Chapter 2, Problem 96RPP

Automatic sliding doors The first automatic sliding doors were described by Hero of Alexandria almost 2000 years ago. The doors were moved by hanging containers that were filled with water. Modern sliding doors open or close automatically. They are equiped with sensors that detect the proximity of a person and an electromic circuit that processes the signals from the sensors and drives the electomotor-based system that moves the doors. The sensors typically emit pulses of infrared light or ultrasound and detect the reflected pulses. By measuring the delay between emitted and received pulses, the system can determine the distance to the object from which the pulse was reflected. The whole system must be carefully designed to ensure safe and accurate functioning. Designers of such doors take into account several variables such as typical walking speeds of people and their dimensions.

Let’s try to learn more about automatic sliding doors by analyzing the motion of a single-side automatic sliding door when a person is walking through the door. Figure 2.30 shows the position-versus-time graph of the motion of the edge of the door (marked with a red cross in the photo) from the moment the door starts opening to when the door is closed while a person walks toward and through the door. The doors are adjusted to start opening when a person is 2.0 m away.

A 50-cm wide person is walking toward the door. What is the maximum walking speed of the person that will allow her to pass through the door without hitting it (assume the person aims for the opening)?

a. 0.6 m/s

b. 1.2 m/s

c. 1.7 m/s

d. 2.5 m/s