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Chapter 13: Q19P (page 380)

what altitude above Earth鈥檚 surface would the gravitational acceleration be4.9m/s2?

Short Answer

Expert verified

The altitude above the earth鈥檚 surface where g is4.9m/s2 is2.6脳106m

Step by step solution

01

The given data

The gravitational accelerationag=4.9m/s2

02

Understanding the concept of Gravitational acceleration

We use the concept of gravitational acceleration which is in terms of G, M, and r. We can write the equation for gravity at height h then we can solve it for h.

Formula:

Gravitational Acceleration, ag=GMr2 (i)

03

Calculation of the altitude above the Earth’s surface

We can write equation (i) using height h,

ag=GMRe+h2Re+h=GMagh=GMag-Re................(1)

Substituting the values of mass & radius of the Earth in equation (1), we get

h=(6.67脳10-11)(5.97脳脳1024)4.9-(6.37脳106)h=2.6脳106m

The altitude above Earth鈥檚 surface is at2.6脳106m

Using Newton鈥檚 law of gravitation, we can find the height h where value of 鈥榞鈥� reduces to half its original value.

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