Top-Rated Free Essay

# Apparent Weight

Good Essays
Apparent Weight: Person on Scale in Elevator
A person with mass, m, who is located at or near the surface of the Earth will always have some weight W=mg. When a person stands on a scale, the reading (the number of pounds or newtons) on the scale is actually the Normal Force that the scale exerts back towards the person to support the person's weight. (Note that the person and the scale are stationary relative to each other, in other words they are always in contact with each other, so they always have equal and opposite action and reaction forces acting between them.) Things get complicated, though, when the scale and the person experience acceleration. This will change the contact force (the Normal Force) between the person and the scale. Let's look at several cases. We will assume that Up is the positive direction and Down is the negative direction. Case 1: No acceleration of elevator If the acceleration of the elevator is zero, then there are two possible scenarios; the elevator can be at rest (stationary, zero velocity) or moving with a constant speed (no acceleration if velocity does not change). In this case, the action and reaction force pair between the person and the scale is just the weight. The person pushes down on the scale with a force of -W=-mg (negative direction) and the scale pushes back up against the man with a Normal Force of FN = +W = +mg. Because the reading on the scale is the magnitude of the normal force, the scale will read the true weight when the elevator is NOT accelerating. Case 2: going up & speeding up (acceleration a is positive (up)) In this case, the elevator and the person are starting from rest at a lower floor. The elevator accelerates upward. The inertia of the person would prefer to stay stationary, so the elevator floor and scale must push up on the person to accelerate him upward along with the elevator. (The person doesn't sink into the floor when the elevator accelerates up. The elevator and the scale and the person all move together.) The scale therefore has to push upward with extra force on the person to accelerate the person's mass upward. This results in a greater contact force between the scale and the person. Therefore the Normal Force is larger, so the reading on the scale is a number that is GREATER than the true weight. Let's consider Newton's 2nd Law (ΣF=ma) acting on the person. The overall acceleration of the person is upward (with the elevator). So ma is positive (upward). The only external forces

acting on the person are the force of gravity acting down (-W=-mg) and the supporting Normal Force FN that the scale applies upward on the person. So ΣF=ma= -mg+FN . We want to know FN because that is the number that we read off the scale. FN =mg+ma, which is GREATER than the true weight. Case 3: going up & slowing down (acceleration a is negative (down)) In this case, the elevator and the person are initially moving upward at a constant speed and slowing down to rest at a higher floor. The acceleration of the elevator is downward (opposite to the upward motion, which causes a reduction of the velocity). The inertia of the person would prefer to keep moving upward at a constant speed, so the elevator floor and scale effectively drop out a little bit from underneath the person as the elevator slows down. The person doesn't float upward, because again the elevator and the person move together, but the contact force between the person and the scale is reduced. The scale therefore has to push upward with less force on the person to support the person's weight. Therefore the Normal Force is smaller, so the reading on the scale is a number that is LESS than the true weight. Let's consider Newton's 2nd Law (ΣF=ma) acting on the person. The overall acceleration of the person is downward (with the elevator). So ma is negative (downward). The only external forces acting on the person are the force of gravity acting down (-W=-mg) and the supporting Normal Force FN that the scale applies upward on the person. So ΣF= -ma= -mg+FN . We want to know FN because that is the number that we read off the scale. FN =mg - ma, which is LESS than the true weight. Case 4: going down & slowing down (acceleration a is positive (up)) In this case, the elevator and the person are initially moving downward at a constant speed and then slow to rest at a lower floor. The elevator accelerates upward (opposite direction to negative/downward velocity to reduce velocity magnitude). The inertia of the person would prefer to keep moving downward at the constant speed, so the elevator floor and scale must push up on the person to accelerate him upward, slowing him down. (The person doesn't sink into the floor here either. Elevator and scale and person move together.) The scale therefore has to push upward with extra force on the person to accelerate the person's mass upward. This results in a greater contact force between the scale and the person. Therefore the Normal Force is larger, so the reading on the scale is a number that is GREATER than the true weight.

Let's consider Newton's 2nd Law (ΣF=ma) acting on the person. The overall acceleration of the person is upward (with the elevator). So ma is positive (upward). The only external forces acting on the person are the force of gravity acting down (-W=-mg) and the supporting Normal Force FN that the scale applies upward on the person. So ΣF=ma= -mg+FN . (Note that this is the same equation as we got in case 2.) We want to know FN because that is the number that we read off the scale. FN =mg+ma, which is GREATER than the true weight. Case 5: going down & speeding up (acceleration a is negative (down)) In this case, the elevator and the person are initially at rest at a higher floor. The elevator then speeds up in the downward direction towards a lower floor. The elevator acceleration of the elevator is negative/downward (increasing the velocity magnitude in the downward direction). The inertia of the person would prefer to stay at rest, so the elevator floor and scale effectively drop out a little bit from underneath the person as the elevator accelerates down. The person doesn't float upward here also, because again the elevator and the person move together, but the contact force between the person and the scale is reduced. The scale therefore has to push upward with less force on the person to support the person's weight. Therefore the Normal Force is smaller, so the reading on the scale is a number that is LESS than the true weight. Let's consider Newton's 2nd Law (ΣF=ma) acting on the person. The overall acceleration of the person is downward (with the elevator). So ma is negative (downward). The only external forces acting on the person are the force of gravity acting down (-W=-mg) and the supporting Normal Force FN that the scale applies upward on the person. So ΣF= -ma= -mg+FN . (Note that this is the same equation that we got for Case 3.) We want to know FN because that is the number that we read off the scale. FN =mg - ma, which is LESS than the true weight. Case 6: freefall (a = -g) If the elevator cable were to break, the whole elevator-scale-person system would all begin to accelerate downward due to the force of gravity. All objects in freefall accelerate downward with the same magnitude (acceleration due to gravity, g). The scale and the person are freefalling together, so there is NO contact force (Normal Force) between the scale and the person. (When they are both falling together, there is no way that the scale can support any of the person's weight.) Note that this is a special case of downward acceleration, which we discussed in Case 3 and Case 5. Just as in Cases 3 and 5, the apparent weight (which is zero when a=-g) is less than the true weight.

