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%