dfrac{C_{A}}{C_{B}} = 0.33$

8 0

3 years ago

A teacher discusses a scientific theory that has been in place for almost a century. which would present the greatest challenge

Umnica [9.8K]

Answer: The theory might have become Obsolete or Superseded

Explanation:

A theory becomes obsolete or superseded if it becomes inadequate, false or incomplete in how its describes reality. It does not matter if it was once accepted. There are some theories such as Lysenkoism that are currently described as being obsolete because it does not conform to current reality. Another example of a theory that was superseded is the phlogiston theory. It was replaced a different theory of energy.

3 0

3 years ago

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