1. Chapter 9 - Simple Machines
9.2 Mechanical Advantage pp

2. 9.2 Mechanical advantage
Mechanical advantage is the ratio of output force to input force.

3. 9.2 Mechanical advantage Machines multiply forces.
One person could lift an elephant—quite a heavy load—with a properly designed system of ropes and pulleys!

4. 9.1 Mechanical Advantage MA = Fo Fi Output force (N) mechanical
Input force (N)

6. 9.2 The Lever
A lever includes a stiff structure (the lever) that rotates around a fixed point called the fulcrum.

7. 9.2 The Lever
Levers are useful because you can arrange the fulcrum and the input arm and output arm to adjust the mechanical advantage of the lever.

9. 9.2 The Lever
Each class of levers is defined by the location of the input and output forces relative to the fulcrum.

10. 9.2 Gears Gears change force and speed.
Many machines require that rotating motion be transmitted from one place to another.
Gears change force and speed.

11. 9.2 Designing Gear Machines
The gear ratio is the ratio of output turns to input turns.
You can predict how force and speed are affected when gears turn by knowing the number of teeth for each gear.

12. 9.2 Gear Ratios To = Ni Ti No Number of teeth on input gear
Turns of output gear
To = Ni
Ti No
Turns of input gear
Number of teeth
on output gear

13. 9.2 Tension Ropes and strings carry tension forces along their length.
If the rope is not moving, its tension is equal to the force pulling on each end.

14. 9.2 Ramps
A ramp is a simple machine that allows you to raise a heavy object with less force than you would need to lift it straight up.
The mechanical advantage of a ramp is the ramp length divided by the height of the ramp.

15. 9.2 Screws A screw is a rotating ramp.
You find the mechanical advantage of a screw by dividing its circumference by the lead.

16. 9.2 Screws
A wedge is like a ramp that can work while in motion (a ramp is always stationary).
A wedge has a side that slopes down to a thin edge.
The mechanical advantage for a wedge is inversely related to the size of the wedge angle.

17. 9.2 Wheel and axle A wheel rotates around a rod called an axle.
The mechanical advantage is the ratio of the radius of the wheel to the radius of the axle.
The wheel and axle move together to move or lift loads.

18. Solving Problems
A crowbar is a type of lever that you use to pull a nail out of a piece of wood.
If the handle of a crowbar is 40 centimeters and the foot is 2 centimeters, what is its mechanical advantage?

19. M.A. = Length of input arm Length of output arm Looking for: Given
Solving Problems
Looking for:
…mechanical advantage of lever
Given
…input arm = 40 cm; output arm = 2 cm
Relationships:
M.A. = Length of input arm
Length of output arm
Solution
M.A. = 40 cm ÷ 2 cm = 20

20. MECHANICAL ADVANTAGE Complete “Your Turn” problems on p. 215
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