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
[tex]W = mg = 60*10 = 600 N[/tex]
normal force on the man will be given as
[tex]F_n = 400 N[/tex]
now net force is given by Newton's II law
[tex]F_{net} = ma[/tex]
[tex]F_g - F_n = ma[/tex]
[tex]600 - 400 = 60*a[/tex]
[tex]a = \frac{200}{60} = \frac{10}{3}[/tex]
a = 3.33 m/s^2
so elevator is accelerating downwards with an acceleration a = 3.33 m/s^2
The acceleration of the elevator is closest to 3.13 m/s² downward.
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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
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 :
[tex]\Sigma F = ma[/tex]
[tex]N - w = ma[/tex]
[tex]N - mg = m a[/tex]
[tex]a = ( N - mg ) \div m[/tex]
[tex]a = ( 400 - 60.0(9.8) ) \div 60.0[/tex]
[tex]a = -188 \div 60.0[/tex]
[tex]a = - \frac{47}{15}[/tex]
[tex]a \approx -3.13 \mathtt{ ~ m/s^2}[/tex]
[tex]\texttt{ }[/tex]
The acceleration of the elevator is closest to 3.13 m/s² downward.
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Grade: High School
Subject: Physics
Chapter: Dynamics
