A 60.0-kg person rides in elevator while standing on a scale. The elevator is traveling downward butslowing down at a rate of 2.00 m/s2. The reading on the scale is closest toA) 589 N.B) 708 N.C) 469 N.D) 120 N.

- Its weight (acting downward), equal to [tex]mg[/tex], where m = 60 kg is the mass of the person and g = 9.81 m/s^2 is the acceleration due to gravity

- The normal reaction of the scale, R, acting upward

According to Newton's second law, the resultant of these two forces must be equal to the product between mass and acceleration:

[tex]mg-R=ma[/tex]

where we know that [tex]a=2.00 m/s^2[/tex] since the elevator is traveling downward at 2.00 m/s^2. Solving the equation for R, we find

[tex]R=m(g-a)=(60 kg)(9.81 m/s^2-2.0 m/s^2)=469 N[/tex]

johanrusli johanrusli · Answer 2 · 2020-01-20T07:55:00+01:00

The reading on the scale is closest to B) 708 N

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Given:

mass of the person = m = 60.0 kg

acceleration of the elevator = a = 2.00 m/s²

Asked:

reading of the scale = N = ?

Solution:

We will use Newton's second law of motion to solve this problem :

[tex]\Sigma F = ma[/tex]

[tex]N - w = ma[/tex]

[tex]N - mg = m a[/tex]

[tex]N = mg + ma[/tex]

[tex]N = m ( g + a )[/tex]

[tex]N = 60.0 ( 9.8 + 2.00 )[/tex]

[tex]N = 60.0 ( 11.8 )[/tex]

[tex]N = 708 \texttt{ N}[/tex]

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Conclusion :

The reading on the scale is closest to 708 N

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Learn more

Impacts of Gravity : https://brainly.com/question/5330244
Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
The Acceleration Due To Gravity : https://brainly.com/question/4189441
Newton's Law of Motion: https://brainly.com/question/10431582
Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics