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Question

A man of mass 50kg is standing in an elevator. If the elevator is moving up with an acceleration g3 then what is the work one by normal reaction of the floor of the elevator on the man when elevator moves by a distance 12m? g=10m/s2


A

8000 J

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B

6000 J

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C

4000 J

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D

2000 J

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Solution

The correct option is A

8000 J


Step 1: Given

Mass of the man: m=50kg

Distance moved by lift: d=12m

Acceleration due to gravity is g.

Acceleration of the lift: aL=-g3 (negative because the lift is going upwards, moving against earth's gravity)

The resultant acceleration is a.

Work done is W.

Step 2: Formula used

  • F=m×a
  • W=F×d

Step 3: Find the resultant acceleration by subtracting the acceleration of lift from acceleration due to gravity.

a=aL-g=-g3-g=-g3-g=-4g3

Step 4: Find the force using the formula and substitute the value of g and m (Take only the magnitude of acceleration as the negative sign only indicate direction and have no affect on value).

F=m×a=50kg×4g3m/s2=50kg×4×103m/s2=20003N

Step 5: Find the work done using the formula

W=F×d=20003N×12m=8000J

Hence, option (A) is correct.


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