Question

A 82-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.2 m/s in 0.74 s. The elevator travels with this constant speed for 5.0 s, undergoes a uniform negative acceleration for 1.4 s, and then comes to rest.

(a) What does the spring scale register before the elevator starts to move?
  N

(b) What does the spring scale register during the first 0.74 s of the elevator's ascent?
  N

(c) What does the spring scale register while the elevator is traveling at constant speed?
  N

(d) What does the spring scale register during the elevator's negative acceleration?
  N

Answer 1

a)

Before the elevator starts to move the man is at rest with no acceleration by the elevator.

Given the mass of the man,

So,The wieght of the man before the elevator starts to move is,

So,The spring scale register before elevator starts to move is the actual wieght of the man which is,

b)

Consider the motion of the elevator during the first 0.74sec time of ascent,Where the elevator starts from rest,

Here the initial velocity of the elevator,

The time taken for this motion of ascent,

The final velocity of the elevator after 0.74sec is,

Now from the Newtons 1st equation of motion,

So,The acceleration of the ascent of the elevator in 0.74sec is,

Here the elevator is moving with uniform acceleration upwards,So,Due to this upward acceleration of the elevator,a pseudoforce is exerted on the man in the opposite direction ie,vertically downward direction.

So,The apparent wieght of the man will be increases in this case where the elevator is accelerating in upward direction.(as a result of the generation of the additional pseudoforce on the man downwards along with the wieght of the man.)

So,Here the apparent wieght of the man,

So,The spring scale register shows the apparent wieght of the man ie,

the spring scale register shows,

c)

When the elevator is travelling at the constant speed,there is no acceleration on the elevator.

So,The man doesnot expirence any additional acceleration or the pseudoforce.

So,The wieght of the man in the elevator is equal to the actual wieght,ie,

So,The spring scale register shows the actual wieght of the man as,

d)

Here in this case,the elevator moving upwards with the negetive acceleration.So,Here the acceleration of the elevator in the downward direction opposing the direction of the motion.

Consider this deccelerated motion of the elevator,

SInce the body is in constant acceleration for the previous 5sec,the velocity of elevator remains same as the final velocity of the earlier accelerated case ie,1.2m/s.

So,Here the initial velocity of the elevator is,

Time taken for the motion,

Since the elevator comes to rest after 1.4s,the final velocity of the elevator,

From the Newtons 1st equation of the motion,

ie,  (Negetive sign due to negetive acceleration)

So,the acceleration of the motion,

  

So,due to this negetive acceleration of the elevator in the downward direction,the man expierience a pseuoforce in the upward direction(opposite to the acceleration of the elevator.)

Here the pseudoforce acting opposite to direction of the wieght of the man.

So,The apparent wieght of the man,

So,The apparent wieght of the man in elevator in this case,

So,The spring scale register shows the apparent wieght of the man,

ie,Spring scale rergister shows,