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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

One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite in a circular orbit 500鈥�kmabove Earth鈥檚 surface collides with a pellet having mass 4.0g.

(a) What is the kinetic energy of the pellet in the reference frame of the satellite just before the collision?

b) What is the ratio of this kinetic energy to the kinetic energy of a 4.0gbullet from a modern army rifle with a muzzle speed of 950m/s?

Question: The orbit of Earth around the Sun is almost circular. The closest and farthest distances are 1.47脳108鈥�kmand 1.52脳108kmrespectively. Determine the corresponding variations in (a) total energy, (b) gravitational potential energy, (c) kinetic energy, and (d) orbital speed. (Hint:Use conservation of energy and conservation of angular momentum.)

A 50Kgsatellite circles planet Cruton every 6.0 h.The magnitude of the gravitational force exerted on the satellite by Cruton is 80 N. (a) What is the radius of the orbit? (b) What is the kinetic energy of the satellite? (c) What is the mass of planet Cruton?

MooneffectSome people believe that the Moon controls their activities. If the Moon moves from being directly on the opposite side of Earth from you to being directly overhead, by what percent does (a) the Moon鈥檚 gravitational pull on you increase and (b) your weight (as measured on a scale) decrease? Assume that the Earth鈥揗oon (center-to-center) distance is3.82脳108mand Earth鈥檚 radius is6.37脳106m.

(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 160kmabove Earth鈥檚 surface?

(b) What is the period of revolution?
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