A pictorial summary of apparent weight:

## You May Also Find These Documents Helpful

• Good Essays

principal, and which will bind his/her principal. Usually, the principal will only be bound by the act of the agent if the agent acts within his/her authority. There are two types of authority which an agent could rely on, namely actual authority and apparent or ostensible authority. Actual authority is the authority given by the principal to the agent and could be in written or oral form. The capacity of an agent to act is the same as the capacity of his/her principal. The express actual authority…

• 1020 Words
• 5 Pages
Good Essays
• Good Essays

in motion by presenting a different wind speed and direction at different heights along the mast. Wind shear occurs because of the greater friction presented by water surface slowing the flow of air, a difference in true wind creates a different apparent wind at different heights. Sailmakers may introduce sail twist in the design of the sail, where the head of the sail is set at a different angle of attack from the foot of the sail in order to change the lift distribution with height. The effect…

• 362 Words
• 2 Pages
Good Essays
• Powerful Essays

terrorism to Singapore is more apparent than real”. Do you agree? “Despite counter-terrorism successes by regional authorities, the terrorist threat in the region and to Singapore remains real.” – Mr K Shanmugam, Minister for Law and Second Minister for Home Affairs (AsiaOne News, July 19th 2010) Introduction Firstly, there is a need to clearly distinguish between apparent threat and real threat. This essay will adopt the definition that apparent threat will mean: threat that…

• 2404 Words
• 10 Pages
Powerful Essays
• Good Essays

Active, Apparent, and Reactive Power According to Chipkin (2009), we could think of Real Power as useful power – a measure of how much work is being done. Apparent Power is the power delivered by a power source to a load like a motor. They also stated that you need to supply more power (Apparent Power) to a device than it will do the work (Real Power). Reactive Power is the (vector) difference between Apparent Power and Real Power. Reactive Power cannot be harnessed to do useful work. Power Quality…

• 1017 Words
• 5 Pages
Good Essays
• Better Essays

affective weight loss program that helps maintain and also supports the people who are overweight and obese. The United States of America has the highest rates in the world of overweight people (68% of the US population) and obesity (34% of the population). According to a new report by the Organization for Economic Co-operation and Development (OECD), 1 in 10 people are obese worldwide! I will be comparing and contrasting Jenny Craig and Weight Watchers for being the best two methods for weight loss programs…

• 1633 Words
• 7 Pages
Better Essays
• Satisfactory Essays

Gaining weight is one of the greatest topic in the world. Thus, people should acknowledge what the cause of gaining weight and how it affects our health. Two causes of gaining weight are laking of sleep and being stress.Lack of sleep is one od the causes of gaining weight. The lack of sleep not only has bad effects on your health but it's also "culprit" to make you gain weight .It slowly increases your appetite and also makes you crave high fat and carbon food.For example, many people can't sleep…

• 344 Words
• 1 Page
Satisfactory Essays
• Good Essays

If you have ever considered losing weight, you have probably heard of the various kinds of diet pills available. Diet pills claim to "melt away the fat." They sound like the perfect solution to shed a few pounds, but research tells a different story. Diet pills became popular in 1996. The most common ingredients were Redux and fenfluramin/phentermine, which posed as appetite suppressants. The pills seemed to suck up the fat, and people were losing anywhere between 25-50 pounds in months. The FDA…

• 799 Words
• 4 Pages
Good Essays
• Good Essays

Part I: Consequences Part I of The Weight of the Nation discussed the effects of the obesity epidemic in America. It immediately grabbed my attention when they stated that more than 18% of American children are obese. Two-thirds of America (or 68.8%) is overweight or obese. There is a strong connection between a high BMI and diabetes mellitus and hypertension, especially when accompanied by a high percentage of abdominal fat. I found it interesting, and important, that the first woman who shared…

• 747 Words
• 3 Pages
Good Essays
• Good Essays

home. Last week on my home from Tampa, I was riveted to the Glamour article “The Secret Way People Are Judging You.” In this article they revealed the results of a poll of more than 1,800 women revealing what they thought about women of various weights. From Glamour’s “Skinny Witch vs. Chubby Fairy” Heavy women were pegged as… All women--skinny or overweight--are being judged with characteristics based only on their size! “lazy” 11 times as often as thin women; “sloppy” nine times;…

• 953 Words
• 4 Pages
Good Essays
• Good Essays

Tips on Weight Loss and Weight Management These days, many teenagers are very concerned about their weight. Many go on crash diets hoping to be transformed into models with svelte figures. Some, who are already slim, embark on such diets to become as skinny as Victoria Beckham. The seriousness with which teens tackle weight issues is worrying as the methods they use, such as going on crash diets and consuming slimming pills, are harmful. This article is therefore written with the aim of giving sensible…

• 488 Words
• 2 Pages
Good Essays