Upload
myra-webster
View
213
Download
1
Embed Size (px)
Citation preview
Measuring Friction between two surfaces
Pull Force
Reaction
Normal Force
Friction
Coefficient of friction = Pull Force/ Normal Force (weight)
Surface
Brick
Free Body Diagram
Since block remains on same horizontal plane, it gains no potential energy.However there is work done to overcome friction. Work = Pull Force X distance.
Weight
Measuring Friction between two surfacesWeight = 20 newtons = normal forcePull force for smooth board = 5 newtonsCoefficient of friction = u = 5/20 = 0.25 AMA = 20/5 = 4IMA = 1Work in = pull force / distance movedWork out = weight X height moved = 0Efficiency = work out/work in = 0Efficiency = is meaningless because we did not lift the weight
Inclined Planes for High School & College StudentsValidation requires measurements of pull force, weight & distances
Friction Force and component of weight
Weight
Reaction Force
Pull Force
Friction Force
Normal Force
Uphill Pull Force = u X Weight X Cos a + Weight X Sin a u = Frictional Force/Normal Force = Frictional Force/ Weight, for a = 0
aa
A = Horizontal Distance
B = Height C = Hypotenuse
A= Horizontal distance, B = Height, C= Hypotenusea = angle IMA = C/B = 1/ Sin a; AMA = Weight/Pull Force; efficiency = AMA/IMAPull Force / Weight = u Cos a + Sin a; Reaction = Normal ForceDownhill Release Force = u X Weight X Cos a – Weight X Sin aIf Downhill Release Force = 0, then u = Tan a.
Free Body DiagramShowing vectors for forces
a = angle
Lever as a Simple Machine
FulcrumForce
Weight
IMA = a/b; AMA = Weight/ Applied Force, efficiency = AMA/IMA
{Vertical Distance moved by applied force}
{Vertical Distance weight moved}
From Geometry, b/a = d/c because of similar triangles.
c
dba
Efficiency = work out/work in = W X d/Force X c = AMA / a/b = AMA/IMA
Free Body Diagram
5
Physics Curriculum for Simple MachinesCalculating IMA, AMA and efficiency
Two pulley system IMA = 2 (theory)AMA and IMA to be measured
Beam
Brick
IMA & AMA is to be determined by the students and may disagree with theory because of friction of pulleys. Efficiency = AMA/IMA
Four pulley system IMA = 4 (theory) AMA and IMA to be measured
Beam
Brick Brick
Beam
Single pulley system to measure friction IMA = 1
6
Physics Curriculum for Simple MachinesCalculation of Tension w/o friction
Beam
Weight
Beam
Weight Weight
Beam
T = W/2 T= W/2
T= W/4T=W/4
T=W/2
T=W/4
Pull tension = W/4
T=W/2
Pull tension =W/2 Pull tension = W
IMA =1 IMA = 4IMA = 2
Presence of friction increases pull tension
Catapult as a Simple Machine
Fulcrum
Spring
Cup
Base
Pull
a
Force
b
IMA = a/b; Pull X a = Force X b; AMA = Force/Pull; eff = work out/work in = Force X b/Pull X a = AMA/IMAEnergy transferred = ½ X m V 2 (to object in cup) ;potential energy of spring = ½ k x2
Eff = ½ mv 2 / ½ k x2 k = spring constant (to be measured)
m = mass of object in cup in slugs v = velocity in ft/secx = displacement of spring in feet
Free Body Diagram
k is in lbs/ft
Catapult as a Simple Machine
a = 23 inches; b = 3 inches; a/b = 7.66 = IMA; Pull = 95 NEWTONS = 21.1 lbs; Force on Spring = 7.66 X 21.1 = 161.6 lbs, Displacement of spring = 2.0 inches = 0.166 feetK = spring constant = 161.6 lbs/0.166 feet = 973.5 lbs/footAMA = Force on Spring/Pull Force = 161.6 lbs/21.1 lbs = 7.66IMA = 7.66; efficiency = IMA/AMA = 100%
Energy imparted to spring = ½ k x2 = 0.5 x 973.5 lbs/foot X 0.166 foot X 0.166 foot = 13.41 lbs-feet Energy imparted to ball = ½ m V2 = 0.5 X (0.25 newtons/4.5 newtons/lb X V2 32.2 ft/sec2
= 0.0008626 lb sec 2/feet; 13.4 1 lbs -feet = 0.0008626 lb. sec2 /foot X V2
V = 124 ft/sec
Wedge as a Simple Machine
Wedge as a Simple Machine
• F3 • N3
N1
W
F1
N2F2
F2N2
Sum of all vertical forces = 0Sum of horizontal forces = 0Sum of all angular forces = 0F1 = u N1 , N1 = P F2 = u N2 , N2 = W Cos a F3 = u N3 , N3 = W
Angle = a
Wedge as a Simple Machine
Push Force, P. has to overcome the weight, W, and two friction forces. Ignore F1. u = coefficient of friction, a= angle P = W Sin a + W u + W u Cos aP = W (Sin a + u + u Cos a)W = 20 newtons, a = 4.67 deg, u = 0.25P = 20 (0.0814 + 0.25 + 0.25 X 0.996)P = 11.6 newtons; AMA = 20/11.6 =1.72 IMA = 13.75/1.125 = 12.2 efficiency = AMA/IMA = 1.72/12.2 = 14%