Problem

1 pts Question 19 You stand on a bathroom scale and it reads $40 \mathrm{~kg}$ (your mass). You put this scale in an elevator. What does it read (in $\mathrm{kg}$ ) when the elevator is just starting to move up, and the upward acceleration is 1 $\mathrm{m} / \mathrm{s}^{2}$ ?

Solution

Step 1 :Given that the mass of the object is 40 kg, the acceleration due to gravity is approximately 9.8 m/s², and the acceleration of the elevator is 1 m/s².

Step 2 :The weight of an object is given by the equation \(W = m \cdot g\), where \(m\) is the mass of the object and \(g\) is the acceleration due to gravity.

Step 3 :When the elevator is accelerating upwards, the effective gravity acting on the object is \(g + a\), where \(a\) is the acceleration of the elevator.

Step 4 :Therefore, the weight of the object in the elevator is given by \(W = m \cdot (g + a)\).

Step 5 :Substituting the given values into the equation, we get \(W = 40 \cdot (9.8 + 1)\).

Step 6 :Solving the equation, we find that \(W = 432.0\).

Step 7 :Final Answer: The scale reads \(\boxed{432}\) kg when the elevator is just starting to move up with an upward acceleration of 1 m/s².

From Solvely APP
Source: https://solvelyapp.com/problems/18260/

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