1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Slav-nsk [51]
3 years ago
9

The acceleration due to gravity, g , is constant at sea level on the Earth's surface. However, the acceleration decreases as an

object moves away from the Earth's surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, g h . Express the equation in terms of the radius R of the Earth, g , and h .
Physics
1 answer:
blsea [12.9K]3 years ago
3 0

Answer:

  g    = g₀   [1- 2 h / Re + 3 (h / Re)²]

Explanation:

The law of universal gravitation is

        F = G m Me / Re²

Where g is the universal gravitational constant, m and Me are the mass of the body and the Earth, respectively and R is the distance between them

      F = G Me /Re²  m

We call gravity acceleration a

       g₀ = G Me / Re².

When the body is at a height h above the surface the distance is

            R = Re + h

Therefore  the attractive force is

      F = G Me m / (Re + h)²

Let's take Re's common factor

      F = G Me / Re²  m / (1+ h / Re)²

As Re has a value of 6.37 10⁶ m and the height of the body in general is less than 10⁴ m, the h / Re term is very small, so we can perform a series expansion

         (1+ h / Re)⁻² = 1 -2 h / Re + 6/2 (h / Re) 2 + ...

Let's replace

       F = G Me /Re²   m [1- 2 h / Re + 3 (h / Re)²]

       F = g₀   m  [1- 2 h / Re + 3 (h / Re)²]

If we call the force of attraction at height

     m g =g₀ m  [1- 2 h / Re + 3 (h / Re)²]

       g    = g₀   [1- 2 h / Re + 3 (h / Re)²]

You might be interested in
1. A 4-N force is used to move an object 2 m in 10 s. Which of the following is the power generated while moving the object?
guajiro [1.7K]

Power is the work done per unit time. Therefore,

\begin{gathered} p=\frac{w}{t} \\ \text{where} \\ w=\text{work done} \\ t=\text{time} \end{gathered}

Therefore,

\begin{gathered} \text{work done=fd} \\ f=force=4N \\ d=\text{displacement}=2m \\ t=2\sec s \\ p=\frac{fd}{t}=\frac{4\times2}{10}=\frac{8}{10}=0.8watts \end{gathered}

4 0
1 year ago
Which energy transformations BEST illustrates why people can walk? A) Chemical energy is being converted into light energy. B) C
Gekata [30.6K]

The answer is letter c.

The explanation behind this is when human consumes a plant or when a human being eats an animal that ate a plant. The chemical energy kept in the plant (or animal) cells is progressed into the cells of the human's body. All of the body progressions, like ingestion, breathing, pumping blood, are driven by cells changing the kept chemical energy into heat and work, in a procedure called respiration. In the muscle cells of the human (or any animal), the chemical energy is converted into mechanical work and heat. The muscle pacts, the legs thrust, and the body jumps into the air. 

5 0
3 years ago
Read 2 more answers
1. How does the structure of a hard-boiled egg compare to the crust, mantle, and core structure of Earth? What do the egg's laye
lutik1710 [3]

Answer:

2. Earth layers compare in egg layer it is hard on the outside

Explanation:

6 0
3 years ago
Read 2 more answers
2NaOH+H2SO4 Na2SO4+H2O the equation is balanced/unbalanced because the number of hydrogen atoms and oxygen/sodium is equal/not e
RUDIKE [14]
Your equation is:
2NaOH + H_{2}SO_{4}  ==\ \textgreater \  Na_{2}SO_{4} + H_{2}O

An equation is balanced only if there are the same number of atoms of each element on both sides of the arrow - aka same number of atoms of each element in both reactants (left of the arrow) and products (right of the arrow). 

It'll be easiest to tackle this by counting up the number of atoms of each element on the left and on the right and comparing those numbers. If there is a number in front of the entire compound, that means that number applies to all elements in the compound. If the number is a subscript (little number to the right of the element), that means that number only applies to the element that the subscript is attached to:
1) On the left, you have:
2NaOH + H_{2}SO_{4}\\
\\
Na:  \: 2 \: atoms\\
O: \: 2 + 4 = 6 \: atoms\\
H: \: 2 + 2 = 4 \: atoms\\
S:  \: 1 \: atom

2) On the right, you have:
Na_{2}SO_{4} + H_{2}O\\
\\ 
Na: \: 2 \: atoms\\ 
O: \: 4 + 1 = 5 \: atoms\\ 
H: \: 2 \: atoms\\ 
S: \: 1 \: atom

You can see that the number of oxygen and hydrogen atoms aren't equal on both the left (reactants) and the right (products), so the equation is unbalanced.

Your final answer is "T<span>he equation is unbalanced because the number of hydrogen atoms and oxygen is not equal in the reactants and in the products."</span>


5 0
3 years ago
Read 2 more answers
If a 12 kg cat is sitting 5 m up in a tree, how much PE does it have?
Helen [10]

Answer:

588 J

Explanation:

PE (potential energy) = (mass) x (gravity) x (height)

mass = 12 kg

gravity = 9.8m/s^2

height = 5 m

PE = (12) x (9.8) x (5) = 588 J (Joules)

5 0
2 years ago
Other questions:
  • What is the main reason why many nuclear power plants are located near bodies of water?
    5·2 answers
  • Write a conclusion to the question, "What happens if we mix different amounts of hot and cold water?"
    13·1 answer
  • Two automobiles are equipped with the same singlefrequency horn. When one is at rest and the other is moving toward the first at
    13·1 answer
  • For hundreds of years humans have been adding chemicals and other pollutants to the earths water supply. Can earths water ever b
    11·1 answer
  • A woman throws a baseball straight up into the air. what is the baseball's acceleration at its highest point?
    10·1 answer
  • A cannon tilted up at a 29.0° angle fires a cannon ball at 81.0 m/s from atop a 22.0 m -high fortress wall. What is the ball's i
    12·1 answer
  • Electricity is produced by falling water is called
    15·1 answer
  • A +15 nC point charge is placed on the x axis at x = 1.5 m, and a -20 nC charge is placed on the y axis at y = -2.0m. What is th
    8·1 answer
  • What would happen if you use a thicker wire around the iron nail of an electromagnet? (thats the whole question)
    15·1 answer
  • An object weighs 2.6 N in air and 2.2N when completely immersed in water. Determine the relative density of the object (2mks​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!