Question

A man standing on a scale in an elevator notices that the scale reads 30 newtons greater than his normal weight. Which type of movement of the elevator could cause this greater-than-normal reading? Explain.

Answer 1

An upwards acceleration of the elevator would cause this greater reading since the scale displays the Normal Force of the object on it. The inertia of the person would prefer to stay stationary, so the scale must push up on the person to accelerate him upward along with the elevator. This results in the following equation:

W = mg + ma

Where mg represents the weight reading without external acceleration and ma as the weight reading due to the external acceleration.

Answer 2

This greater-than-normal reading is caused by the elevator that is moving upward with acceleration a.

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.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

We will use Newton's 2nd law formula for this problem.

$\Sigma F = ma$

$N - w = ma$

$N - mg = ma$

$N = mg + ma$

If the scale reads 30 newtons greater than his normal weight , then it means that the elevator is moving upward with acceleration a.

$\texttt{ }$

How about if the elevator is moving downward with acceleration a?

$\Sigma F = ma$

$w - N = ma$

$mg - N = ma$

$N = mg - ma$

The scale will read 30 newtons less than his normal weight if the elevator is moving downward with acceleration a.

$\texttt{ }$

How about if the elevator is moving downward with acceleration g?

$\Sigma F = ma$

$w - N = mg$

$mg - N = mg$

$N = mg - mg$

$N = 0$

The scale will read 0 newtons if the elevator is moving downward with acceleration g. The man will feel weightless in this condition.

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

Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant