Section 2 review
The pulley and the wheel and axle are two other categories of simple machines related to the lever. Pulleys can be used to redirect a force, and combinations of pulleys used in block-and-tackle systems can significantly multiply force. The wheel and axle multiplies force by the ratio of the wheel to axle radius. When the axle drives the wheel, the output force is reduced as a tradeoff for increased speed. Losses such as friction cause real machines to have less than 100% efficiency and lower output forces than expected from their ideal mechanical advantage. Read the text aloud
tension, pulley, block and tackle, efficiency, ideal mechanical advantage, wheel and axle, gear, gear ratio

η= W o W i
M A ideal = d i d o
M A wa = r w r a
M A g = τ o τ i = output teeth input teeth

Review problems and questions

  1. Describe the measurements and calculations that you need to make to determine the mechanical advantage of a
    1. lever,
    2. block and tackle,
    3. wheel and axle. Read the text aloud Show
  1. A force is applied to a large gear with 51 teeth. That large gear then turns a smaller gear with only 17 teeth.
    1. What is the gear ratio of the two gears?
    2. What is the mechanical advantage of the two gears?
    3. If the small gear instead were to turn the large gear, what is the gear ratio?
    4. Likewise, what is the mechanical advantage when the small gear turns the large gear? Read the text aloud Show
  1. In a car, when the steering wheel is turned it causes the steering column (the axle) to turn. Why wouldn’t you want to design the car to simply have a steering axle? Use forces in your answer. Read the text aloud Show
  1. In a winch, a crank with a radius of 50 cm is turned to cause a rope to wrap around a drum with a radius of 10 cm.
    1. What is the ideal mechanical advantage of this machine?
    2. If the winch had friction that caused the efficiency to be 60%, what would be its mechanical advantage? Read the text aloud Show

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