A 96.6-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 1.79 m/s2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.14 m/s2?
AWeight=mg+ma
a. m(9.8+1.79)
b. m(9.8+0)
c. m(9.8-1.14)
To find the apparent weight in different scenarios, we need to consider the forces acting on the person. When the person is standing on a scale in an elevator, two forces are acting on them: their weight (mg) acting downward and the normal force acting upward.
(a) When the elevator is accelerating upward with an acceleration of 1.79 m/s^2, the apparent weight can be found using the equation:
Apparent weight = Normal force
Here's how to find the normal force:
1. Calculate the net force acting on the person by subtracting the weight force from the mass times acceleration:
Net force = (mass) x (acceleration) = (96.6 kg) x (1.79 m/s^2) = 173.094 N
2. Since the normal force and the net force are in the same direction, the normal force is equal to the net force:
Normal force = Net force = 173.094 N
Thus, the apparent weight when the elevator is accelerating upward is 173.094 N.
(b) When the elevator is moving upward at a constant speed, the apparent weight is equal to the actual weight. This is because there is no net force acting on the person in the vertical direction. So, the apparent weight is equal to the person's weight:
Apparent weight = Weight = mass x gravity
= (96.6 kg) x (9.8 m/s^2) ≈ 947.88 N
Thus, the apparent weight when the elevator is moving upward at a constant speed is approximately 947.88 N.
(c) When the elevator is accelerating downward with an acceleration of 1.14 m/s^2, the apparent weight can be found using the equation:
Apparent weight = Normal force
Here's how to find the normal force:
1. Calculate the net force acting on the person by adding the weight force to the mass times acceleration:
Net force = (mass) x (acceleration) + (mass) x (gravity)
= (96.6 kg) x (-1.14 m/s^2) + (96.6 kg) x (9.8 m/s^2)
≈ -110.244 N + 947.88 N
≈ 837.636 N
2. Since the normal force and the net force are in opposite directions, the normal force is the difference between them:
Normal force = Net force = 837.636 N
Thus, the apparent weight when the elevator is accelerating downward is 837.636 N.