Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.0 s after the elevator starts moving, then 930 N for the next 3.0 s. What is the elevator’s velocity 6.0 s after starting?

Answer :

Answer:

The elevator's velocity after 6 seconds is 3.189m/s

Explanation:

Using Newton's 2nd law:Fnet = ma

Mg - N = ma

Where m = mass

N = normal force

a = acceleration

g = acceleration due to gravity

Substituting the given values and finding acceleration

(95kg)(9.8m/s^2) - 830N = 95kg x a

a = (931 -830) / 95

a = 101/95

a = 1.063m/s^2

After 3 seconds, the weight 0f the person is equal to the actual weight of the person, thus the elevator will be moving at a constant velocity.

Using kinematic equation:

V = u + at

Where V = final velocity

U = initial velocity = 0

a = acceleration

t = time

V = 0 + 1.063 × 3

V = 3.189m/s

This velocity does not change . The elevator travels the test of the time at the same velocity. Therefore,the velocity at 6 seconds = 3.189m/s

The motion of an elevator accelerating downwards, makes the passengers feel lighter, and when accelerating upwards, the passengers feel heavier

The elevator's velocity 6.0 s after starting is approximately 3.283 m/s

The reason the above value above value is correct is given as follows:

The known parameters:

Henry's mass, m = 95 kg

After the elevator starts moving;

The reading on the scale for the first 3.0 seconds = 830 N

The reading on the scale for the next 3.0 seconds = 930 N

Required:

The velocity of the elevator 6.0 s after starting

Solution:

Weight = mass × Acceleration due to gravity

Henry's weight, W = 95 kg × 9.8 m/s² ≈ 930 N

The apparent weight in downward motion is less than the weight

[tex]F_{scale} = 830 \, N[/tex]

With regards to the weight, W, we have;

[tex]F_{scale} = W - m\cdot a = m \cdot ( g- a)[/tex]

Therefore;

In the first 3 seconds, we have;

[tex]a_{(0\, s \ to \ 3 \, s)} = g - \dfrac{F_{scale}}{m} = 9.81 \ m/s^2 - \dfrac{830 \, N}{95 \, kg} \approx 1.073 \ m/s^2[/tex]

[tex]a_{(0\, s \ to \ 3 \, s)} \approx 1.073 \ m/s^2[/tex]

In the next 3 seconds, we have;

[tex]a_{(3\, s \ to \ 6 \, s)} = 9.81 \ m/s^2 - \dfrac{930 \, N}{95 \, kg} \approx 0.021\ m/s^2[/tex]

[tex]a_{(3\, s \ to \ 6 \, s)} \approx 0.021\ m/s^2[/tex]

Which gives;

v = u + a·t

u = 0

The velocity after the first 3 seconds, v₃, is given as follows;

v₃ = 0 + 1.073 m/s² × 3.0 s ≈ 3.22 m/s

v₃ ≈ 3.22 m/s

The velocity after the next 3 seconds, (t = 3), v₆, is given as follows;

v₆ = v₃ + [tex]a_{(3\, s \ to \ 6 \, s)}[/tex] × 3

∴ v₆ ≈ 3.22 + 0.021 × 3 = 3.283

The elevator's velocity 6.0 s after starting, v₆ ≈ 3.283 m/s

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