Question

A pendulum clock in an elevator ticks with a period of T=1.7 s when the elevator is at rest. The elevator starts to move and the period increases to Tnew = 1.87 s.

1. How is the elevator moving? Select the correct answer:

a) accelerating, upward

b) accelerating, downward

c) constant speed, upward

d) constant speed, downward

2. Identify the correct acceleration for the elevator. You must show your work to get credit for your selection.

a) 1.7 m/s^2

b) -0.89 m/s^2

c) 2.06 m/s^2

d) 0.89 m/s^2

e) -1.7 m/s^2

Answer 1

The period of the pendulum is given by
   
where, g is acceleration due to gravity. When g decreases, the time period T increases.
And as the elevator moves downward, the effective acceleration due to gravity decreases, and so,
   
And so,

And so, we see that the time period increases.
So, option (b) is correct, i.e., the elevator is accelerating downward.

2)
And from the given values, we get
  
   
  
   
     
And so, as T' = 1.87 sec, T = 1.7 sec, g = 9.8 m/s^2, and so,
  
  
So, option (a) is correct.
Note : please be careful, whether you define the acceleration upward as positive or negative. In my convention, acceleration downward is positive, that is why the answer comes out to be positive. If you define acceleration upward as positive, then the acceleration downward to be negative. In that case, the acceleration downward will be = - 1.7 m/s^2. Please check your convention.