Measuring Friction between two surfaces
Free Body Diagram
Weight
Normal Force
Brick
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
Normal Force
Friction Force
a
a = angle
Free Body Diagram
Showing vectors for
forces
Pull Force
C = Hypotenuse
B = Height
a Reaction Force
A = Horizontal Distance
Weight
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
c
Force
a
b
d
{Vertical Distance
weight moved}
Weight
Fulcrum
{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
Brick
Beam
Brick
Beam
Brick
Two pulley system
Single pulley system Four pulley system
IMA = 2 (theory)
to measure friction
IMA = 4 (theory)
AMA and IMA to be IMA = 1
AMA and IMA to be measured
measured
IMA & AMA is to be determined by the students
and may disagree with theory because of friction
of pulleys. Efficiency = AMA/IMA
5
Physics Curriculum for Simple Machines
Calculation of Tension w/o friction
Beam
Beam
T=W/2
Beam
T=W/4
T= W/4
T=W/4
T=W/2
T = W/2
T= W/2
Weight
Weight
Pull tension =W/2
IMA = 2
Pull tension = W
IMA =1
Weight
Pull tension = W/4
IMA = 4
Presence of friction increases pull tension
6
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
Pull
Cup k = spring constant (to be measured)
k is in lbs/ft
a
Fulcrum
b
Spring
Force
Base
m = mass of object in cup in slugs
v = velocity in ft/sec
x = displacement of spring in feet
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
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
N2
•
•
F2
Angle = a
F3
N3
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%