Scale Readings and Weight PDF

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Lecture Topic: Scale Readings and Weight Technically speaking, a scale does not measure one's weight. While we use a scale to measure one's weight, the scale reading is actually a measure of the upward force applied by the scale to balance the downward force of gravity acting upon an object. When an object is in a state of equilibrium (either at rest or in motion at constant speed), these two forces are balanced. The upward force of the scale upon the person equals the downward pull of gravity (also known as weight). And in this instance, the scale reading (that is a measure of the upward force) equals the weight of the person. However, if you stand on the scale and bounce up and down, the scale reading undergoes a rapid change. As you undergo this bouncing motion, your body is accelerating. During the acceleration periods, the upward force of the scale is changing. And as such, the scale reading is changing. Is your weight changing? Absolutely not! You weigh as much (or as little) as you always do. The scale reading is changing, but remember: the SCALE DOES NOT MEASURE YOUR WEIGHT. The scale is only measuring the external contact force that is being applied to your body. Now consider Otis L. Evaderz who is conducting one of his famous elevator experiments. He stands on a bathroom scale and rides an elevator up and down. As he is accelerating upward and downward, the scale reading is different than when he is at rest and traveling at constant speed. When he is accelerating, the upward and downward forces are not equal. But when he is at rest or moving at constant speed, the opposing forces balance each other. Knowing that the scale reading is a measure of the upward normal force of the scale upon his body, its value could be predicted for various stages of motion. For instance, the value of the normal force (Fnorm) on Otis's 80-kg body could be predicted if the acceleration is known. This prediction can be made by simply applying Newton's second law as discussed in Unit 2. As an illustration of the use of Newton's second law to determine the varying contact forces on an elevator ride, consider the following diagram. In the diagram, Otis's 80-kg is traveling with constant speed (A), accelerating upward (B), accelerating downward (C), and free falling (D) after the elevator cable snaps. In each of these cases, the upward contact force (Fnorm) can be determined using a free-body diagram and Newton's second law. The interaction of the two forces - the upward normal force and the downward force of gravity - can be thought of as a tug-of-war. The net force acting upon the person indicates who wins the tug-of-war (the up force or the down force) and by how much. A net force of 100N, up indicates that the upward force "wins" by an amount equal to 100 N. The gravitational force acting upon the rider is found using the equation Fgrav = m*g.

The normal force is greater than the force of gravity when there is an upward acceleration (B), less than the force of gravity when there is a downward acceleration (C and D), and equal to the force of gravity when there is no acceleration (A). Since it is the normal force that provides a sensation of one's weight, the elevator rider would feel his normal weight in case A, more than his normal weight in case B, and less than his normal weight in case C. In case D, the elevator rider would feel absolutely weightless; without an external contact force, he would have no sensation of his weight. In all four cases, the elevator rider weighs the same amount - 784 N. Yet the rider's sensation of his weight is fluctuating throughout the elevator ride. Weightlessness in Orbit Earth-orbiting astronauts are weightless for the same reasons that riders of a free-falling amusement park ride or a free-falling elevator are weightless. They are weightless because there is no external contact force pushing or pulling upon their body. In each case, gravity is the only force acting upon their body. Being an action-at-a-distance force, it cannot be felt and therefore would not provide any sensation of their weight. But for certain, the orbiting astronauts weigh something; that is, there is a force of gravity acting upon their body. In fact, if it were not for the force of gravity, the astronauts would not be orbiting in circular motion. It is the force of gravity that supplies the centripetal force requirement to allow the inward acceleration that is characteristic of circular motion. The force of gravity is the only force acting upon their body. The astronauts are in free-fall. Like the falling amusement park rider and the falling elevator rider, the astronauts and their surroundings are falling towards the Earth under the sole influence of gravity. The astronauts and all their surroundings - the space station with its contents - are falling towards the Earth without colliding into it. Their tangential velocity allows them to remain in orbital motion while the force of gravity pulls them inward. Many students believe that orbiting astronauts are weightless because they do not experience a force of gravity. So to presume that the absence of gravity is the cause of the weightlessness experienced by orbiting astronauts would be in violation of circular motion principles. If a person believes that the absence of gravity is the cause of their weightlessness, then that person is hard-pressed to come up with a reason for why the astronauts are orbiting in the first place. The fact is that there must be a force of gravity in order for there to be an orbit. One might respond to this discussion by adhering to a second misconception: the astronauts are weightless because the force of gravity is reduced in space. The reasoning goes as follows: "with less gravity, there would be less weight and thus they would feel less than their normal weight." While this is

partly true, it does not explain their sense of weightlessness. The force of gravity acting upon an astronaut on the space station is certainly less than on Earth's surface. But how much less? Is it small enough to account for a significant reduction in weight? Absolutely not! If the space station orbits at an altitude of approximately 400 km above the Earth's surface, then the value of g at that location will be reduced from 9.8 m/s/s (at Earth's surface) to approximately 8.7 m/s/s. This would cause an astronaut weighing 1000 N at Earth's surface to be reduced in weight to approximately 890 N when in orbit. While this is certainly a reduction in weight, it does not account for the absolutely weightless sensations that astronauts experience. Their absolutely weightless sensations are the result of having "the floor pulled out from under them" (so to speak) as they are free falling towards the Earth. Still other physics students believe that weightlessness is due to the absence of air in space. Their misconception lies in the idea that there is no force of gravity when there is no air. According to them, gravity does not exist in a vacuum. But this is not the case. Gravity is a force that acts between the Earth's mass and the mass of other objects that surround it. The force of gravity can act across large distances and its effect can even penetrate across and into the vacuum of outer space. Perhaps students who own this misconception are confusing the force of gravity with air pressure. Air pressure is the result of surrounding air particles pressing upon the surface of an object in equal amounts from all directions. The force of gravity is not affected by air pressure. While air pressure reduces to zero in a location void of air (such as space), the force of gravity does not become 0 N. Indeed, the presence of a vacuum results in the absence of air resistance; but this would not account for the weightless sensations. Astronauts merely feel weightless because there is no external contact force pushing or pulling upon their body. They are in a state of free fall....