# Gravitation attraction of a mountain

• ac7597
In summary, the ball is attracted to the Earth by a local gravitational force, but this force is not strong enough to support the weight of the ball.
ac7597
Homework Statement
Mason and Dixon are surveying a peculiar region: a flat plain with a single giant mountain sticking up out of the ground. The mountain has a very round shape. "It looks like the mountain is sitting on the plain," says Dixon, "but miners have discovered that the mountain extends down below the surface. It appears that the mountain is half-buried in the dirt."

When they are still a distance 15000 meters away from the mountain, they make a local gravitational force measurement: they hang a ball of mass 11.5 kg from a string. The string doesn't hang vertically, but tilts very slightly towards the mountain. Dixon estimates the angle to be 0.00050 degrees.

Estimate the mass of the mountain.

The mountain is shaped like a giant sphere (half of which is buried underground), and appears to be made of ordinary rock. Estimate its height above the ground.
Relevant Equations
G=6.72 * 10^(-11)
I tried to solve for mass of the mountain by:

(mass of ball) (9.8m/s^2)= G(mass of ball)(mass of mountain)/ (15000m)^2
The mass of the ball cancels out leaving with mass of mountain=33.04 * 10^(18) kg.

Your equation says that the force with which the Earth attracts the ball is equal to the force with which the mountain attracts the ball. That is simply not true. Draw a free body diagram showing all the forces acting on the ball and find the resultant by vector addition. You know that the resultant should be at 0.00050 degrees.

y direction: (11.5kg)(9.8m/s^2)sin(0.0005) =0.983 * 10^(-3) N
x direction: ((11.5kg)(9.8m/s^2)cos(0.0005) =112.7 N ?

ac7597 said:
y direction: (11.5kg)(9.8m/s^2)sin(0.0005) =0.983 * 10^(-3) N
x direction: ((11.5kg)(9.8m/s^2)cos(0.0005) =112.7 N ?
Directions x and y are meaningless without a diagram. Please show and post a diagram showing all the forces acting on the ball and label them appropriately. Write equations derived from that diagram. Don't forget that you need to introduce the unknown mass of the mountain. The equations in post #3 are independent of it.

kuruman said:
Directions x and y are meaningless without a diagram. Please show and post a diagram showing all the forces acting on the ball and label them appropriately. Write equations derived from that diagram. Don't forget that you need to introduce the unknown mass of the mountain. The equations in post #3 are independent of it.

I got up to m(ax) =m1(mx)(G)/(r^2)-m1(g)cos(0.0005)

#### Attachments

• fullsizeoutput_9.jpeg
45.2 KB · Views: 247
Is the ball suspended in mid air with only the two gravitational forces acting on it?

The question doesn't specify but I think when it said 'hang vertically' it means it's in midair. I can't solve for (mx) without knowing the acceleration (ax).

ac7597 said:
When they are still a distance 15000 meters away from the mountain, they make a local gravitational force measurement: they hang a ball of mass 11.5 kg from a string. The string doesn't hang vertically, but tilts very slightly towards the mountain. Dixon estimates the angle to be 0.00050 degrees.

assume string is massless

ac7597 said:
assume string is massless
That's not what @kuruman was asking. Isn't the string attached to the mass? Is the string slack?

String is not slack. Is the body diagram correct?

ac7597 said:
String is not slack. Is the body diagram correct?
The free body diagram is not correct. If the string is not slack, it follows that it must be under tension. This tension acts on the ball. Add it to your diagram. Also, the acceleration of the ball is zero; the ball just hangs there motionless at the given very small angle relative to the vertical. Should you require more help, please post your revised diagram and a complete revised attempt at a solution.

kuruman said:
The free body diagram is not correct. If the string is not slack, it follows that it must be under tension. This tension acts on the ball. Add it to your diagram. Also, the acceleration of the ball is zero; the ball just hangs there motionless at the given very small angle relative to the vertical. Should you require more help, please post your revised diagram and a complete revised attempt at a solution.
AND, please make it larger / more legible this time.

kuruman
Is this the answer for part 1?

#### Attachments

• UkZEVr6rTS2QczQVpeZGiA.jpg
33.3 KB · Views: 205
ac7597 said:
Is this the answer for part 1?

Last edited:
ac7597 said:
Is this the answer for part 1?
The thumbnail sketch in the middle looks right, but it should be several times as large.
You don't need to show the mountain in an FBD of the bob, just the force it exerts.
None of the rest belongs in an image. Per forum rules, please take the trouble to type in your working. Not only does that make it much easier to read, it is also easier to comment on specific steps.

## 1. What is the gravitational force of a mountain?

The gravitational force of a mountain is the pull of the Earth's gravity on the mass of the mountain. This force is determined by the mass of the mountain and its distance from the center of the Earth.

## 2. How does the gravitational attraction of a mountain affect nearby objects?

The gravitational attraction of a mountain can affect nearby objects by pulling them towards the mountain. This is because the mountain has a large mass, which creates a strong gravitational force.

## 3. Is the gravitational attraction of a mountain stronger or weaker than that of a smaller object?

The gravitational attraction of a mountain is stronger than that of a smaller object, such as a rock or a tree. This is because the larger mass of the mountain creates a stronger gravitational force.

## 4. Can the gravitational attraction of a mountain be measured?

Yes, the gravitational attraction of a mountain can be measured using instruments such as a gravimeter. This device measures the strength of the gravitational force at different locations on or near the mountain.

## 5. How does the shape of a mountain affect its gravitational attraction?

The shape of a mountain can affect its gravitational attraction by changing its mass and distance from the center of the Earth. A taller and wider mountain will have a greater mass and therefore a stronger gravitational force compared to a smaller and narrower mountain.

Replies
8
Views
2K
Replies
38
Views
3K
Replies
5
Views
12K
Replies
7
Views
455
Replies
5
Views
2K
Replies
3
Views
1K
Replies
4
Views
1K
Replies
10
Views
2K
Replies
5
Views
2K
Replies
9
Views
4K