The force exerted on a passenger by the floor of the elevator is not to exceed 1.59 times the passenger's weight. The elevator accelerates upward with constant acceleration for a distance of 3.7m and then starts to slow down. What is the maximum speed of the elevator?

Question

badhi · Answer

Consider the forces applied on the passenger

1) The weight($Mg$)
2) The force exerted by the elevator($R=1.59Mg$)

Apply $F=ma$ to the passenger to find the maximum acceleration($a_{max}$) that passenger can get (which will be independent from M). since the elevator and the passenger are in contact, the   acceleration of the elevator should be same as the accleration of the passenger. Therefore the maximum acceleration that can be taken by the elevator is also should be $a_{max}$. Can you find the maximum velocity of the elevator from that?