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Answer :
Final answer
This force is the sum of his actual weight and the force needed to accelerate him, resulting in a total normal force of 498 N. The correct answer is a) 498 N.
Explanation:
The scale measures the normal force exerted by the man's feet on it. To calculate this force, we need to consider the forces acting on the man. At rest, the only vertical force is his weight, mg, which acts downward (where m is the mass, and g is the acceleration due to gravity, 9.8 m/s²).
When the elevator accelerates upwards, there is an additional force acting on him, the normal force from the scale, which now must overcome both gravity and the man's inertia.
Using Newton's second law, ΣF = ma, where ΣF is the sum of the forces and a is the acceleration, we find the normal force:
ΣF = ma
N - mg = ma
N = m(a + g)
Substitute the given values: m = 57 kg, a = 5.5 m/s², g = 9.8 m/s²
N = 57 kg * (5.5 m/s² + 9.8 m/s²) = 57 kg * 15.3 m/s² = 498 N
The man's weight remains constant, but the normal force increases to support his increased apparent weight due to the upward acceleration of the elevator. This force is the sum of his actual weight and the force needed to accelerate him, resulting in a total normal force of 498 N.
The correct answer is a) 498 N.
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