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Question

A student stands on a bathroom scale in an elevator AT REST on the 64th floor of a building. The scale reads 836N

As the elevator moves up, the scale reading increases to 936N, then decreases back to 836N.

Find the acceleration of the elevator.

plz help, and explain if you can
thank you!

Answer 1

Correct equations are written in one of the answers. Here I try to explain how the quations come about. Scale shows the reaction of the floor to student's legs/body. What are the real forces of interaction acting on his legs/body? One gravity due to earth. This is 836 N as measured when at rest. Another is reaction of the scale as the spring in the scale is compressed. This is measured as 936 N. In the beginning the elevator has to accelerate otherwise it cannot gain velocity. Note that 836 N act downward as it is due to earth and 936 N act upwards as it is due to compressed spring. It is the difference of these two forces which gives the student upward acceleration a.

So we have 936 - 836 = m a.

Now you may be wondering how to know m , it is given by the condition of rest or of uniform velocity either upward or downward. Because then the force due to earth is balanced by
the reaction of the spring upward

836 = m g

Also note that there has to be acceleration upward in the beginning otherwise how does it gain velocity.

Now you may be wondering this is students acceleration and not of the elevator but that acceleration is common. Then the data supplied is of teh student's not elevator's

Answer 2

At rest.
W= m*g.
In the elevator ascending.
W= m*(g + a)
In the elevator descending.
W = m*(g - a)
Where, W is weight, g acceleration of gravity 9,81 m/sec^2.
m = mass
a = elevator's acceleration.
Solve this equations and you will find the elevator's acceleration.

Answer 3

you need force = mass x acceleration

at rest you have 836 = M x 10 (let's assume earth gravy is 10)
M = 83.6

when accelerating, you have 936 = 83.6 x A

so A = 11.2

but 10 of that is due to earth gravy, so the other 1.2 is due to the elevator