Question

A 62-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 821 N. What is the acceleration of the elevator?

Answer 1

3.24
`m/s^(2)`

Step-by-step explanation:

Using Newton's law of motion,

F = ma ..........................(i)

where;

F = net force acting on the object (or body)

m = mass of the object (or body)

a = acceleration of the body.

In this case,

Two forces are acting;

(i)The weight (W) of the man = m x g = 62 x 10 = 620N

(ii)The tension (T) on the scale of the elevator = 821N

The weight(W) of the man is a downward force while the tension (T) on the scale of the elevator is an upward force. Since the elevator rises upward is positive.

Therefore,

Net force (F) = Total upward force(s) - Total downward force(s)

Net force (F) = 821 - 620

F = 201N

To calculate the acceleration of the elevator,

substitute the values of F = 201N and m = 62 into equation (i) above;

=> F = ma

=> 201 = 62 x a

=> a = 210 / 62

=> a = 3.24
`m/s^(2)`

Therefore the acceleration of the elevator is 3.24
`m/s^(2)`

Answer 2

Acceleration of the elevator = 13.242 m/s2.

Step-by-step explanation:

Force is defined as the push or pull on an object with mass in kg that causes a change velocity. Force as a vector means it has both magnitude and direction.

Mathematically,

F = M*a

Where

F = force in Newton.

M = mass of the object in kg.

a = acceleration due to gravity in 9.81 m/s2.

Acceleration of the elevator = 821/62

= 13.242 m/s2.