Inclined Planes - Ek vs TPR explanation

[sv3]

Hi,

I was hoping to just get some clarification on forces and inclined planes (just started studying physics). TPR states that mgsin0 is the gravitational force acting on an object on a plane and that mgcos0 is the normal force. And if I wanted to figure out frictional force, I would use mgcos0 with the frictional coeffecient. I totally got that, felt great, then reviewed Ek and now feel lost. Ek states mgsin0 is the sum of the normal force and the force of gravity. They state it a few times so I don't think its another error and was hoping to get some insight on this.

thanks in advance

steve

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[BerkReviewTeach]

Hi,

I was hoping to just get some clarification on forces and inclined planes (just started studying physics). TPR states that mgsin0 is the gravitational force acting on an object on a plane and that mgcos0 is the normal force. And if I wanted to figure out frictional force, I would use mgcos0 with the frictional coeffecient. I totally got that, felt great, then reviewed Ek and now feel lost. Ek states mgsin0 is the sum of the normal force and the force of gravity. They state it a few times so I don't think its another error and was hoping to get some insight on this.

thanks in advance

steve

This is best dealt with by drawing a free body diagram.

The normal force is perpedicular to the surface of the plane, while the gravitational force (mg) points straight down. This means tat they are not collinear, so one of them must be split to be able to get a resultant vector. Upon splitting the gravitation force vector into two components (sin and cos), you'll see that the normal force is equal in magnitude and opposite in direction to the cos component of mg. So, we say that N = mg costheta. The resultant vector is mg sintheta, which is the portion of the gravitational force that is acting on the object.

Technically speaking, based on what you have stated, EK is more accurate (being that it is a resultant term). But, I personally think that for the MCAT, the PR method you just described is an easier way to think about it. The forces acting on the object are mg sintheta (pointing down the ramp) and frictional force (opposing the velocity if its kinetic OR opposing mg sintheta if it static).

 

[Bernoull]

Hi,

I was hoping to just get some clarification on forces and inclined planes (just started studying physics). TPR states that mgsin0 is the gravitational force acting on an object on a plane and that mgcos0 is the normal force. And if I wanted to figure out frictional force, I would use mgcos0 with the frictional coeffecient. I totally got that, felt great, then reviewed Ek and now feel lost. Ek states mgsin0 is the sum of the normal force and the force of gravity. They state it a few times so I don't think its another error and was hoping to get some insight on this.

thanks in advance

steve

Which TPR book do you have? I have EK, TPR PS review (2003) and TPR MCAT CBT 2nd Ed. All of them explain inclined planes correctly and are thus consistent.

The normal force is mgcosQ, the resultant force is mgsinQ and you of course have mg. In fact mgsinQ - mgcosQ = mg due to the fact that mg and mgcosQ point kinda opposite directions (actually there are separated by angle Q) so their vector sum is substractive.

So to sum up, weight in classical physics is always mg (always), frictional force is always Fn (normal force) * frictional constant, Fn is equal and opposite to mg in noninclined planes (flat surfaces) and in inclined planes Fn = mgcosQ , mgsinQ is your net force and gsinQ is your net acceleration (always between 0 and g)

 

[sv3]

for some reason I understand TPR but not Ek even though both are correct. I'll have to look over this again.

So far, when I'm trying to find the acceleration of a box down a ramp (with friction), i do the following and it works:

net force = mgsinQ - mgcosQ(Uk). Then i just get the acceleration. It's worked everytime. So when I read Ek, i understand it to mean to just use mgsinQ so I don't understand how the normal force (and thus friction) are taken into account doing it their way. Unfortunately there aren't examples in there like in TPR.

Perhaps i shouldn't use both sources........

PS (I have TPR hyperlearning 07 and the newest Ek content books)

thanks very much
steve

 

[Bernoull]

for some reason I understand TPR but not Ek even though both are correct. I'll have to look over this again.

