Understanding Mass and Weight Learning Goal: To understand the distinction betwe
ID: 1314400 • Letter: U
Question
Understanding Mass and Weight
Learning Goal:
To understand the distinction between mass and weight and to be able to calculate the weight of an object from its mass and Newton's law of gravitation.
The concepts of mass and weight are often confused. In fact, in everyday conversations, the word "weight" often replaces "mass," as in "My weight is seventy-five kilograms" or "I need to lose some weight." Of course, mass and weight arerelated; however, they are also very different.
Mass, as you recall, is a measure of an object'sinertia (ability to resist acceleration). Newton's 2nd law demonstrates the relationship among an object's mass, its acceleration, and the net force acting on it: Fnet=ma. Mass is an intrinsic property of an object and is independent of the object's location.
Weight, in contrast, is defined as the force due to gravity acting on the object. That force depends on the strength of the gravitational field of the planet: w=mg, where w is the weight of an object, m is the mass of that object, and g is the local acceleration due to gravity (in other words, the strength of the gravitational field at the location of the object). Weight, unlike mass, is not an intrinsic property of the object; it is determined by both the object and its location.
Punch Taut is a down-on-his-luck heavyweight boxer. One day, he steps on the bathroom scale and "weighs in" at 236 lb. Unhappy with his recent bouts, Punch decides to go to a different planet where he would weigh in at 118 lb so that he can compete with the bantamweights who are not allowed to exceed 118 lb. His plan is to travel to Xobing, a newly discovered star with a planetary system. Here is a table listing the planets in that system:
In this table, the mass and the radius of each planet are given in terms of the corresponding properties of the earth. For instance, Tehar has a mass equal to 2.1 earth masses and a radius equal to 0.80 earth radii.
Part E
If acceleration due to gravity on the earth is g, which formula gives the acceleration due to gravity on Loput?
Part F
If the acceleration due to gravity on the earth is 9.8 m/s2, what is the acceleration due to gravity on Rams?
Name Mass( Mearth) Radius
( Rearth) Tehar 2.1 0.80 Loput 5.6 1.7 Cremury 0.36 0.30 Suven 12 2.8 Pentune 8.3 4.1 Rams 9.3 4.0
Explanation / Answer
on Loput,
g = GMplanet / Rplanet2 = G5.6Mearth / (1.7Rearth)2 = g(5.6 / 1.72) =g(5.6 / 1.72)
on Rams
g = G9.3Mearth / (4Rearth)2 = (9.3/16) x g = (9.3/16) x 9.8 = 5.69625 ms-2
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