Measuring Friction between two surfaces Free Body Diagram Weight Brick Normal Force Friction Pull Force Reaction Surface Coefficient of friction = Pull Force/ Normal Force (weight) 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.

Measuring Friction between two surfaces Weight = 20 newtons = normal force Pull force for smooth board = 5 newtons Coefficient of friction = u = 5/20 = 0.25 AMA = 20/5 = 4 IMA = 1 Work in = pull force / distance moved Work out = weight X height moved = 0 Efficiency = work out/work in = 0 Efficiency = is meaningless because we did not lift the weight

Inclined Planes for High School & College Students Validation requires measurements of pull force, weight & distances Pull Force Normal Force C = Hypotenuse B = Height Friction Force a Reaction Force a A = Horizontal Distance a = angle Weight Free Body Diagram Showing vectors for forces Friction Force and component of weight Uphill Pull Force = u X Weight X Cos a + Weight X Sin a u = Frictional Force/Normal Force = Frictional Force/ Weight, for a = 0 A= Horizontal distance, B = Height, C= Hypotenuse a = angle IMA = C/B = 1/ Sin a; AMA = Weight/Pull Force; efficiency = AMA/IMA Pull Force / Weight = u Cos a + Sin a; Reaction = Normal Force Downhill Release Force = u X Weight X Cos a – Weight X Sin a If Downhill Release Force = 0, then u = Tan a.

Lever as a Simple Machine Free Body Diagram {Vertical Distance weight moved} d a b c Weight Fulcrum Force {Vertical Distance moved by applied force} IMA = a/b; AMA = Weight/ Applied Force, efficiency = AMA/IMA From Geometry, b/a = d/c because of similar triangles. Efficiency = work out/work in = W X d/Force X c = AMA / a/b = AMA/IMA

Physics Curriculum for Simple Machines Calculating IMA, AMA and efficiency Beam Beam Beam Brick Brick Brick Two pulley system IMA = 2 (theory) AMA and IMA to be measured Single pulley system to measure friction IMA = 1 Four pulley system IMA = 4 (theory) AMA and IMA to be measured IMA & AMA is to be determined by the students and may disagree with theory because of friction of pulleys. Efficiency = AMA/IMA

Physics Curriculum for Simple Machines Calculation of Tension w/o friction T=W/2 Beam Beam Beam T=W/4 T= W/4 T=W/4 T=W/2 T= W/2 T = W/2 Weight Weight Weight Pull tension = W Pull tension =W/2 Pull tension = W/4 IMA = 2 IMA =1 IMA = 4 Presence of friction increases pull tension

Catapult as a Simple Machine Free Body Diagram IMA = a/b; Pull X a = Force X b; AMA = Force/Pull; eff = work out/work in = Force X b/Pull X a = AMA/IMA Energy transferred = ½ X m V 2 (to object in cup) ;potential energy of spring = ½ k x2 Eff = ½ mv 2 / ½ k x2 Cup k = spring constant (to be measured) Pull k is in lbs/ft a m = mass of object in cup in slugs v = velocity in ft/sec x = displacement of spring in feet Fulcrum b Spring Force Base

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 feet K = spring constant = 161.6 lbs/0.166 feet = 973.5 lbs/foot AMA = Force on Spring/Pull Force = 161.6 lbs/21.1 lbs = 7.66 IMA = 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 Sum of all vertical forces = 0 Sum of horizontal forces = 0 Sum of all angular forces = 0 F1 = u N1 , N1 = P F2 = u N2 , N2 = W Cos a F3 = u N3 , N3 = W F1 N1 W N2 F2 F2 N2 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 a P = W (Sin a + u + u Cos a) W = 20 newtons, a = 4.67 deg, u = 0.25 P = 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%