A 58.0 kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.55 m/s in 1.25 s. It travels with this constant speed for the next 8.00 s. The elevator then slows down (undergoes a uniform acceleration in the negative y direction) for 2.25 s and comes to rest. What does the bathroom scale register during the first 1.25 s? Answer in units of N. (Hint: find the acceleration first.)

To find what the bathroom scale registers during the first 1.25 s, we need to calculate the acceleration first.

Given:
Mass of the man (m) = 58.0 kg
Initial speed of the elevator (u) = 0 m/s
Final speed of the elevator (v) = 1.55 m/s
Time taken to reach the final speed (t) = 1.25 s

We can calculate the acceleration (a) using the formula:
a = (v - u) / t

Substituting the given values:
a = (1.55 m/s - 0 m/s) / 1.25 s
a = 1.55 m/s / 1.25 s
a = 1.24 m/s²

Now that we have the acceleration, we can calculate the force that the bathroom scale registers during the first 1.25 s using Newton's second law:

Force (F) = Mass (m) × Acceleration (a)

Substituting the given mass:
F = 58.0 kg × 1.24 m/s²
F ≈ 71.92 N

Therefore, the bathroom scale registers a force of approximately 71.92 N during the first 1.25 s.

To find what the bathroom scale registers during the first 1.25 s, we need to determine the acceleration of the elevator during this time period.

First, let's find the acceleration of the elevator during the upward acceleration phase. We can use the equation:

v = u + at

where:
v = final velocity = 1.55 m/s (maximum speed)
u = initial velocity = 0 m/s (starting from rest)
t = time = 1.25 s

Substituting the given values, we have:

1.55 m/s = 0 m/s + a * 1.25 s

Simplifying the equation, we get:

a = (1.55 m/s - 0 m/s) / (1.25 s)
a = 1.24 m/s²

Next, let's find the acceleration during the deceleration phase. We know that the elevator comes to rest after 2.25 s. Since the acceleration is uniform, we can use Newton's second law:

F = ma

where F = force, m = mass, and a = acceleration.

The force on the man is given by the weight, which can be calculated using the equation:

weight = mass * acceleration due to gravity

weight = 58.0 kg * 9.8 m/s² (acceleration due to gravity)
weight = 568.4 N

Now, we can calculate the acceleration:

568.4 N = 58.0 kg * a

a = 568.4 N / 58.0 kg
a = 9.8 m/s²

Since the acceleration is in the negative y direction, the acceleration value is -9.8 m/s².

Finally, to find what the bathroom scale registers during the first 1.25 s, we need to calculate the net force experienced by the man using Newton's second law:

F = ma

where F = force, m = mass, and a = acceleration.

During the first 1.25 s, the elevator is undergoing upward acceleration with a magnitude of 1.24 m/s². Thus, the net force can be calculated as:

F = m * a
F = 58.0 kg * 1.24 m/s²
F = 71.92 N

Therefore, the bathroom scale would register a force of 71.92 N during the first 1.25 s.