Transcript U3-2 ME 2 - Pulleys_ Gears

Get out Work problem sheet
(we are going to review #4)
What Classes of Lever Do You See?
Unit 3: Engineering Design
Topics in Mechanical Engineering
1.
Simple Machines
Lever, Wheel-and-axle, Pulley, Inclined Plane, Wedge, Screw
2.
3.
4.
Gears and Belts
Cams, Pistons, and Cranks
Other Mechanisms
LEVERS
1.
Conditions for Static Equilibrium
2.
SF = 0 – Sum of Forces equals 0
SM = 0 – Sum of Moments equals 0
3.
F x dF = L x dL
1.
2.
3 Classes
3.
Mechanical Advantage: the # of times a system multiplies
the applied force.
MA = L / F = dF / dL
LEVERS
1.
If MA = 4…
1.
What does this tell us about the relationship between L and F?
The system multiplies F by 4, so L is 4x F
2.
What does it tell us about the relationship between dF & dL?
dF is 4x greater than dL. In other words, F needs to travel 4
times as far as L.
3.
Conservation of Energy
Work performed by L must equal Work performed by F
4.
Force Multiplier: pays for it by travelling greater distance
5.
Distance Multiplier: pays for it by requiring greater force
INCLINED PLANE
1.
Inclined Plane
Slanted surface used to raise an object
2.
3.
4.
Wedge
Screw
Conservation of Energy: W1 = W2
1
2
PULLEYS
• Wheel-and-Axle is in the family of levers:
Pulley
Tire on Road
• MA, F, L, df, dL
• Other examples of uses?
Steering Wheel
PULLEYS
1st Class
2nd Class
3rd Class
PULLEYS
• A pulley is an adaptation of a wheel and axle.
• A single pulley simply reverses the direction of a force.
• When two or more pulleys are connected together, they
permit a heavy load to be lifted with less force.
• The trade-off is that the end of the rope must move a greater
distance than the load.
PULLEYS
M.A. = Total number of strands supporting the load
MA = L / F
PULLEYS
Fixed Pulley – when a pulley is attached or fixed to a strong
member, which will not move.




How many strands are supporting the load? 1
What is the MA of a fixed pulley? 1
How many lbs of force are required to lift 100 lbs of load? 100
When a fixed pulley is used, the force needed to lift a weight
does not change.
PULLEYS
Movable Pulley – splits the work in half.




How many strands are supporting the load? 2
What is the MA of a movable pulley? 2
How many lbs of force are required to lift 100 lbs of load? 50
When a movable pulley is used, the force needed to lift a load
is half that of the load.
PULLEYS
Block and Tackle – a system of two or more pulleys
usually used to lift or pull heavy loads.




How many strands are supporting the load? 3
What is the MA of a movable pulley? 3
How many lbs of force are required to lift 120 lbs of load? 40
When a block and tackle is used, the force needed to lift a load
is 1/3 that of the load.
GEARS & BELTS
SPEED
1.
2.
3.
Which point on this circle travels fastest?
What is an equation for speed/velocity?
v=d/t
In one rotation, how far has each traveled?
d = C = pD
1
2
3
GEARS & BELTS
FORCE
1.
2.
The Force is multiplied the larger the wheel, for 2nd class system
The distance required to travel is greater, for 2nd class system
2nd Class
GEARS & BELTS
BICYCLE EXAMPLE – Front Sprocket
1.
2.
3.
4.
We have 3 different “gears” attached to the pedal
Where is F applied? Where is resistance L?
In order of greatest MA to least:
1, 2, 3 – why?
MA = L / F = dF / dL
In order of greatest v to least:
3, 2, 1 – why?
5.
1
2
3
GEARS & BELTS
BICYCLE EXAMPLE – Rear Sprocket
1.
2.
3.
4.
We have 4 different “gears” attached to the rear sprocket
Where is F applied? Where is resistance L?
In order of greatest MA to least:
4, 3, 2, 1
In order of greatest speed to least:
1, 2, 3, 4
1
2
3
4
GEARS & BELTS
BICYCLE EXAMPLE
How does the force required and the speed (distance) alter?
1
2
3
4
1
2
3
GEARS & BELTS
BELTS and CHAINS
Connecting two wheels (or gears) of equal or different diameter
(circumference).
Rotation is in SAME direction for both
GEARS & BELTS
How gears and belts control movement depends on:
The sizes of the two connecting wheels
GEARS & BELTS
CIRCUMFERENCE
1.
How do you measure the circumference of a circle?
1.
2.
3.
2.
Flexible measuring tape
C = pD
Count teeth
1.
20 – small
2.
30 – large
Gear Ratio
1.
1.5:1, master to slave
GEAR VIDEO 1
GEARS & BELTS
GEAR RATIO
What is the gear ratio of this system?
What does this tell us?
GEAR VIDEO 2
Lever Problems
1.
2.
3.
4.
A user is capable of applying 80 lbs. to a 1st-class lever. The
mechanical advantage of the user’s current lever setup is 3.
What is the maximum load the user is capable of lifting?
A gardener is capable of applying 70 lbs. to lift a wheelbarrow.
His hands are placed 4.25 feet from the axle of the
wheelbarrow. The weight of the compost that he carries is 2.5
feet from the axle of the wheelbarrow. What is the maximum
weight of compost he can carry? What is the mechanical
advantage of this setup?
A 3rd-class mechanical lever is used to remove snow without
damaging the paved surface beneath it. The machine is capable
of applying 600 lbs of force. The distance from the load to the
fulcrum is 8 feet. The distance from the applied force to the
fulcrum is 4 feet. What is the maximum amount of snow the
machine can move at one time? What is the mechanical
advantage of the machine?
What is the maximum mechanical advantage of a third-class
lever?
Pulley Problems
1.
2.
3.
A fixed pulley system is used to lift a
bucket from a well. How many pounds of
force are required to lift 60 pounds of
water?
A movable pulley system is used to
accomplish the same task as in #1 above.
How many pounds of force are required?
A block-and-tackle pulley system is used
to accomplish the same task as in #1
above. How many pounds of force are
required?