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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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Most popular questions from this chapter

The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4脳106mwith a period of7h39min .Calculate the mass of Mars from this information.

An asteroid, whose mass is 2.0脳10鈭�4times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is twice Earth鈥檚 distance from the Sun.

(a) Calculate the period of revolution of the asteroid in years.

(b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth?

We watch two identical astronomical bodies Aand B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation isRi. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this two body system. Use the principle of conservation of mechanical energy (Kf+ Uf=Ki +Ui ) to find the following when the center-to-center separation is 0.5Ri:

(a) the total kinetic energy of the system,

(b) the kinetic energy of each body,

(c) the speed of each body relative to us, and

(d) the speed of body Brelative to body A. Next assume that we are in a reference frame attached to body A(we ride on the body). Now we see body Bfall from rest toward us. From this reference frame, again useKf+Uf=Ki+Uito find the following when the center-to-center separation is0.5Ri:

(e) the kinetic energy of body Band

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(g) Why are the answers to (d) and (f) different? Which answer is correct?

The three spheres in Fig. 13-45, with massesmA=80kg, mB=10g, and mC=20g , have their centers on a common line,withL=12cm and d=4.0cm . You move sphereBalong the lineuntil its center-to-center separation fromCis d=4.0cm . Howmuch work is done on sphereB(a) by you and (b) by the net gravitational force onBdue to spheresAandC?

A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on r2 because A=蟺谤2. Determine how the following properties of the satellite depend on r:

(a) period,

(b) kinetic energy,

(c) angular momentum, and

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