Question

A person is standing on a spring bathroom scale on the floor of an elevator which is moving up and slowing down at the rate of 2.1 m/s 2 . The acceleration of gravity is 9.8 m/s 2 . If the person’s mass is 77.6 kg, what does the scale read? Answer in units of n

Answer 1

Answer:  

923.4 N

Explanation:

from the question we are given the following:

upward acceleration (a) = $2.1 \frac{m}{s^{2} }$

downward acceleration (acceleration due to gravity (g)) =   $9.8 \frac{m}{s^{2} }$

mass (m) = 77.6 kg

the net acceleration is going to be the resultant of the upward and downward acceleration.

For the accelerations, let upward be positive and downward be negative

Therefore

net acceleration = g - (-a)  (note that the negative sign in front of "a"  (-a) is because the person was decelerating)

= 9.8 - (-2.1) = 11.9

now we can get the reading on the scale from F = m x a

F = 77.6 x 11.9 = 923.4 N

Answer 2

Answer:

923.44N

Explanation:

Obviously Fn cannot equal Fg since the elevator is moving up  

Where Fn is the force read on the scale

Fg is gravitational force=mg=77.6 x 9.8=760.48N

So we use this equation:  

Fnet = Fn - Fg  

ma = Fn - mg

77.6 x 2.1 = Fn – 760.48

162.96N = Fn – 760.48N  

923.44 N = Fn

The answer is 923.44 N