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Chapter 2: Q79E (page 67)

At Earth's location, the intensity of sunlight is 1.5 kW / m2. If no energy escaped Earth, by how much would Earth's mass increase in 1 day?

Short Answer

Expert verified

The increase in Earth鈥檚 mass for no escape of Sun鈥檚 energy from Earth is 7.34脳105kg.

Step by step solution

01

Identification of given data

The intensity of sunlight on Earth is I=1.5kW/m2.

The number of seconds in a day on Earth is t=1day=86400s.

The energy received by Earth per unit surface area from the sun is called the solar constant.

02

Determination of energy received by Earth in one day

The energy received by Earth in time t is given as:

E=I.A.t

Here, A is the surface area of Earth and its value is 5.10脳1014m2.

For the given values, equation becomes-

E=1.5kW/m2103J/s1kW5.10脳101486400sE=6.61脳1022J

03

Determination of increase in Earth’s mass

The increase in Earth鈥檚 mass is given as:

E=mc2

Here, c is the speed of light in vacuum and its value is 3脳108m/s

6.61脳1022J=m3脳108m/s2m=7.34脳105kg

Therefore, the increase in Earth鈥檚 mass for no escape of energy from Earth is 7.34脳105kg.

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Most popular questions from this chapter

Is it possible for the momentum of an object to be mc. If not. why not? If so, under what condition?

(a) Determine the Lorentz transformation matrix giving position and time in frame s'from those in the frame sfor the case 谓=0.5c.

(b) If frame s''moves at 0.5crelative to frame , the Lorentz transformation matrix is the same as the previous one. Find the product of two matrices, which gives x''and t'' from x and t .

(c) To what single speed does the transformation correspond? Explain this result.

A proton is accelerated from rest through a potential difference of 500MV.

(a) What is its speed?

(b) Classical mechanics indicates that quadrupling the potential difference would double the speed. Were a classical analysis valid, what speed would result from a 2000MVpotential difference?

(c) What speed actually results?

Question: A rocket maintains a constant thrust F, giving it an acceleration of g

(i.e.,9.8m/s2).

(a) If classical physics were valid, how long would it take for the rocket鈥檚 speed to reach 0.99c??

(b) Using the result of exercise 117(c), how long would it really take to reach 0.99c??

u=11+(Ft/mc)2FTt

From a standstill. you begin jogging at5m/s directly toward the galaxy Centaurus A. which is on the horizon 2脳1023maway.

(a) There is a clock in Centaurus A. According to you. How Will readings on this clock differ before and after you begin jogging? (Remember: You change
frames.)

(b) The planet Neptune is between Earth and Centaurus 4.5脳109mis from Earth- How much readings a clock there differ?

(c)What would the time differences if had instead begun jogging in the opposite direction?

(d) What these results tell you about the observations of a traveling twin who accelerates toward his Earth-bound twin? How would these observation depend on the distance the twins?
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