1. 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.

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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 = X 21.1 = lbs,
Displacement of spring = 2.0 inches = feet
K = spring constant = lbs/0.166 feet = lbs/foot
AMA = Force on Spring/Pull Force = lbs/21.1 lbs = 7.66
IMA = 7.66; efficiency = IMA/AMA = 100%
Energy imparted to spring = ½ k x2 = 0.5 x lbs/foot X foot X foot
= 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
= lb sec 2/feet; lbs -feet = lb. sec2 /foot X V2
V = 124 ft/sec

9. Wedge as a Simple Machine

10. Wedge as a Simple MachineF3 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

11. 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 ( X 0.996)
P = newtons; AMA = 20/11.6 =1.72
IMA = 13.75/1.125 = 12.2
efficiency = AMA/IMA = 1.72/12.2 = 14%