A 80-kg man stands on a bathroom scale inside an elevator.

(a) The elevator accelerates upward from rest at a rate of 1.40 m/s2 for 1.50 s. What does the scale read during this 1.50 s interval?
N

(b) The elevator continues upward at constant velocity for 8.50 s. What does the scale read now?
N

(c) While still moving upward, the elevator's speed decreases at a rate of 0.700 m/s2 for 3.00 s. What is the scale reading during this time?
N

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To solve these problems, we will use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. We can then use this information to find the normal force acting on the man, which is the reading on the scale.

(a) During the upward acceleration, the net force acting on the man is the sum of the gravitational force (mg) and the force due to the acceleration (ma). The normal force is equal in magnitude but opposite in direction to the gravitational force, so the equation becomes:
net force = ma + mg.

Using the given values:
mass (m) = 80 kg
acceleration (a) = 1.40 m/s^2
gravitational force (mg) = (80 kg) * (9.8 m/s^2) = 784 N.

net force = (80 kg) * (1.40 m/s^2) + 784 N = 112 N + 784 N = 896 N.

So, the reading on the scale during this 1.50 s interval is 896 N.

(b) When the elevator continues upward at a constant velocity, the acceleration is zero, and the net force acting on the man is only the gravitational force. Therefore, the normal force is equal in magnitude but opposite in direction to the gravitational force, which is still 784 N.

So, the reading on the scale now is 784 N.

(c) During the upward deceleration, the net force acting on the man is again the sum of the gravitational force (mg) and the force due to the deceleration (ma). The normal force is equal in magnitude but opposite in direction to the gravitational force, so the equation becomes:
net force = mg - ma.

Using the given values:
mass (m) = 80 kg
deceleration (a) = 0.700 m/s^2
gravitational force (mg) = 784 N.

net force = (80 kg) * (9.8 m/s^2) - (80 kg) * (0.700 m/s^2) = 784 N - 56 N = 728 N.

So, the reading on the scale during this time is 728 N.

To find the answer to these questions, we need to consider the forces acting on the man in each situation.

(a) During the upward acceleration phase, the scale reading will be equal to the normal force exerted by the man on the scale.

We can start by calculating the net force acting on the man using Newton's second law: F_net = ma. Here, the mass (m) of the man is 80 kg, and the acceleration (a) is 1.40 m/s^2. Thus, F_net = (80 kg)(1.40 m/s^2) = 112 N.

Next, we need to consider the gravitational force acting on the man. The weight of the man, which is equal to the force of gravity, can be calculated using the formula: weight (W) = mg, where g is the acceleration due to gravity and is approximately 9.8 m/s^2. So, W = (80 kg)(9.8 m/s^2) = 784 N.

During this upward acceleration phase, the net force acting on the man is the difference between the gravitational force and the normal force exerted by the man on the scale. So, F_net = W - N, where N is the normal force.

Since we know that F_net = 112 N, we can rearrange the equation to solve for N: N = W - F_net = 784 N - 112 N = 672 N.

Therefore, the scale reading during this 1.50 s interval will be 672 N.

(b) During the constant velocity phase, the net force acting on the man is zero. This means that the normal force exerted by the man on the scale is equal in magnitude and opposite in direction to the weight of the man. Hence, the scale reading will be equal to the weight of the man, which is 784 N.

Therefore, the scale reading during this phase will be 784 N.

(c) During the deceleration phase, we can use the same approach as in part (a).

First, calculate the net force acting on the man using F_net = ma. The mass (m) of the man is still 80 kg, and the acceleration (a) is -0.700 m/s^2 since the elevator's speed is decreasing. Thus, F_net = (80 kg)(-0.700 m/s^2) = -56 N.

Again, consider the gravitational force acting on the man, which is 784 N.

During this deceleration phase, the net force acting on the man is the sum of the gravitational force and the normal force exerted by the man on the scale. So, F_net = W + N.

Since we know that F_net = -56 N, we can rearrange the equation to solve for N: N = F_net - W = -56 N - 784 N = -840 N.

However, the scale reading cannot be negative, as it represents the magnitude of the normal force. So, the scale reading during this 3.00 s interval is 0 N.

Therefore, the scale reading during this deceleration phase will be 0 N.

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