Q64P A satellite orbits a planet of u... [FREE SOLUTION]

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Chapter 13: Q64P (page 383)

A satellite orbits a planet of unknown mass in a circle of radius $2.0 脳 10^{7} m$ . The magnitude of the gravitational force on the satellite from the planet is $F = 80 鈥� N$ .
(a) What is the kinetic energy of the satellite in this orbit?
(b) What would F be if the orbit radius were increased to $3.0 脳 10^{7} m$ ?

Short Answer

Expert verified

Kinetic energy of the satellite $K = 8.0 脳 10^{8} J$
Gravitational force when the orbit radius is increased to $3 脳 10^{7} m 鈥塱蝉鈥� (F_{2}) = 35.5 鈥� N$

Step by step solution

Listing the given quantities

$r_{1} = 2 脳 10^{7} m$

$F_{1} = 80 鈥� N$

$r_{2} = 3 脳 10^{7} m$

Understanding the concept of gravitational force and kinetic energy

Using the given gravitational force and kinetic energy formula, we can findthekinetic energy of the satellite ( $K_{s}$ ). Using $F 鈭� \frac{1}{r^{2}},$ we can find gravitational force $F_{2}$ when the radius is increased to ${3脳10}^{7} 鈥尘$

Formula:

$K= \frac{GMm}{2 (r)}$

$F= \frac{GMm}{r^{2}}$

(a) Calculation of kinetic energy of satellite

$K= \frac{GMm}{2 (r_{1})}$

$F_{1} = \frac{GMm}{r_{1}^{2}}$

$F_{1} {脳谤}_{1} = \frac{GMm}{r_{1}}$

Using this in kinetic energy equation (1),

$\begin{matrix} K = \frac{1}{2} F_{1} 脳 r_{1} \\ = \frac{1}{2} 80 鈥塏脳 2 脳 10^{7} 鈥尘 \\ = 8.0 脳 10^{8} 鈥� J \end{matrix}$

(b) Calculation of Gravitational force when the orbit radius is increased

$\begin{matrix} F_{1} 鈭� \frac{1}{r_{1}^{2}} \\ F_{2} 鈭� \frac{1}{r_{2}^{2}} \\ \frac{F_{1}}{F_{2}} = \frac{r_{2}^{2}}{r_{1}^{2}} \\ \frac{F_{1}}{F_{2}} = \frac{{(2 脳 10^{7} 鈥尘)}^{2}}{{(3 脳 10^{7} 鈥尘)}^{2}} \\ \frac{F_{1}}{F_{2}} = \frac{4}{9} \end{matrix}$

Using the given value of $F_{1}$

$\begin{matrix} F_{2} = \frac{4 脳 80 鈥塏}{9} \\ = 35.5 鈥� N \end{matrix}$

Gravitational force when the orbit radius is increased to $3 脳 10^{7} m 鈥� is 鈥� F_{2} = 35.5 N$

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Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of gravitational force and kinetic energy

(a) Calculation of kinetic energy of satellite

(b) Calculation of Gravitational force when the orbit radius is increased

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91影视

A satellite orbits a planet of unknown mass in a circle of radius 2.0脳107m. The magnitude of the gravitational force on the satellite from the planet is F=80鈥�N.(a) What is the kinetic energy of the satellite in this orbit?(b) What would F be if the orbit radius were increased to3.0脳107m ?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of gravitational force and kinetic energy

(a) Calculation of kinetic energy of satellite

(b) Calculation of Gravitational force when the orbit radius is increased

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Magnetism

Classical Mechanics

Modern Physics

Turning Points in Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.