A 42 kg man stands on a bathroom scale in an elevator. Starting from rest at the bottom floor, the elevator ascends, attaining its maximum speed of 1.95 m/s in 1.22 s. It travels with this constant speed for the next 7.80 s. The elevator then slows down for 2.20 s and comes to rest at the top level.

a) What is the acceleration of the man during the first 1.22 s? Answer in units of m/s2 and use the upward direction as positive.

b) How many forces act on the Man during this elevator ride?

c) What does the bathroom scale register in N during the first 1.22 s?

d) What does the bathroom scale register in N during the 7.80 s period?

e) What does the bathroom scale register in N during the 2.20 s period?

Use 10 N/kg for g and the upward direction as positive.

I think I've found everything but e. Here is my work

a) acceleration = v-u/t
a = 1.95/1.22
a = 1.6
b) 2, gravity and the normal force
c) F = m(g – a)
F= 42(10-1.6)
F = 352.8

d) acceleration = v-u/t
a= 1.95/7.8
a= .25
F= m(g-a)
F= 42(10-.25)
F= 409.5

Does anyone else know what e would be though?

To solve these problems, we'll need to apply the principles of Newton's laws of motion. Let's go through each question step by step:

a) What is the acceleration of the man during the first 1.22 s?

To find the acceleration, we can use the formula:

acceleration = change in velocity / time

Given that the elevator starts from rest and attains a maximum speed of 1.95 m/s in 1.22 s, the change in velocity is equal to the final velocity minus the initial velocity:

change in velocity = 1.95 m/s - 0 m/s = 1.95 m/s

Now we can calculate the acceleration:

acceleration = change in velocity / time = 1.95 m/s / 1.22 s ≈ 1.598 m/s²

Therefore, the acceleration of the man during the first 1.22 s is approximately 1.598 m/s².

b) How many forces act on the man during this elevator ride?

There are two forces acting on the man in this situation:

1. The force due to the gravitational pull (weight): This force always acts downwards and is given by the equation:

force(weight) = mass * gravity

where mass is the man's mass (42 kg) and gravity is the acceleration due to gravity (10 N/kg). Therefore:

force(weight) = 42 kg * 10 N/kg = 420 N

2. The normal force: This is the force exerted by the scale on the man to support his weight. In this case, since the elevator is in motion, the normal force will be different depending on the acceleration or deceleration of the elevator.

c) What does the bathroom scale register in N during the first 1.22 s?

During the first 1.22 s, when the elevator is accelerating upwards, the bathroom scale registers a greater normal force than just the weight of the man. This is due to the acceleration. The net force acting on the man will be the sum of the force due to gravity and the upward force required to accelerate the man.

Using Newton's second law:

net force = mass * acceleration

net force = 42 kg * 1.598 m/s² = 67.116 N

Therefore, the bathroom scale registers a force of approximately 67.116 N during the first 1.22 s.

d) What does the bathroom scale register in N during the 7.80 s period?

During this period, the elevator is moving at a constant speed of 1.95 m/s. According to Newton's first law, when the elevator moves at a constant velocity, there is no net force acting on the man.

So the bathroom scale registers only the weight of the man, which is 420 N.

e) What does the bathroom scale register in N during the 2.20 s period?

During the 2.20 s period, the elevator is decelerating to come to a stop. The net force acting on the man will be the difference between the force due to gravity and the upward force required to decelerate the man.

Using Newton's second law once again:

net force = mass * acceleration

Since the elevator is decelerating and the upward direction is taken as positive, the acceleration will be negative. The acceleration can be calculated using the formula:

acceleration = change in velocity / time

The change in velocity is given by the initial velocity minus the final velocity:

change in velocity = 1.95 m/s - 0 m/s = 1.95 m/s

Now we can calculate the acceleration:

acceleration = change in velocity / time = 1.95 m/s / 2.20 s ≈ 0.886 m/s² (negative sign indicates deceleration)

Now we can find the net force:

net force = mass * acceleration = 42 kg * (-0.886 m/s²) ≈ -37.212 N

Therefore, the bathroom scale registers a force of approximately -37.212 N during the 2.20 s period (negative sign indicates downwards force).