Where have you seen an inclined plane used before?

January 5, 2009

DRILL

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1. To understand and calculate Mechanical Advantage (MA) for various simple mechanisms

2. To review 3D Quiz 2

3. To know and apply the three simple mechanisms based on the inclined plane

TODAY’S OBJECTIVES

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MECHANICAL ADVANTAGE

FORCE MULTIPLIERS

FL

DL DF

For All Lever Classes

What are the units for MA?There are no units – it’s a ratio

DFDL

M.A.= LF

=

MA is the number of times a mechanical device multiplies

the Applied Force

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You now have 2 equations:

L x DL = F x DF

DF L

DL F

FORCE MULTIPLIERS

=

Hint: They’re really the same equation rearranged

• Machines are… – artifacts that transmit or change the application of power,

force, or motion.

• What is an artifact?– something created by humans usually for a practical

purpose.

• Machines can be simple or complex– Complex machines are comprised of…. Simple Machines

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• Simple machines work on 2 basic principles:

LEVER

INCLINED PLANE

Principle: a law of nature underlying the working of an artificial device

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• There are 3 classes of lever:

Third Class

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1. A 1st-class lever is used to lift a bureau that weighs 80 lbs. The bureau is located 3 feet from the fulcrum. A child who applies the force to the other side of the lever has only 20 lbs. of strength to push. How far from the fulcrum should the child apply the force? (HINT: Sketch a picture, list the given information, write your equation, and solve for the unknown)

80 lbs.

3 ft. DF = ?

F = 20 lbs.

L = 80 lbs.

DF = ?

DL = 3 ft.

F = 20

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80 lbs.

3 ft. DF = ?

F = 20 lbs.

L = 80 lbs.

DF = ?

DL = 3 ft.

F = 20L x DL = F x DF

80 lbs x 3 ft = 20 lbs x DF

240 ft-lbs = 20 lbs x DF

20 ft 20 ft

DF = 12 ft U3d-L8

80 lbs.

3 ft. DF = ?

F = 20 lbs.

L = 80 lbs.

DF = ?

DL = 3 ft.

F = 20

DF = 12 ft

What is the Mechanical Advantage of this lever?DF

DLM.A.=

12 ft. 3 ft.

= 4=

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80 lbs.

3 ft. DF = ?

F = 20 lbs.

L = 80 lbs.

DF = ?

DL = 3 ft.

F = 20 lbs.

DF = 12 ft

MA = 4

What does

F x MA = ?LU3d-L8

2 ft 2 ft

2. A gardener is capable of applying 40 lbs. to lift a wheelbarrow. Her hands are placed 3 feet from the axle of the wheelbarrow. The weight of the compost that she carries is 2 feet from the axle of the wheelbarrow. What is the maximum weight of compost she can carry?

L =

DL =

F =

DF =

?

2 ft.

40 lbs.

3 ft.

L x DL = F x DF

L x 2 ft = 40 lbs x 3 ft

L x 2 ft = 120 ft-lbs

L = 60 lbs.

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80 lbs.

3 ft. DF = ?

F = 20 lbs.

L = 60 lbs.

DF = 4 ft.

DL = 2 ft.

F = 30 lbs.

What is the Mechanical Advantage of this lever?DF

DLM.A.=

4 ft. 2 ft.

= 2=

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This problem is asking 2 questions. What are they?

L =

DL =

F1 =

DF =

20 lbs.

20”

25 lbs.

?

25 lbs 25 lbs

L x DL = F x DF

20 lbs x 20” = 25 lbs x DF

400 in-lbs = 25 lbs x DF

DF = 16”

DL = 20”DF = 16”

3. A water pump at the State Park is set up as a 3rd-class lever. The load that the suction inside the pump weighs is 20 lbs. The distance from the load to the fulcrum is 20 inches. The park ranger is wondering where an adult who can apply a force of 25 lbs. should put her hand to lift the pump. The ranger is also wondering where another adult who can apply a force of 10 lbs. should put her hand to lift the pump.

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L =

DL =

F1 =

DF =

20 lbs.

20”

10 lbs.

?

10 lbs 10 lbs

L x DL = F x DF

20 lbs x 20” = 10 lbs x DF

400 in-lbs = 10 lbs x DF

DF = 40”

DL = 20”DF = 40”

3. A water pump at the State Park is set up as a 3rd-class lever. The load that the suction inside the pump weighs is 20 lbs. The distance from the load to the fulcrum is 20 inches. The park ranger is wondering where an adult who can apply a force of 25 lbs. should put her hand to lift the pump. The ranger is also wondering where another adult who can apply a force of 10 lbs. should put her hand to lift the pump.

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M.A. = Radius (D) to Force (F) = DF

Radius (D) to Load (L) DL

• Rotary Motion • the circular motion which occurs when the wheel and

axle are rotated about the centerline axis. • Linear Motion

• the straight-line motion which occurs when a wheel rolls along a flat surface. The linear distance traveled when the wheel completes one revolution is equal to the circumference of the wheel.

Circumference = Pi * Wheel diameter U3d-L8

WHEEL AND AXLE

• 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.

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PULLEY

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M.A. = Total number of strands supporting the load

MA = L / F

PULLEY

• Fixed Pulley – when a pulley is attached or fixed to a strong member, which will not move.

• How many strands are supporting the load?

• What is the MA of a fixed pulley?

• How many lbs of force are required to lift 100 lbs of load?

• When a fixed pulley is used, the force needed to lift a weight does not change.

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11

100

PULLEY

• Movable Pulley – splits the work in half.• How many strands are supporting the load?• What is the MA of a movable pulley?• How many lbs of force are required to lift 100 lbs of load?• When a movable pulley is used, the force needed to lift a

load is half that of the load.

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2

50

2

PULLEY

• Block and Tackle – a system of three pulleys• How many strands are supporting the load?• What is the MA of a movable pulley?• How many lbs of force are required to lift 120 lbs of load?• When a block and tackle is used, the force needed to lift a

load is 1/3 that of the load.

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40

33

PULLEY

• 3 Categories of simple machines based on the principle of the INCLINED PLANE:

INCLINED PLANE

Inclined Plane Wedge Screw

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• Inclined Plane – sloped surfaces used to make a job easier– Easier to go up a slope than a vertical surface

• Wedge – used to split, separate, and grip– Wood chisel, firewood axe, doorstop

• Screw – an inclined plane wrapped around a shaft– 1/2-inch x 12 machine screw

• ½” diameter• 12 threads per inch

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• The inclined plane is the simplest machine of all the machines.

• An inclined plane is a flat sloping surface along which an object can be pushed or pulled. An incline plane is used to move an object upward to a higher position.

H

D

L

F

M.A.= Distance = D

Height H

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Effort

Wedge -Comparison to the Inclined Plane

Inclined Plane

Effort

Wedge

Wedges can be single or double:

Single Double

L

H

L

H

FORCE

Effort

Wedge -Comparison to the Inclined Plane

Inclined Plane

Effort

Wedge

Wedges can be single or double:

Single Double

L

H

L

H

FORCE

1. During its use, an inclined plane remains stationary, while the wedge moves.

2. With an inclined plane the effort force is applied parallel to the slope of the incline.

3. With a wedge the effort force is applied to the vertical edge (height) incline.

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D

HM.A.=

Effort

Wedge -Comparison to the Inclined Plane

Inclined Plane

Effort

Wedge

Wedges can be single or double:

Single Double

L

H

L

H

FORCE FORCE

DD

H H

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Complete the Simple Mechanism Problems worksheet