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402-H: Elevators 1: Drawing a Free-Body Diagram Given Acceleration of an Elevator

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402-H: Elevators 1: Drawing a Free-Body Diagram Given Acceleration of an Elevator

BACK to Ladder Quantitative Dynamics (Newton's Second Law)

In levels 1 and 2, we have learned to use free-body diagrams and Newton's Second Law. Here on level 3, we will use problems where you need to identify individual forces using the principles of those forces. For these problems, regarding a person inside of an elevator, there are only two forces involved: gravity and normal force, but you need to understand each force in order to use it.

You may have completed some of the block dragging problems already. In these problems, the magnitude normal force is equal to the magnitude of gravitational force of the block. However, this is not always the case. Rather, there is a procedure for finding the magnitude of normal force that requires you to know the net force first. In these problems, we will begin using that procedure.

Forces Involved

For someone riding an elevator, there are always two forces acting on them: The force of gravity is acting downward and the normal force is acting upward. Gravity, always has the same force, but the normal force acn be greater or lesser, so it looks something like this:

Other Principles

  1. Newton's Second Law is crucial towards understanding these elevator problems. Note that the direction of the net force is always the same as the direction of the acceleration.

    $$ \Sigma F = m a $$

  2. Newton's First Law states that whenever an object is not moving or moving at a constant velocity, the net force acting on that object is zero.
  1. Esther is standing in an elevator. Ester has a mass of 80.0 kg. The elevator is moving downwards and is accelerating upwards at a rate of 0.200 m/s2.
    1. What is the magnitude and direction of net force acting on Esther?
  2. Edgar is standing in an elevator. Edgar has a mass of 70.0 kg. The elevator is moving downwards and is accelerating downwards at a rate of 0.400 m/s2.
    1. What is the magnitude and direction of net force acting on Edgar?
  3. Esther is standing in an elevator. Esther has a mass of 64.0 kg. The elevator is moving downwards and is accelerating downwards at a rate of 0.900 m/s2.
    1. What is the magnitude and direction of net force acting on Esther?
  4. Ezekiel is in the elevator. Ezekiel has a mass of 68.0 kg. The elevator is moving upwards and accelerating upwards at a rate of 0.800 m/s2.
    1. What is the magnitude and direction of net force acting on Ezekiel?
  5. Eddie is standing in an elevator, and the elevator is not moving. Eddie has a mass of 70.0 kg.
    1. What is the net force acting on Eddie? How do you know?
  6. Evelyn is standing in an elevator. It is moving upward at a constant velocity. Evelyn has a mass of 60.0 kg.
    1. What is the net force acting on Evelyn? How do you know?

    BACK to Ladder Quantitative Dynamics (Newton's Second Law)

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