Help meeee! (for anyone good @ physics)

[Daveman]

Here's this quetion:
A block of mass m is released from rest at a height of R above a horizontal surface, the acceleration due to gravity is g.

(mspaint is cool!)

What is the magnitude of the normal force exerted on the block by the hoop when the block has reached the bottom?

It's a multiple choice problem, and the answer key says the answer is 3mg, I need to know how/why it's 3mg =/

(there is a previous question that says the speed at the bottom of the hoop is v^2=2gR incase it helps determine the normal force).


Here's what me and a friend think: since mg would be the force of gravity, and the normal is 3mg, there has to be a force of 2mg pushing down on the block in addition to gravity, but we can't figure out where this 2mg comes from. Our 3rd theory is the answer key is wrong, but we're not gonna bank on that =P (other answers were: 0, mg^2/R, mg, 2mg) our gut instinct says it should be just mg, but we're not trusting it.

 

[KuroSan]

My head hurts by looking at it. Thank god I'm not in High School anymore.

 

[Daveman]

Meh we're going with the answer key typo:

Batman! says:
anyways
Batman! says:
so
Batman! says:
what have we learned about 3mg
Batman! says:
the answer: NOTHING
Batman! says:
lets assume a typo and it's 3mg
Batman! says:
because for that instant in time there would be no downard force other than gravity
Batman! says:
all the speed and w/e would be pointing in the x axis
Batman! says:
the only thing going down would be mg, making the normal mg

If anyone sees how it could be 3mg or flaw in my logic deciding that it -has- to be mg, let me know =D

In my class we make bets on who does the best on tests, I got $6 riding on me doing better than a certain 3 people on this!

 

[resipsa]

It's been a long time since I studied any "earthly" physics, so take this with a grain of salt.

I think your missing 2mg might be found in the inward net force due to circular motion.

Fnet=m*(v^2/R)=m*(2gR/R) = m*2g = 2mg

Fnet is the sum of all other forces acting on the object.

The force of gravity downward is 1mg, in the opposite direction of Fnet, so we can call it -1mg. The normal force (in this case centripetal force) exerted by the hoop has to overcome the -1mg to produce an Fnet of 2mg. -1mg(gravity)+3mg(normal force)=2mg.

 

[resipsa]

Batman! says:
because for that instant in time there would be no downard force other than gravity

I think this statement is the flaw in Batman's logic. There is no "instant in time" where moving objects are concerned. Time is infinitely divisible into periods. No matter how short a period of time you measure, the block has moved some distance during that time. If the block is moving in a circular path, there is a Net Force pushing the block to the center of the circle - Centripetal Force.

 

[Daveman]

oooooo thanks alot ^^

Now I get it =D thanks, this one question was bugging me because I really didn't know where to start ~.~, In my mind the floor itself was doing the normal, I didn't think of the fact that since it was the hoop pushing back, there'd be a constant centriptal force acting as the normal, since I was using a string on a ball model also in my mind to think of the whole circular motion.

Just one last question to make sure of something: If it was a string and a ball, would you still call the centriptal force a normal force? or would it be something else? (doesn't pretain to current material, but can't hurt to know =D ).

Thanks again, not only does this help with that 1 question, but it opens up alot of thinking, since my teacher loves to throw curveball questions at us that the whole class gets wrong on tests ~.~

 

[KuroSan]

That's funny =D so did my teachers XD

 

[resipsa]

Just one last question to make sure of something: If it was a string and a ball, would you still call the centriptal force a normal force? or would it be something else? (doesn't pretain to current material, but can't hurt to know =D ).

I'm not sure. My recollection is the normal force is a force that keeps 2 objects from occupying the same space, so I don't think it would be called a normal force if 2 objects aren't colliding. I'm only guessing at this point though.

 

[exodusamphi]

With the question about the string and the ball, there would be no normal force IFF the ball isnt "rolling" on the circular wall.

For instance, if the ball and string is just being spun in open air, the force going towards the middle at any point would b Fac, Where Fac = m(of ball) * (V^2 / R)

If the ball was rolling through a circular loop, then the normal force is active at all times. With or against gravity.

In short, i wish i oculd help yoou, but resipsa seems to have already have