Section 4 review
A compound machine is a machine that is made up of two or more simple machines that work together. All compound machines, from a Roman crane to the modern automobile, can be broken down into different components that fall within one of the six kinds of simple machines. Even the human body can be modeled as a compound machine; each joint in the human arm and leg acts as either a first- or third-class lever, depending on which muscle is being used. The bicycle is a compound machine. Its drivetrain is composed of a front wheel-and-axle system called the crank, a chain connecting the front and back gears, and a rear wheel-and-axle system. Read the text aloud
compound machine, biomechanics

Review problems and questions

  1. During the dissection of a human cadaver, a medical student makes the following measurements: The biceps are attached 1.25 cm below the elbow; the triceps are attached 0.8 cm above the elbow; the upper arm is 30 cm long; and the distance between the elbow and middle fingertip is 45 cm.
    1. What was the ideal mechanical advantage of the forearm when contracting the arm?
    2. What was the ideal mechanical advantage of the forearm when extending the arm?
    3. If, during a range of motion extending the arm, the upper arm had a mechanical advantage of 0.15, what was the combined mechanical advantage of the full arm? Read the text aloud Show
  1. A block and tackle with a mechanical advantage of 3.0 is used to pull a boat up a ramp. The ramp is 1.5 m high and 5.0 m long.
    1. What is the combined mechanical advantage of this arrangement?
    2. How much input force must be applied to obtain the needed output force of 3,500 N? Read the text aloud Show
  1. When early humans were hunting large game, why would small mechanical advantages of their legs be advantageous? Read the text aloud Show
  1. A bicycle’s crank has two front gears, with 39 and 52 teeth. The rear cassette has five gears, with 15, 17, 19, 22, and 25 teeth.
    1. What are all the possible gear ratios for the bicycle?
    2. What are all the possible mechanical advantages? Read the text aloud Show
  1. Nadja has the multispeed bicycle described in the last problem and is stopped at a traffic light.
    1. When the light turns green, what mechanical advantage should she use at first, low or high? What gear ratio, low or high? Which gears should she use? Why?
    2. As she goes faster and faster, what gear ratio and mechanical advantage should she use, low or high? Which gears should she use? Why? Read the text aloud Show

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