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2 years ago

15

How far from Earth must a space probe be along a line toward the Sun so that the Sun's gravitational pull on the probe balances

Earth's pull?

1 answer:

Tatiana [17]2 years ago

7 0

Answer:

258774.9441 m

Explanation:

x = Distance of probe from Earth

y = Distance of probe from Sun

Distance between Earth and Sun = $x+y=149.6\times 10^6\ m$

G = Gravitational constant

$M_s$ = Mass of Sun = $1.989\times 10^{30}$

$M_e$ = Mass of Earth = $5.972\times 10^{24}\ kg$

According to the question

$\frac{GM_sm}{x^2}=\frac{GM_em}{y^2}\\\Rightarrow \frac{M_s}{x^2}=\frac{M_e}{y^2}\\\Rightarrow x=\sqrt{\frac{M_s\times y^2}{M_e}}\\\Rightarrow x=\sqrt{\frac{1.989\times 10^{30}\times y^2}{5.972\times 10^{24}}}\\\Rightarrow x=577.10852y$

$x+y=149.6\times 10^6\\\Rightarrow 577.10852y+y=149.6\times 10^6\\\Rightarrow 578.10852y=149.6\times 10^6\\\Rightarrow y=\frac{149.6\times 10^6}{578.10852}\\\Rightarrow y=258774.9441\ m$

The probe should be 258774.9441 m from Earth

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An electron, moving south, enters a magnetic field of certain strength. Because of this field the electron curves upward. What i

e-lub [12.9K]

Answer: The magnetic field points to the west.

Explanation:

If we take the plane as:

North = positive y-axis

East = positive x-axis.

We have that the electron is moving south, so the velocity of the electron can be written in vector form as:

V = (0, -v, 0)

Now, when the electron interacts with the magnetic field, the electron moves upwards.

We know that the interaction between an electron and a magnetic field is:

F = q*VxB

So we have that this force acts on the z-direction.

Now, to solve this we can use the righ hand rule.

First, we point wit our hand to the direction of the velocity (negative y-axis) now, we want that our thumb points up (the direction of the force) so the side where our palm faces is the direction of the field B.

But, remember that an electron has a negative charge, so the actual equation is:

F = -q*VxB

So the magnetic field actually points in the opposite direction of our palm, to the west.

Now, we can also solve it mathematically as:

F = (0, 0, f) = -q*(0, -v,0)x(a, b, c)

where B = (a, b, c) is the vector of the magnetic field.

(0, 0, f) = -q*(-v*b -0, -0 + 0, 0 -(- a*v)) = -q*(-v*b, 0, a*v)

then we have that b must be equal to zero, and that:

f = -q*a*v

and f is positive, then we have:

a = -(f/q*v)

then the vector of the magnetic field is:

B = (-(f/q*v), 0, 0)

so it points in the negative x-axis, that is the West, as we found earlier.

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3 years ago

)If a force of 5.00 N is needed to open a 90.0 cm wide door when applied at the edge opposite the hinges, what force must be app

masha68 [24]

Answer:

A force of 12.857 newtons must be applied to open the door.

Explanation:

In this case, a force is exerted on the door, a moment is performed and the door is opened. If moment remains constant, the force is inversely proportional to distance respect to axis of rotation passing through hinges. That is:

$F \propto \frac{1}{r}$

$F = \frac{k}{r}$ (Eq. 1)

Where:

$F$ - Force, measured in newtons.

$k$ - Proportionality ratio, measured in newton-meters.

$r$ - Distance respect to axis of rotation passing through hinges, measured in meters.

From (Eq. 1) we get the following relationship and clear the final force within:

$F_{A}\cdot r_{A} = F_{B}\cdot r_{B}$

$F_{B}=\left(\frac{r_{A}}{r_{B}} \right)\cdot F_{A}$ (Eq. 2)

Where:

$F_{A}$ , $F_{B}$ - Initial and final forces, measured in newtons.

$r_{A}$ , $r_{B}$ - Initial and final distances, measured in meters.

If we know that $F_{A} = 5\,N$ , $r_{A} = 0.9\,m$ and $r_{B} = 0.35\,m$ , then final force is:

$F_{B}= \left(\frac{0.9\,m}{0.35\,m} \right)\cdot (5\,N)$

$F_{B} = 12.857\,N$

A force of 12.857 newtons must be applied to open the door.

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2 years ago

The transfer of heat by the movement of a fluid is called:

rusak2 [61]

Answer: C

Explanation:

Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer.

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3 years ago

What is a good example for newton's 1st law

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A billiard ball. unless hit, the balls stay at rest. however when hit into another, the balls do not stop unless acted upon by another force.

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