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zepelin [54]
3 years ago
13

It is observed that the number of asteroids (or meteoroids) of a given diameter is roughly inversely proportional to the square

of the diameter.
Part A

Assuming a density of 3000 kg/m3 and approximating the actual distribution of asteroids and meteoroids as a single 1000-km body (Ceres), one hundred 100-km bodies, 10 thousand 10-kmbodies, and so on, calculate the total mass in the form of 1000-km bodies.

Part B

Calculate the total mass in the form of 100-km bodies.

Part C

Calculate the total mass in the form of 10-km bodies.

Part D

Calculate the total mass in the form of 1-km bodies.
Physics
1 answer:
MaRussiya [10]3 years ago
4 0

Answer:

(a) M =  =1.57 *10²¹kg

(b) M =  =1.57 *10²⁰kg

(c) M =  =1.57 *10¹⁹kg

(d) M =  =1.57 *10¹⁸kg

Explanation:

(a) For 1000km body, diameter D = 1000km = 1,000,000 m

and N = (1000/D)² = (1000/1000km)² =  1

substituting into the formula, we have

M = 1 * 4/3 π*3000*[1000000/2]³

   =1.57 *10²¹kg

(b) For 100km body, diameter D = 100km = 100,000 m

and N = (1000/D)² = (1000/100km)² =  100

substituting into the formula, we have

M = 1 * 4/3 π*3000*[100000/2]³

   =1.57 *10²⁰kg

(C) For 10km body, diameter D = 10km = 10,000 m

and N = (1000/D)² = (1000/10km)² =  100

substituting into the formula, we have

M = 1 * 4/3 π*3000*[10000/2]³

   =1.57 *10¹⁹kg

(C) For 1km body, diameter D = 1km = 1,000 m

and N = (1000/D)² = (1000/1km)² =  100

substituting into the formula, we have

M = 1 * 4/3 π*3000*[1000/2]³

   =1.57 *10¹⁸kg

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If the velocity of a pitched ball has a magnitude of 47.0 m/s and the batted ball's velocity is 55.0 m/s in the opposite directi
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Data provided in the question

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At locations A and B, the electric potential has the values VA=1.51 VVA=1.51 V and VB=5.81 V,VB=5.81 V, respectively. A proton r
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Answer:

<u>For proton:</u>

A. The proton is released from Vb (highest potential)

B. v = 2.9x10⁴ m/s

<u>For electron:</u>

A. The electron is released from Va (lowest potential)

B. v = 1.2x10⁶ m/s    

Explanation:

<u>For a proton we have</u>:

A. To find the origin from which the proton was released we need to remember that in a potential difference, a proton moves from the highest potential to the lowest potential.                

Having that:

Va = 1.51 V and Vb = 5.81 V

We can see that the proton moves from Vb to Va, hence the proton was released from Vb.

B. We now that the work done by an electric field is given by:

W = \Delta Vq    (1)                                        

Where:

q: is the proton's charge = 1.6x10⁻¹⁹ C    

V: is the potential    

Also, the work is equal to:

W = \Delta K = (K_{a} - K_{b}) = \frac{1}{2}mv_{a}^{2} - \frac{1}{2}mv_{b}^{2}     (2)      

Where:

K: is the kinetic energy

m: is the proton's mass = 1.67x10⁻²⁷ kg

v_{a}: is the velocity in the point a

v_{b}: is the velocity in the point b = 0 (starts from rest)

Matching equation (1) with (2) we have:

\Delta Vq = \frac{1}{2}mv_{a}^{2}

(5.81 V - 1.51 V)*1.6 \cdot 10^{-19} C = \frac{1}{2}1.67 \cdot 10^{-27} kg*v_{a}^{2}

v_{a} = 2.9 \cdot 10^{4} m/s

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A. For an electron we know that it moves from the lowest potential (Va) to the highest potential (Vb), so it is released from Va.

B. The speed is:

\Delta Vq = \frac{1}{2}mv_{b}^{2} - \frac{1}{2}mv_{a}^{2}

Since v_{a} = 0 (starts from rest) and m_{e} = 9.1x10⁻³¹ kg (electron's mass), we have:

(5.81 V - 1.51 V)*1.6 \cdot 10^{-19} C = \frac{1}{2}9.1 \cdot 10^{-31} kg*v_{b}^{2}    

v_{b} = 1.2 \cdot 10^{6} m/s

I hope it helps you!

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