A 62-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 843 N. What is the acceleration of the elevator?
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To find the acceleration of the elevator, we need to use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, the net force acting on the man in the elevator is equal to the weight of the man, which can be calculated using the formula: weight = mass * gravitational acceleration (W = m * g).
Given that the mass of the man is 62 kg, we can calculate his weight as follows: weight = 62 kg * 9.8 m/s^2 (acceleration due to gravity) = 607.6 N.
Now, when the elevator is rising, the scale reading of 843 N includes both the weight of the man and the upward force exerted by the elevator, which we need to determine.
Let's denote the upward force of the elevator as F_e.
Since the scale reading is 843 N, we can set up the following equation: F_e + weight = 843 N.
Substituting the known values, we get: F_e + 607.6 N = 843 N.
To solve for F_e (the upward force of the elevator), we subtract the weight from both sides of the equation: F_e = 843 N - 607.6 N.
Calculating this, we find that F_e = 235.4 N.
Finally, to find the acceleration of the elevator, we use Newton's second law: F_e = m * a.
Substituting the values we know, we have: 235.4 N = 62 kg * a.
To solve for the acceleration, we divide both sides of the equation by 62 kg: a = 235.4 N / 62 kg.
Calculating this, we find that the acceleration of the elevator is approximately 3.79 m/s^2.