A 96.4-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 1.86 m/s2, (b) moving upward at a constant speed
To determine the apparent weight of a person in an elevator, we need to consider the two cases separately: when the elevator is accelerating and when the elevator is moving at a constant speed.
(a) When the elevator is accelerating upward with an acceleration of 1.86 m/s^2:
The apparent weight of the person in this case can be calculated using 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. In this case, the net force is the difference between the person's actual weight (mg) and the normal force exerted by the scale.
1. Determine the actual weight of the person:
Weight = mass * gravity
Weight = 96.4 kg * 9.8 m/s^2 ≈ 944.72 N
2. Calculate the net force:
Net force = mass * acceleration
Net force = 96.4 kg * 1.86 m/s^2 ≈ 179.304 N
3. Calculate the apparent weight:
Apparent weight = actual weight - net force
Apparent weight = 944.72 N - 179.304 N ≈ 765.416 N
Therefore, the apparent weight of the person when the elevator is accelerating upward with an acceleration of 1.86 m/s^2 is approximately 765.416 N.
(b) When the elevator is moving upward at a constant speed:
When the elevator is moving with a constant velocity, the acceleration is zero. Therefore, the person experiences a normal force equal to their actual weight.
In this case, the apparent weight of the person is equal to their actual weight:
Apparent weight = actual weight = 944.72 N
Therefore, the apparent weight of the person when the elevator is moving upward at a constant speed is 944.72 N.