A community for students.
Here's the question you clicked on:
 0 viewing
AravindG
 4 years ago
doubts on gravitation continued
AravindG
 4 years ago
doubts on gravitation continued

This Question is Closed

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1a hole is drilled from the surface of the earth and a ball is thrown inside .the ball executes SHM why?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Could you draw for the earth and this hole? I think I know what you mean but just to be sure

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1The force acting on the falling object acts opposite direction of its displacementdw:1329322341910:dwtoward the center of mass of the earth (the equilibrium position of the falling object)\[F_g\proptox\]so there is always a restoring force acting to move the object toward the center of the earth. However when the object passes through the center point of the earth all the potential energy it started with is now kinetic, so it will pass through and gravity will act in the opposite direction. This will continue indefinitely unless a dampening force acts to slow the motion of the object.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1329322653275:dwset up a coordinate axis to define positive and negative direction and it's easy to convince yourself that the force acts with opposite sign as displacement.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i dont get wat the restoring force is

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Yes, as explained here. The gravitational force acting on a mass \( m \) inside a solid like the earth of mass \( M \) and radius \( R \) at a radial distance \( r \)d is \[ F_g = \frac{GMm}{R^2}\frac{r}{R} \] Notice that the first fraction there is a constant. What is varying linearly is the r/R term. Notice also when r=R, that the force is exactly what you expect it to be. Now, given that what don't you understand?

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i havent studied that expression

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3In every case, the force acts towards the center of the earth. Hence the force is always in the opposite direction of the displacement from the center of the earth. This is _exactly_ like a spring, where \[ F = kx \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Well, I'm telling you it right now. This is the only way to answer this question.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1hm so gravitational force acts towards centre of earth??

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3If you like, write \[ F_g = kr \] where \[ k = \frac{GMm}{R^3} \] === Yes, by virtue of the negative sign, F_g always points towards the center of the earth.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1oh but i thoug the acceleration is maximum on surface of earth

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3It is. For r < R, F_g is less that it is on the surface of the earth. That follows immediately from the equations above, where F_g is proportional to r.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i hav studied this eqn can u relate the answer with this?? dw:1327512111726:dw where d is the depth

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1turing u can also join he discussion

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1James has a handle on it...

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Yes. \[ r = R_e  d \] and \[ g = \frac{GM}{R_e^2} \] Hence \[ g' = g(1  d/R_e) \] \[ = \frac{GM}{R_e^2} \frac{R_e  d}{R_e} \] \[ = \frac{GM}{R_e^2} \frac{r}{R_e} \] \[ = \frac{GM}{R_e^3} r \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Therefore the force acting of mass \( m\) at a depth of \( d \), i.e., at a radial distance from the center of the earth of \( r = R_e  d \) is \[ F_g = mg' \] \[ =  \frac{GMm}{R_e^3} r \] I've put the minus sign in here to indicate the direction of the force, which is in the negative rdirection.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i hav a funny doubt :u see the force of gravity is towards the centre,, then y does it decrease from the surface???it should be increasing ryt?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Suppose you were in the center of the earth. What would gravity there be?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Right, because there is mass all around you, the force of which cancels itself out. Indeed, for any distance below the surface of the earth, the deeper you go, the more cancelation you get from mass 'above' you. That's why it decreases as we head towards the center of the earth until finally we arrive at zero force.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1can u show the path of the ball in a diag

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i mean will the ball move from one end to other end?

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1so wen the ball moves towards centre the foce is towards surface?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3The force always points towards the center of the earth, exactly the like the force of spring always points towards the relaxed/equilibrium state of the spring: \[ F_g = kr, \ \ \ F_{spring} = kx \]

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1then the ball is also moving towards centre

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3Force is not always in the direction of motion, you know that. Acceleration changes direction of motion, that is velocity. But direction of velocity need not equal direction of acceleration, just like with a spring.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3With a spring, the mass is moving half the time in the direction of the force; half the time in the opposite direction as the force.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1^which highlights the same point: acceleration is proportional to negative displacement.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1srry guys but i cant catch up with that point

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3First you drop the ball, acceleration is toward the center of the earth and the ball moves in that direction. Then the ball gets the center of the earth. Then it keeps moving past the center of the earth towards the other side of the earth. But now the acceleration is in the opposite direction, toward the center of the earth. This acceleration slows the balls until ... ...it reaches the other side of the earth and has zero velocity. Acceleration continues acting on it toward the center of the earth, and now it starts to move towards the center of the earth again, and continues to do so until it reaches the center of the earth ... and then it moves past the center of the earth and the acceleration is in the opposite direction to motion ... and the whole pattern repeats.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1wow i got it ,, but one doubt y does the ball continue moving after reaching centre?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3because exactly at the center it has kinetic energy and momentum, but the force is zero.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1k i got that :P thx i hav some more doubts

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3so there's nothing to stop it at the center of the earth.

AravindG
 4 years ago
Best ResponseYou've already chosen the best response.1i will post in new tab k?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.3I'm going, sorry. I've got my own problems to solve! ;)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.