After an annual checkup, you leave your physician's office,...

After an annual checkup, you leave your physician's office, where you weighed $683 \mathrm{~N}$. You then get into an elevator that, conveniently, has a scale. Find the magnitude and direction of the elevator's acceleration if the scale reads (a) $725 \mathrm{~N}$ and (b) $595 \mathrm{~N}$.

Key Concepts

Newton's Second Law

This is a fundamental principle in mechanics that states the net force on an object is equal to its mass multiplied by its acceleration (F_net = ma). It provides the foundation for analyzing the forces acting on an object, especially when those forces include both gravitational pull and other accelerative effects, such as in an elevator.

Normal Force

The normal force is the supportive force exerted perpendicular to the surface of contact—in this case, the force the elevator floor exerts on the person. It is measured by the scale and can vary depending on the elevator's acceleration, contributing to the apparent weight observed.

Apparent Weight

Apparent weight is the reading on a scale, which reflects the normal force, and can differ from the actual weight (the gravitational force on the object) when the object is accelerating. In accelerated systems like an elevator, the apparent weight increases if the acceleration is upward and decreases if it is downward.

Non-Inertial Reference Frames

A non-inertial reference frame is one that is accelerating relative to an inertial frame, meaning extra, fictitious forces must be considered when applying Newton's laws. An elevator is a common example where the apparent forces or weights differ from those in a stationary or uniformly moving system, necessitating adjustments in calculations.

Transcript

00:03 All right, so what we have here is a fun little problem that tells us or illuminates to us how scales work.

00:13 And what the scale is doing is that it's not measuring your actual mg vector, but rather it is measuring the strength of the normal force because that's how much is pressing.

00:29 So in this example, we're going to say that our weight is to three significant figures, 383 newtons and then what i just said will make more sense when i draw a free body diagram so oops meant to draw than a different color but you know if this is you and you have an weight vector of m g pointing downward again what the scale is measuring is the normal force n and not m g because when you are in an elevator that is either accelerating or decelerating.

01:08 You know, it's the ground, the bottom of the elevator that's pressing up against you.

01:12 So your normal force vector can actually change.

01:14 You get bigger or smaller because your weight is not changing.

01:17 And this is illuminated by the fact that the scale readings will differ.

01:22 Oops, sorry, the scale readings will differ depending on, you know, whether you're an elevator that's not accelerating or, you know, accelerating or decelerating.

01:31 So what i meant to do is say that that is your weight in general.

01:35 But in part a, scale is going to say that your weight is actually 725 newton's, because we are in the portion where we are accelerating upward.

01:49 So it's 725 newton's not your actual way at that moment of time, but rather your normal force.

01:58 So what i mean by that is that we need to apply newton's second law.

02:06 The mass times the acceleration.

02:09 And at that moment in time, the normal force exceeds your weight.

02:12 So it's going to be n minus w.

02:17 So there's a little bit of algebraic gymnastics that i want to do, but isn't necessarily necessary.

02:24 So we want to solve for the acceleration at that moment in time...