So far, when I'm trying to find the acceleration of a box down a ramp (with friction), i do the following and it works:

net force = mgsinQ - mgcosQ(Uk). Then i just get the acceleration. It's worked everytime. So when I read Ek, i understand it to mean to just use mgsinQ so I don't understand how the normal force (and thus friction) are taken into account doing it their way. Unfortunately there aren't examples in there like in TPR.

Perhaps i shouldn't use both sources........

PS (I have TPR hyperlearning 07 and the newest Ek content books)

thanks very much
steve

Physics is just physics, it's not going to change between books although some books explain some concepts better than others. With this in mind, when EK or anyone else says netforce = mgsinQ the implication is that the inclined plane is frictionless.

The net force is down the plane and causes the object to slide down (frictionless planes). Friction opposes relative motion b/t contiguous surfaces therefore when friction is present, it opposes mgsinQ and the net force (as you correctly stated) = mgsinQ-(mgcosQ*Uf); where Uf is the coefficient of friction -static or kinetic.

 

[sv3]

gotcha. Thanks. I always worry when I get things right but don't know how I did it. It makes sense now. TPR taught it with friction and Ek without and I missed the distinction. I think I also get how the normal force now plays a role in the creation of the resultant vector mgsinq although i'll look at that one more time (originally I thought only gravity played a role in that)

thanks very much, that cleared up alot for me

steve

 

[BerkReviewTeach]

So far, when I'm trying to find the acceleration of a box down a ramp (with friction), i do the following and it works:

net force = mgsinQ - mgcosQ(Uk). Then i just get the acceleration. It's worked everytime. So when I read Ek, i understand it to mean to just use mgsinQ so I don't understand how the normal force (and thus friction) are taken into account doing it their way. Unfortunately there aren't examples in there like in TPR.

thanks very much
steve

That is for a system sliding down the ramp with friction. Make sure you consider frictionless systems (where the mgcostheta(muk) drops out). Here is a good example of that from the new BR book.

View attachment 12689

 

[sv3]

That is for a system sliding down the ramp with friction. Make sure you consider frictionless systems (where the mgcostheta(muk) drops out). Here is a good example of that from the new BR book.

View attachment 12689

Talk about making me regret my TPR and Ek purchases....that explanation attached is killer! Also, the trick about testing the limits - awesome! I never even thought of that and it wasn't presented in my prep materials!I've been looking for these tips and tricks everywhere. Thanks very much! Sucks that I did chem and orgo already - wish I had visited this board first. I'm in Canada and BR is just now starting to get lots of attention up here- I was just a bit too early!

I thought the normal force cancelled out the the vertical part of the W vector but wasn't sure till I confirmed it in the explanation. Makes sense why the net force is just the mgsinq vector. I was just looking for proof instead of my own assumption

cheers!
steve

 

[Malayna]

That is for a system sliding down the ramp with friction. Make sure you consider frictionless systems (where the mgcostheta(muk) drops out). Here is a good example of that from the new BR book.

When did the new book come out, because my page 73 doesn't have that? My book doesn't have the explanations to the b-questions, which I would have really liked. That was about my only complaint about the physics books.

Talk about making me regret my TPR and Ek purchases....that explanation attached is killer! Also, the trick about testing the limits - awesome! I never even thought of that and it wasn't presented in my prep materials! I've been looking for these tips and tricks everywhere. Thanks very much! Sucks that I did chem and orgo already - wish I had visited this board first. I'm in Canada and BR is just now starting to get lots of attention up here- I was just a bit too early!

I thought the normal force cancelled out the the vertical part of the W vector but wasn't sure till I confirmed it in the explanation. Makes sense why the net force is just the mgsinq vector. I was just looking for proof instead of my own assumption

cheers!
steve

That's what I loved about the BR books so much. They give two explanations, one based on the technical information and then the second using test strategies. I was really surprised how much those tips really helped me. I seriously think that was the difference between getting an 8 on the PS versus getting an 12 or 13 (please let my real MCAT be as good as my practice ones).