Question

A 60.0-kg person rides in an elevator while standing on a scale. the scale reads 400 n. the acceleration of the elevator is closest to

Answer 1

The acceleration of the elevator is closest to 3.13 m/s² downward.

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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.

$\boxed {F = ma }$

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

reading of the scale = N = 400 N

gravitational acceleration = g = 9.8 m/s²

Asked:

acceleration of the elevator = a = ?

Solution:

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

$\Sigma F = ma$

$N - w = ma$

$N - mg = m a$

$a = ( N - mg ) \div m$

$a = ( 400 - 60.0(9.8) ) \div 60.0$

$a = -188 \div 60.0$

$a = - \frac{47}{15}$

$a \approx -3.13 \mathtt{ ~ m/s^2}$

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Conclusion :

The acceleration of the elevator is closest to 3.13 m/s² downward.

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Learn more

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

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Answer 2

Reading of the scale will be given as Normal force on the man

So here we can say that

weight of the mas will be

$W = mg = 60*10 = 600 N$

normal force on the man will be given as

$F_n = 400 N$

now net force is given by Newton's II law

$F_{net} = ma$

$F_g - F_n = ma$

$600 - 400 = 60*a$

$a = \frac{200}{60} = \frac{10}{3}$

a = 3.33 m/s^2

so elevator is accelerating downwards with an acceleration a = 3.33 m/s^2