Where is there potential energy in this system?

A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE g

7nadin3 [17]

Answer:

(a) r = 1.062·R $_E$ = $\frac{531}{500} R_E$

(b) r = $\frac{33}{25} R_E$

(c) Zero

Explanation:

Here we have escape velocity v $_e$ given by

$v_e =\sqrt{\frac{2GM}{R_E} }$ and the maximum height given by

$\frac{1}{2} v^2-\frac{GM}{R_E} = -\frac{GM}{r}$

Therefore, when the initial speed is 0.241v $_e$ we have

v = $0.241\times \sqrt{\frac{2GM}{R_E} }$ so that;

v² = $0.058081\times {\frac{2GM}{R_E} }$

v² = ${\frac{0.116162\times GM}{R_E} }$

$\frac{1}{2} v^2-\frac{GM}{R_E} = -\frac{GM}{r}$ is then

$\frac{1}{2} {\frac{0.116162\times GM}{R_E} }-\frac{GM}{R_E} = -\frac{GM}{r}$

Which gives

$-\frac{0.941919}{R_E} = -\frac{1}{r}$ or

r = 1.062·R $_E$

(b) Here we have

$K_i = 0.241\times \frac{1}{2} \times m \times v_e^2 = 0.241\times \frac{1}{2} \times m \times \frac{2GM}{R_E} = \frac{0.241mGM}{R_E}$

Therefore we put $\frac{0.241GM}{R_E}$ in the maximum height equation to get

$\frac{0.241}{R_E} -\frac{1}{R_E} =-\frac{1}{r}$

From which we get

r = 1.32·R $_E$

(c) The we have the least initial mechanical energy, ME given by

ME = KE - PE

Where the KE = PE required to leave the earth we have

ME = KE - KE = 0

The least initial mechanical energy to leave the earth is zero.

3 0

2 years ago

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If the atoms and molecules of a substance are moving very fast, the substance is _________.

lana66690 [7]

A. hot is the correct answer.
Hope it helps!

5 0

2 years ago

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Explain the importance of measurement<br>Physics.<br><br>

KiRa [710]

Answer:

Measurements are an important part of comparing things, as they provide the basis on comparing objects to other objects. Measurements allow us to recognize three hours and see how it's shorter than five hours, without having to observe the hours passing by themselves.

7 0

2 years ago

Calculate the induced electric field (in V/m) in a 40-turn coil with a diameter of 18 cm that is placed in a spatially uniform m

kozerog [31]

Answer:

ε = 6.617 V

Explanation:

We are given;

Number of turns; N = 40 turns

Diameter;D = 18cm = 0.18m

magnetic field; B = 0.65 T

Time;t = 0.1 s

The formula for the induced electric field(E.M.F) is given by;

ε = |-NAB/t|

A is area

ε is induced electric field

While N,B and t remain as earlier described.

Area = π(d²/4) = π(0.18²/4) = 0.02545

Thus;

ε = |-40 × 0.02545 × 0.65/0.1|

ε = 6.617 V

(we ignore the negative sign because we have to take the absolute value)

6 0

2 years ago

John is traveling north at 20 meters/second and his friend Betty is traveling south at 20 meters/second. If north is the positiv

Tpy6a [65]

I think it's just 20/20

3 0

3 years ago

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