- #1
smsport
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Ʃ
A car of mass 2,000 kg is moving round a curve on a
banked track (see diagram-We were actually only given the top picture "a" and not the bottom one, but both are relevant) at a constant speed. The
coefficient of static friction between the car's tires and
the track is μs = 0.140. The radius of curvature of the
car's path is r = 200m, and the angle of bank of the track
is θ = 10.0o . Showing all your work, find the speed
that the car must travel such that the force of static
friction parallel to the slope is zero.
Ʃ Fx= Fnx= Fnsin10=Fc = mv^2/r (No Ffrictionx because it should =0) Equation #1
Ʃ Fy= Fny -Ffrictiony-mg=0
Ffrictiony= 0.140 sin 10
Fny= Fncos10
ƩFy= Fncos10-0.140Fnsin10=mg Equation #2
Divide equation 1 by equation 2:
(mv^2/r =Fnsin10)/(mg=Fn(cos10-0.140sin10):
m's cancel and Fn's cancel then solve for v:
v=√(rg(sin10/cos10-0.140sin10)
v=18.8 m/s
My question is this: I understand that the so-called design speed is the speed a car can get around the track without friction and that this is expressed as v=√(rgtan theta) because there is no element of friction to use. For the problem above, I initially solved it using this simpler "design speed" formula and got an answer very close to my answer above. However, close is not necessarily right! I looked at the question again and figured that since the coefficient of static friction was given that I needed to include the Ffriction in the y direction. Am I right on this?
I am finding banked curve free body diagrams with friction to be confusing. There seem to be so many elements and it's hard to keep track. I also have some difficulty understanding the X and Y directions of friction as for what they really mean. I get that the x direction in this problem involves the Fnx as the only force acting as the centripetal force only because the problem states that the x direction static friction is zero. If it didn't and was perhaps asking for the min speed it could go around curve w/o slipping then I would have Fstaticfriction in the opposite direction as Fnx (ie: static friction away from center)? I am having a hard time wrapping my brain around these banked tracks problems.
Am I at least on the correct path with how I worked the problem above?
Thanks!
Homework Statement
A car of mass 2,000 kg is moving round a curve on a
banked track (see diagram-We were actually only given the top picture "a" and not the bottom one, but both are relevant) at a constant speed. The
coefficient of static friction between the car's tires and
the track is μs = 0.140. The radius of curvature of the
car's path is r = 200m, and the angle of bank of the track
is θ = 10.0o . Showing all your work, find the speed
that the car must travel such that the force of static
friction parallel to the slope is zero.
Homework Equations
Ʃ Fx= Fnx= Fnsin10=Fc = mv^2/r (No Ffrictionx because it should =0) Equation #1
Ʃ Fy= Fny -Ffrictiony-mg=0
Ffrictiony= 0.140 sin 10
Fny= Fncos10
ƩFy= Fncos10-0.140Fnsin10=mg Equation #2
The Attempt at a Solution
Divide equation 1 by equation 2:
(mv^2/r =Fnsin10)/(mg=Fn(cos10-0.140sin10):
m's cancel and Fn's cancel then solve for v:
v=√(rg(sin10/cos10-0.140sin10)
v=18.8 m/s
My question is this: I understand that the so-called design speed is the speed a car can get around the track without friction and that this is expressed as v=√(rgtan theta) because there is no element of friction to use. For the problem above, I initially solved it using this simpler "design speed" formula and got an answer very close to my answer above. However, close is not necessarily right! I looked at the question again and figured that since the coefficient of static friction was given that I needed to include the Ffriction in the y direction. Am I right on this?
I am finding banked curve free body diagrams with friction to be confusing. There seem to be so many elements and it's hard to keep track. I also have some difficulty understanding the X and Y directions of friction as for what they really mean. I get that the x direction in this problem involves the Fnx as the only force acting as the centripetal force only because the problem states that the x direction static friction is zero. If it didn't and was perhaps asking for the min speed it could go around curve w/o slipping then I would have Fstaticfriction in the opposite direction as Fnx (ie: static friction away from center)? I am having a hard time wrapping my brain around these banked tracks problems.
Am I at least on the correct path with how I worked the problem above?
Thanks!