How to Calculate Fn, Highest Point, and Acceleration on an Inclined Plane?

[killerinstinct]

Inclined Plane Problem.

An object of mass M is positioned on an inclined plane with an angle theta. A force of Fp parallel to the base of inclined plane and opposite of the object's x motion is acted upon the object. Suppose there is friction of Uk between the object and inclined plane, and suppose that the force will make the object go up the inclined plane slightly, calculate Fn, the highest point, and acceleration at the end of the inclined plane as it comes down, in terms of m, Fw, sin, cos, Ff, theta, etc.

Preferably using real physics. if not, derived physics, and cosine!

 

[killerinstinct]

okay i understand an downward inclined plane problem.
Fw sinx - Ff = mgsinx - u.k mg cosx = mg (sinx-ukcosx) = Fnet
a = Fnet/m = g(sinx -uk cosx)

but how do you do it when a force is applied parrallel to the base against the natural motion of the object? Physics III problem...

 

[Diane_]

OK, I'm not quite following this problem. You have an object on an inclined plane, with the coefficient of friction (presumably kinetic friction) between it and the plane of Uk. That much I get. Now - you're going to impose a force on the object which acts "parallel to the base of the plane" - does that mean horizontal? In that case, the force will have components both into the plane (normal to it) and parallel to the plane (pushing the object upwards along the plane). Clearly, then, the applied force will both tend to move the object upwards along the plane and will increase friction with the plane. Do I have this right?

Beyond that, you say it makes the object go up the plane "slightly". That is too vague to work with. Perhaps it means that the force is just enough to cause the object to move upwards along the plane? In that case, we can calculate a limiting value - i.e. what is the largest such force that will not cause the object to move. In that case, we could then say that the actual applied force must be larger than that.

Next - you're talking about the "highest point" and the acceleration as the object comes back down. If the force we've discussed continues to be applied, the object will never come back down, unless we know the height at which the plane ends and we're talking about pushing it off the top. If the object does come back down, then we must at some earlier point cease to apply the force that pushed it up the plane to begin with, but you give no information on when or how that happens. This would appear to be insoluable.

Lastly - you say you'd rather we use "real" physics instead of "derived" physics, and I am at a loss as to what that means.

 

[killerinstinct]

Yes, you've interpreted the problem very well. Exactly what you said in the previous post!
Use "real" physics and not some kind of memorized math equation...

 

[Diane_]

I'm still not sure what constitutes "real" physics, unless you mean physical reasoning. Physical reasoning will give you a good qualitative answer, but you're going to have to use the mathematical models to get any quantitative results.

Anyway - this one will work like any inclined plane problem. Draw a free body diagram of the object, including all of the forces that act. Resolve those forces into a convenient set of coordinate axes - I would suggest parallel to and perpendicular to the plane. Those forces will then be orthogonal to each other, so write the net force in each direction as the vector sum of the appropriate components. There will be some overlap - as, for instance, the fact that the frictional force, which acts parallel to the plane, depends on the normal force which is (obviously) perpendicular to the plane. Those overlaps mean you should end up with a set of simultaneous equations - most likely two equations in two unknowns. Solve them as you would any math problem.

Is that sufficient?