A person of mass equal to 600 kg stands in an elevator a Det

A person of mass equal to 60.0 kg stands in an elevator.

a) Determine the magnitude and direction of the force of the floor of the elevator on the person’s feet as the elevator travels upward with constant velocity.

b) Determine the magnitude and direction of the force of the floor of the elevator on the person’s feet as the elevator travels upward with acceleration equal to 2.00 m/s².

c) Assume the elevator accelerates downward for 2.0 seconds and travels 6.0 m in that time. Determine the magnitude and direction of the force of the floor of the elevator on the person’s feet while it is accelerating.

d) Assume the elevator goes into free fall. What is the magnitude and direction of the force of the elevator floor on the person’s feet? Do not do a calculation, just state and justify your answer.

Solution

a.) For the elevator moving upwards with constant velocity, the floor would have been only balancing the weight of the person.

That is, the force it would apply on the feet would be upwards and of magnitude 60g = 588.6 N

b.) Now for acceleration upwards, the elevator\'s floor would balance the weight of the person, plus, it would also push it up so as to accelerate the person upwards with it.

net force would still be upwards and equal to 60(g + a) = 708 N

c.) While acceleration downwards, the floor would be exerting an upwards force on the feet, however, it would let the person accelerate downwards with 2 m/s^2 under the effect of gravity.

hence, the net force on the feet would be upwards and equal to 60(g - a) = 468.6 N

d.) As the elevator goes in a free fall, it would offer no upward force on the person\'s feet and would allow him to accelerate freely under the effect of gravity. Hence the force on the feet by the floor would be zero.

NOTE: It would be convenient to imagine yourself in an elevator moving upwards and downwards. You would feel a similar effect in a flight while take off and landing. The body of the elevator would push you up with increased forced while accelerating you upwards. While accelerating, downwards, it would let you accelerate downwards however with an acceleration lesser than the gravitaional acceleration, unless it is not in free fall.