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Chapter 9 - Simple Machines

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Chapter 9 - Simple Machines

9.2 Mechanical Advantage

pp. 210-216

- Mechanical advantageis the ratio of output force to input force.

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

Output force (N)

MA = Fo

Fi

mechanical

advantage

Input force (N)

- A lever includes a stiff structure (the lever) that rotates around a fixed point called the fulcrum.

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

- Each class of levers is defined by the location of the input and output forces relative to the fulcrum.

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

- 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.

Number of teeth

on input gear

To=Ni

Ti No

Turns of output gear

Turns of input gear

Number of teeth

on output gear

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

- 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.

- A screwis a rotating ramp.
- You find the mechanical advantage of a screw by dividing its circumference by the lead.

- A wedgeis 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.

- 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.

- 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?

- 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

- M.A. = Length of input arm
- Solution
- M.A. = 40 cm ÷ 2 cm = 20

- Complete “Your Turn” problems on p. 215
- Complete Skill Sheet