Get out Work problem sheet (we are going to review #4)

What Classes of Lever Do You See?

Topics in Mechanical Engineering

1. Simple MachinesLever, Wheel-and-axle, Pulley, Inclined Plane, Wedge, Screw

2. Gears and Belts3. Cams, Pistons, and Cranks4. Other Mechanisms

Unit 3: Engineering Design

1. Conditions for Static Equilibrium1. SF = 0 – Sum of Forces equals 02. SM = 0 – Sum of Moments equals 03. F x dF = L x dL

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 F2. 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 EnergyWork performed by L must equal Work performed by F

4. Force Multiplier: pays for it by travelling greater distance5. Distance Multiplier: pays for it by requiring greater force

LEVERS

1. Inclined PlaneSlanted surface used to raise an object

2. Wedge3. Screw4. Conservation of Energy: W1 = W2

INCLINED PLANE

12

• Wheel-and-Axle is in the family of levers:

• MA, F, L, df, dL

• Other examples of uses?

PULLEYS

Pulley Tire on Road Steering Wheel

PULLEYS

1st Class 2nd Class 3rd Class

• 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? 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.

1

1

100

PULLEYS

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.

2

50

2

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? 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.

40

3

3

PULLEYS

SPEED1. Which point on this circle travels fastest?2. What is an equation for speed/velocity?

v = d / t3. In one rotation, how far has each traveled?

d = C = pD

GEARS & BELTS

1 2 3

FORCE1. The Force is multiplied the larger the wheel, for 2nd class system2. The distance required to travel is greater, for 2nd class system

GEARS & BELTS

2nd Class

GEARS & BELTS

1

2

3

BICYCLE EXAMPLE – Front Sprocket1. We have 3 different “gears” attached to the pedal2. Where is F applied? Where is resistance L?3. In order of greatest MA to least:

1, 2, 3 – why? MA = L / F = dF / dL

4. In order of greatest v to least:3, 2, 1 – why?

5.

GEARS & BELTS

12

4

BICYCLE EXAMPLE – Rear Sprocket1. We have 4 different “gears” attached to the rear sprocket2. Where is F applied? Where is resistance L?3. In order of greatest MA to least:

4, 3, 2, 14. In order of greatest speed to least:

1, 2, 3, 4

3

GEARS & BELTS

12

4

BICYCLE EXAMPLEHow does the force required and the speed (distance) alter?

3

1

2

3

GEARS & BELTS

BELTS and CHAINSConnecting two wheels (or gears) of equal or different diameter (circumference).Rotation is in SAME direction for both

GEARS & BELTSHow gears and belts control movement depends on:

The sizes of the two connecting wheels

GEARS & BELTS

CIRCUMFERENCE1. How do you measure the circumference of a circle?

1. Flexible measuring tape2. C = pD3. Count teeth

1. 20 – small2. 30 – large

2. Gear Ratio1. 1.5:1, master to slave

GEAR VIDEO 1

GEARS & BELTS

GEAR RATIOWhat is the gear ratio of this system?What does this tell us?

GEAR VIDEO 2

1. 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?

2. 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?

3. 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?

4. What is the maximum mechanical advantage of a third-class lever?

Lever Problems

1. 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?

2. A movable pulley system is used to accomplish the same task as in #1 above. How many pounds of force are required?

3. A block-and-tackle pulley system is used to accomplish the same task as in #1 above. How many pounds of force are required?

Pulley Problems