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Akimi4 [234]
3 years ago
15

The escape velocity is defined to be the minimum speed with which an object of mass m must move to escape from the gravitational

attraction of a much larger body, such as a planet of total mass M. The escape velocity is a function of the distance of the object from the center of the planetR, but unless otherwise specified this distance is taken to be the radius of the planet because it addresses the question "How fast does my rocket have to go to escape from the surface of the planet?" What is the total mechanical energy Etotal of the object at a very large (i.e., infinite) distance from the planet? Find the escape velocity ve for an object of mass m that is initially at a distance R from the center of a planet of mass M. Assume that R≥Rplanet, the radius of the planet, and ignore air resistance. Express the escape velocity in terms of R, M, m, andG, the universal gravitational constant.
Physics
1 answer:
s344n2d4d5 [400]3 years ago
6 0

Answer:

v = √2G M_{earth} / R

Explanation:

For this problem we use energy conservation, the energy initiated is potential and kinetic and the final energy is only potential (infinite r)

        Eo = K + U = ½ m1 v² - G m1 m2 / r1

        Ef = - G m1 m2 / r2

When the body is at a distance R> Re, for the furthest point (r2) let's call it Rinf

       Eo = Ef

       ½ m1v² - G m1 M_{earth} / R = - G m1 M_{earth} / R

      v² = 2G M_{earth} (1 / R - 1 / Rinf)

If we do Rinf = infinity     1 / Rinf = 0

       v = √2G M_{earth} / R

      Ef = = - G m1 m2 / R

The mechanical energy is conserved  

 

      Em = -G m1  M_{earth} / R

      Em = - G m1  M_{earth} / R

     R = int        ⇒  Em = 0

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A hydrometer is made of a tube of diameter 2.3cm.The mass of the tube and it's content is 80g. If it floats in a liquid density
iris [78.8K]

Answer:

The depth to which the hydrometer sinks is approximately 24.07 cm

Explanation:

The given parameters are;

The diameter of the hydrometer tube, d = 2.3 cm

The mass of the content of the tube, m = 80 g

The density of the liquid in which the tube floats, ρ = 800 kg/m³

By Archimedes' principle, the up thrust (buoyancy) force acting on the hydrometer = The weight of the displaced liquid

When the hydrometer floats, the up-thrust is equal to the weight of the hydrometer which by Archimedes' principle, is equal to the weight of the volume of the liquid displaced by the hydrometer

Therefore;

The weight of the liquid displaced = The weight of the hydrometer, W = m·g

Where;

g = The acceleration due to gravity ≈ 9.81 m/s²

∴ W = 80 g × g

The volume of the liquid that has a mass of 80 g (0.08 kg), V = m/ρ

V = 0.08 kg/(800 kg/m³) = 0.0001 m³ = 0.0001 m³ × 1 × 10⁶ cm³/m³ = 100 cm³

The volume of the liquid displaced = 100 cm³ = The volume of the hydrometer submerged, V_h

V_h = A × h

Where;

A = The cross-sectional area of the tube = π·d²/4

h = The depth to which the hydrometer sinks

h = V_h/A

∴ h = 100 cm³/( π × 2.3²/4 cm²) ≈ 24.07 cm

The depth to which the tube sinks, h ≈ 24.07 cm.

3 0
3 years ago
A ball with a weight of 2 N is attached to the end of a cord of length 2m . The ball is whirl in a vertical circle counterclockw
ZanzabumX [31]

Answer:

we agree with

Edgar: The net force on the ball at the top position is 9 N. Both the tension and the weight are acting downward so you have to add them.

Explanation:

Weight of the ball is given as

W = 2N

so we have

m = \frac{W}{g}

m = 0.204 kg

now tension force at the top is given as

T_{top} = 7 N

T_{bottom} = 15 N

Now at the top position by force equation we can say that ball will have two downwards forces

1) Tension force

2) Weight of the ball

so net force on the ball is given as

F_{net} = T + W

F_{net} = 7 + 2 = 9 N

So we agree with

Edgar: The net force on the ball at the top position is 9 N. Both the tension and the weight are acting downward so you have to add them.

8 0
3 years ago
Joe rides his bicycle in a straight line for 2 hour with an average velocity of 13 km/h south, how far has he ridden?
dmitriy555 [2]

Answer:

ans is 3.125 km

i hope this is correct

8 0
3 years ago
Match each item with the clean water regulation it describes. (2 points)
Leona [35]

The correct match of each item to the clean water regulation it describes is as follows:

  • Regulates pollutants discharged into surface waters: Clean water act
  • Covers both surface and ground waters: Safe drinking water act
  • Authorizes the EPA to establish minimum standards for tap water: Safe drinking water act
  • Funds sewage treatment plants: Clean water act

<h3>What are the functions of clean water regulation?</h3>

Clean Water Act (CWA) is a regulatory body that establishes the basic structure for the regulation of pollutants discharge and maintenance of quality standards of the surface waters.

On the other hand, the Safe Drinking Water Act was founded to oversee the protection of the quality drinking water. The regulatory body is primarily concerned with potable water all waters, whether from above ground or underground sources.

Therefore, the correct match of each item to the clean water regulation it describes is as follows:

  • Regulates pollutants discharged into surface waters: Clean water act
  • Covers both surface and ground waters: Safe drinking water act
  • Authorizes the EPA to establish minimum standards for tap water: Safe drinking water act
  • Funds sewage treatment plants: Clean water act

Learn more about clean water regulation at: brainly.com/question/2142268

#SPJ1

6 0
2 years ago
Three parachutists have the following masses: A: 50 kg, B: 40 kg, C: 75 kg Which one has the greatest terminal velocity?
allochka39001 [22]

Answer:

A: 50 kg

Explanation:

5 0
3 years ago
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