Page 76 - Fisika Terapan for Engineers and Scientists

276 CHAPTER 9 Gravitation

The magnitude of the force due to the Earth on the Moon is

GM M M
E
F EM 2
R
EM
11 2 2 24 22
6.67 10 N m /kg 5.98 10 kg 7.35 10 kg

8
(3.84 10 m) 2
20
1.99 10 N
The direction of each force on the Moon is toward the body producing that force,
as indicated in Fig. 9.4a. We choose the x axis along the Moon–Sun direction and
add the two forces vectorially as shown in Fig. 9.4b. By resolving F into com-
EM
ponents, we see that the resultant force F has x component
net
F F F cos 45.0
net,x SM EM
20
20
20
4.34 10 N 1.99 10 N cos 45.0 5.75 10 N
and y component
20
20
F F sin45.0 1.99 10 N sin 45.0 1.41 10 N
net,y EM
Thus the resultant force has magnitude
2 2
F 2F F
net net,x net,y
20 2 20 2 20
2(5.75 10 N) (1.41 10 N) 5.92 10 N
F net,y 1.41 10 N
20
The direction of F is given by tan 0.245.
net 20
F 5.75 10 N
net,x
With a calculator, we find that the inverse tangent of 0.238 is
13.8

✔ Checkup 9.1

QUESTION 1: Neptune is about 30 times as far away from the Sun as the Earth.
Compare the gravitational force that the Sun exerts on a 1-kg piece of Neptune with
the force it exerts on a 1-kg piece of the Earth. By what factor do these forces differ?
QUESTION 2: Saturn is about 10 times as far away from the Sun as the Earth, and its
mass is about 100 times as large as the mass of the Earth. Is the force that the Sun
exerts on Saturn larger, smaller, or about equal to the force it exerts on the Earth? Is
the acceleration of Saturn toward the Sun larger, smaller, or about equal to the accel-
eration of the Earth?
QUESTION 3: Equation (9.6) gives the gravitational acceleration at the surface of the
Earth, that is, at a radial distance of r R from the center. What is the gravitational
E
acceleration at a radial distance of r 2R ? At r 3R ?
E E
QUESTION 4: Uranus has a larger mass than the Earth, but a smaller gravitational
acceleration at its surface. How could this be possible?
QUESTION 5: Consider a particle located at the exact center of the Earth. What is the
gravitational force that the Earth exerts on this particle?
QUESTION 6: If the radius of the Earth were twice as large as it is but the mass remained
unchanged, what would be the gravitational acceleration at its surface?
1 1
(A) g (B) g (C) g (D) 4g (E) 8g
8 4