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What is the “theoretical slope” for  “part 1 case” and "part 2 case"?

What is the “theoretical slope” for  “part 1 case” and "part 2 case"?

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter5: Newton's Law Of Motion
Section: Chapter Questions
Problem 23P: While sliding a couch across a floor, Andrea and Jennifer exert forces FA and FJ on the couch....
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What is the “theoretical slope” for  “part 1 case” and "part 2 case"?

The motion of the system is analyzed by applying Newton's 2nd Law to each mass separately. The string and the pulley are assumed to have negligible mass. M Above: horizontal force acting on the mass of the rider Right: vertical forces acting on the hanging mass T-Ma If we assume the air track is frictionless, then the only force acting on the mass of the rider, M, in the horizontal direction is the tension T in the string, so that Newton's 2nd Law gives: mg - T = ma m (2) Considering the hanging mass, m, there are two forces acting on it in the vertical direction: the tension T and the force of gravity mg. Newton's 2nd Law in this case gives: (3) Elimination of T between Equations (2) and (3) leads to mg = (m + M)a This is the equation you will work with in this experiment. Ing (4) PART I: CONSTANT MASS, VARIABLE FORCE In this case, the quantity m+M in Equation (4) will be kept constant, but different combinations of m and M will be used for a number of different data taking runs (which will improve the accuracy of the experiment). This implies that, as the hanging mass m (and, therefore, accelerating force) varies, the acceleration a will vary. Equation (4) can be viewed as a linear equation representing a straight line with mg as the dependent variable, a as the independent variable, and m+M as the slope. You will use this fact in testing Equation (4). PART II: CONSTANT FORCE, VARIABLE MASS In this case, the hanging mass m (and accelerating force mg) will be kept constant but the rider mass M (and, therefore, the total mass m+M) will be varied for a number of different data taking runs (again, for improving the accuracy of the experiment). In this scenario, it is more convenient to rewrite Equation (4) in the form: a = mg (¹M) m+M/ (5) Equation (5) can, again, be viewed as a linear equation representing a straight line but, here, the acceleration a is the dependent variable, 1/(m+M) is the independent variable, and the slope is mg.
Transcribed Image Text:The motion of the system is analyzed by applying Newton's 2nd Law to each mass separately. The string and the pulley are assumed to have negligible mass. M Above: horizontal force acting on the mass of the rider Right: vertical forces acting on the hanging mass T-Ma If we assume the air track is frictionless, then the only force acting on the mass of the rider, M, in the horizontal direction is the tension T in the string, so that Newton's 2nd Law gives: mg - T = ma m (2) Considering the hanging mass, m, there are two forces acting on it in the vertical direction: the tension T and the force of gravity mg. Newton's 2nd Law in this case gives: (3) Elimination of T between Equations (2) and (3) leads to mg = (m + M)a This is the equation you will work with in this experiment. Ing (4) PART I: CONSTANT MASS, VARIABLE FORCE In this case, the quantity m+M in Equation (4) will be kept constant, but different combinations of m and M will be used for a number of different data taking runs (which will improve the accuracy of the experiment). This implies that, as the hanging mass m (and, therefore, accelerating force) varies, the acceleration a will vary. Equation (4) can be viewed as a linear equation representing a straight line with mg as the dependent variable, a as the independent variable, and m+M as the slope. You will use this fact in testing Equation (4). PART II: CONSTANT FORCE, VARIABLE MASS In this case, the hanging mass m (and accelerating force mg) will be kept constant but the rider mass M (and, therefore, the total mass m+M) will be varied for a number of different data taking runs (again, for improving the accuracy of the experiment). In this scenario, it is more convenient to rewrite Equation (4) in the form: a = mg (¹M) m+M/ (5) Equation (5) can, again, be viewed as a linear equation representing a straight line but, here, the acceleration a is the dependent variable, 1/(m+M) is the independent variable, and the slope is mg.
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