74.0-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 1.10 m/s2,


(b) moving upward at a constant speed, and

(c) accelerating downward with an acceleration of 1.00 m/s2?

(a) accelerating upward with an acceleration of 1.10 m/s2,

F(net) = F(up) + F(down)
ma = Fup + Fg
(74.0kg)(1.10m/s^2) = Fup + (74.0kg)(-9.8m/s^2)
Find Fup to get the scale reading
(The scale reading is the value of the upward force of the spring inside the scale)
(b) moving upward at a constant speed,
F(net) = F(up) + F(down)
0 = F(up) + F(down)
F(up) = -F(down)
(c) accelerating downward with an acceleration of 1.00 m/s2
(74.0kg)(-1.00m/s^2) = Fup + (74.0kg)(-9.8m/s^2)
Find F(up)

To calculate the apparent weight in the different scenarios, we need to consider the forces acting on the person and use Newton's second law (F = ma).

(a) When the elevator is accelerating upward with an acceleration of 1.10 m/s^2:

The apparent weight can be calculated as the sum of the actual weight (mg) and the net force (ma) acting on the person.

Apparent weight = actual weight + net force

Since the elevator is accelerating upward, the net force is the difference between the actual weight and the force of gravity.

The actual weight (mg) is equal to the mass of the person (74.0 kg) multiplied by the acceleration due to gravity (9.8 m/s^2).

Actual weight = mass * acceleration due to gravity = 74.0 kg * 9.8 m/s^2 = 725.2 N

The net force is the mass of the person multiplied by the acceleration of the elevator.

Net force = mass * elevator acceleration = 74.0 kg * 1.10 m/s^2 = 81.4 N

Apparent weight = actual weight + net force = 725.2 N + 81.4 N = 806.6 N

Therefore, the apparent weight when the elevator is accelerating upward with an acceleration of 1.10 m/s^2 is 806.6 N.

(b) When the elevator is moving upward at a constant speed:

In this scenario, the elevator is not accelerating, so the net force acting on the person is zero.

Apparent weight = actual weight = 725.2 N

Therefore, the apparent weight when the elevator is moving upward at a constant speed is 725.2 N.

(c) When the elevator is accelerating downward with an acceleration of 1.00 m/s^2:

The apparent weight in this scenario can be calculated using the same formula as in part (a).

Apparent weight = actual weight + net force

The actual weight (mg) is 725.2 N (calculated previously).

The net force is the difference between the actual weight and the force of gravity since the elevator is accelerating downward.

Net force = actual weight - force of gravity

Force of gravity = mass * acceleration due to gravity = 74.0 kg * 9.8 m/s^2 = 725.2 N

Net force = 725.2 N - 725.2 N = 0 N

Apparent weight = actual weight + net force = 725.2 N + 0 N = 725.2 N

Therefore, the apparent weight when the elevator is accelerating downward with an acceleration of 1.00 m/s^2 is 725.2 N.

To find the apparent weight of a 74.0-kg person in each scenario, we need to consider Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration. The apparent weight can be calculated by comparing the gravitational force acting on the person (mg) to the net force acting on the person in each scenario.

(a) When the elevator is accelerating upward with an acceleration of 1.10 m/s^2:

In this case, the net force acting on the person is the sum of the gravitational force (mg) and the force due to acceleration (ma), where m is the mass of the person and a is the acceleration. The net force is given by F_net = mg + ma.

Substituting the given values, we have:
m = 74.0 kg (mass of the person)
g = 9.8 m/s^2 (acceleration due to gravity)
a = 1.10 m/s^2 (acceleration of the elevator)

F_net = (74.0 kg)(9.8 m/s^2) + (74.0 kg)(1.10 m/s^2)
= 725.2 N + 81.4 N
= 806.6 N

The apparent weight of the person in this scenario is 806.6 N.

(b) When the elevator is moving upward at a constant speed:

When the elevator is moving at a constant speed, it means that it is not accelerating. In this case, the net force acting on the person is zero. Therefore, the apparent weight of the person is equal to the weight due to gravity (mg).

The weight due to gravity can be calculated by multiplying the mass of the person by the acceleration due to gravity:

Apparent weight = mg = (74.0 kg)(9.8 m/s^2)

The apparent weight of the person in this scenario is 725.2 N.

(c) When the elevator is accelerating downward with an acceleration of 1.00 m/s^2:

Similar to part (a), the net force acting on the person is the sum of the gravitational force (mg) and the force due to acceleration (ma). However, in this case, the acceleration is in the opposite direction (downward), so it has a negative sign.

F_net = mg - ma

Substituting the given values:
m = 74.0 kg (mass of the person)
g = 9.8 m/s^2 (acceleration due to gravity)
a = -1.00 m/s^2 (acceleration of the elevator)

F_net = (74.0 kg)(9.8 m/s^2) - (74.0 kg)(1.00 m/s^2)
= 725.2 N - 74.0 N
= 651.2 N

The apparent weight of the person in this scenario is 651.2 N.