# Newton's Laws problems:confused:

1. Sep 24, 2005

### chipsdeluxe

can someone please help me with these problems? i'm completely lost.

1. Synchronous communications satellites are placed in a circular orbit that is 2.32 x 107 m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?

2. A woman stands on a scale in a moving elevator. Her mass is 62.2 kg, and the combined mass of the elevator and scale is an additional 836 kg. Starting from rest, the elevator accelerates upward. During the acceleration, the hoisting cable applies a force of 9110 N. What does the scale read during the acceleration?

for number 2:
i think i use the equation Fn=mg+ma. for m do i use the total mass or just the woman's mass? g is 9.8 right? but i don't know what the accerlataion is cause the problem doesn't say.

for number 1:
i tried using the law of universal gravitation but that was wrong. i don't know how to find the acceleration with the information given. i know the mass of earth and the radius. but i don't know how to use the info.

the hw is due at 11 pm which is in 5 hours. and i don't have any idea how to solve it. any help would be great. thanks

Last edited: Sep 24, 2005
2. Sep 24, 2005

### lightgrav

For #2:
The Free-Body-Diagram of an object
includes Forces applied TO the object.
The "Scale Reading" is the Force applied
by the scale to the object on TOP of the scale.
(you've seen these things, haven't you?)
. . . Use the Equation: Sum F_onA = ma_A !
which is Fn - mg = ma , or Fn = mg + ma .
But if you start at the *beginning*,
then it's obvious which mass you should use.
The acceleration of the elevator+scales+woman
is caused by the cable Tension (Sum F = ma).

For #1 you use universal gravitation GMm/r^2 ,
but r is the distance center-of-mass to c.o.m.

Sorry I didn't see your post until just now.

3. Sep 24, 2005

### Andrew Mason

1. You are correct to use Newton's law of gravitation:

$$a = \frac{GM_e}{r^2}$$

where r is the distance from the satellite to the centre of the earth. You have to add the earth's radius to the distance above the surface.

2. The cable provides the force to balance the weight of the elevator and woman plus the acceleration. From the cable force, you can find a:

$$F = m(g+a)$$
$$a = \frac{F}{m} - g$$

From that you should be able to determine the scale reading (which depends only on the woman's weight and acceleration).

AM

4. Sep 25, 2005

### chipsdeluxe

thanks for the help guys