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Question

In a lift, when will the apparent weight become twice the actual weight?


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Solution

Step 1: Apparent weight

  1. The perceived weight of an object is a physical property that indicates how heavy it is.
  2. The apparent weight of an object differs from the weight of the object when the force of gravity acting on it is not balanced by an equal but opposing normal force.

Step 2: Working of elevator.

  1. Because inertia prefers the passenger to remain stationary, the elevator floor and scale must press upon him to propel him higher with the elevator.
  2. The scale must press upon the body with higher force in order to stimulate the person's bulk upward.
  3. When the scale and the human come closer together, something happens.
  4. Demonstrating with the help of a figure

Step 3: Analyzing

  1. As a result, the Normal Force is more powerful, and the scale reading is higher than the true weight.
  2. According to Newton's 2nd Law, F=m×a[F=Force,m=mass,a=acceleration] is operating on the person.
  3. The person's overall speed is increasing (with the elevator). As a result, ma is a positive parameter (upward).
  4. The only external forces acting on the person are gravity acting downward, W=mg, and sustaining normal force.
    while the lift is ascending at a high rate of g acceleration
  5. R=m(g+a)=m(g+g)=2mg
  6. As a result, the perceived weight becomes twice the actual weight when climbing up and speeding up (acceleration and is positive).

Hence, while going up & speeding up the apparent weight become twice the actual weight.


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