You’re standing on a normal bathroom scale in an elevator. At time t1, while the
ID: 1967601 • Letter: Y
Question
You’re standing on a normal bathroom scale in an elevator. At time t1, while the elevator is at rest, you look down and note that the scale reads 75kg. The doors close, and a few seconds later, at time t2, you look down and notice that the scale now reads 60kg. What can you say about the motion of the elevator at time t2?Question:
-What do you know about the y acceleration at t1? What does this mean for the forces in the y direction? Can you find your mass and weight?
-Given the scale reading, what do you know about the forces in the y direction at t2? What, if anything, does this tell you about the elevator’s position? What about velocity? What about acceleration?
Explanation / Answer
let T be the tension on the elevator cable, a be the acceleration of the man/lift
net force = T-mg,when the body is moving up with an acceleration
ma=T-mg, T = mg+ma, when body moves up
mg-T=ma, when body moves down with an acceleration
T=mg-ma=m(g-a)
The body of the man exerts the same force on the ground of the elevator,as both the man and the elevator moves together. and this force is the reading shown on the scale.
as the reading is lesser than when it is at rest, clearly the body is moving down with an acceleration(2nd case)
m=72kg ...reading shown when rest
force on the scale=72g when rest, 60g when moving
mg-ma = 60g
72g-72a=60g
12g=72a
a=0.167m/s2
the lift is moving downwards with an acceleration of 0.167 m/s2
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