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Notice that the sign of the acceleration depends on the relative masses of the two objects. For which case will the acceleration be negative? O m, > m2 O mị < m2 m1 = m2 EXERCISE Suppose that in the same Atwood setup another string is attached to the bottom of m, and a constant force f is applied, retarding the upward motion of m,. If m, = 6.60 kg and m, = 10.00 kg, what value of f (in N) will reduce the acceleration of the system by 52%? Hint N Need Help? Read It

Notice that the sign of the acceleration depends on the relative masses of the two objects. For which case will the acceleration be negative? O m, > m2 O mị < m2 m1 = m2 EXERCISE Suppose that in the same Atwood setup another string is attached to the bottom of m, and a constant force f is applied, retarding the upward motion of m,. If m, = 6.60 kg and m, = 10.00 kg, what value of f (in N) will reduce the acceleration of the system by 52%? Hint N Need Help? Read It

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The Atwood Machine sign convention, the y-component of the net force exerted on object 1 is T- m,9, and the y-component of the net When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass as in figure (a), the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to determine the value of g. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight string. force exerted on object 2 is given by which of the following expressions? O m,g - m,9 O m,T + m,T The Atwood machine. (a) Two objects connected by a massless inextensible (b) The free-body diagrams for O m,g + T string over a frictionless pulley. the two objects. O mɔg - T From the particle under a net force model, apply Newton's second law to object 1. (Use the following as necessary: ay 9, and m.) (1) ,-T- m,g - Apply Newton's second law to object 2. (Use the following as necessary: ay 9, and m2.) (2) E,- m,g -T = SOLUTION Add Equation (2) to Equation (1), noticing that T cancels: Conceptualize Imagine the situation pictured in figure (a) in action: as one object moves upward, the other object -m,g + m,g - m,a, + mza, moves downward. Because the objects are connected by an inextensible string, the magnitude of the acceleration Solve for the acceleration. (Use the following as necessary: m, m, and g.) of m, must be --Select--- v the magnitude of the acceleration of m,. (3) a,- Categorize The objects in the Atwood machine are subject to the gravitational force as well as to the forces exerted by the strings connected to them. Therefore, we can categorize this problem as one involving two particles ---Select--- Analyze The free-body diagrams for the two objects are shown in figure (b). Two forces act on each object: the upward force T exerted by the string and the downward gravitational force. In problems such as this one in which the pulley is modeled as massless and frictionless, the tension in the string on both sides of the pulley is ---Select--- v. If the pulley has mass or is subject to friction, the tensions on either side are not the same and the situation requires techniques we will learn in a later chapter. Substitute Equation (3) into Equation (1) to find T. (Use the following as necessary: m, m2, and g): (4) T- m,(g + a,) = We must be very careful with signs in problems such as this one. In figure (a), notice that if object 1 accelerates upward, object 2 accelerates downward. Therefore, for consistency with signs, if we define the upward direction as positive for object 1, we must define the downward direction as positive for object 2. With this sign convention, both objects accelerate in ---Select--- v as defined by the choice of sign. Furthermore, according to this Finalize The acceleration given by Equation (3) can be interpreted as the ratio of the magnitude of the unbalanced force on the system (m, - m,)g to the total mass of the system (m, + m,), as expected from Newton's second law.
Transcribed Image Text:The Atwood Machine sign convention, the y-component of the net force exerted on object 1 is T- m,9, and the y-component of the net When two objects of unequal mass are hung vertically over a frictionless pulley of negligible mass as in figure (a), the arrangement is called an Atwood machine. The device is sometimes used in the laboratory to determine the value of g. Determine the magnitude of the acceleration of the two objects and the tension in the lightweight string. force exerted on object 2 is given by which of the following expressions? O m,g - m,9 O m,T + m,T The Atwood machine. (a) Two objects connected by a massless inextensible (b) The free-body diagrams for O m,g + T string over a frictionless pulley. the two objects. O mɔg - T From the particle under a net force model, apply Newton's second law to object 1. (Use the following as necessary: ay 9, and m.) (1) ,-T- m,g - Apply Newton's second law to object 2. (Use the following as necessary: ay 9, and m2.) (2) E,- m,g -T = SOLUTION Add Equation (2) to Equation (1), noticing that T cancels: Conceptualize Imagine the situation pictured in figure (a) in action: as one object moves upward, the other object -m,g + m,g - m,a, + mza, moves downward. Because the objects are connected by an inextensible string, the magnitude of the acceleration Solve for the acceleration. (Use the following as necessary: m, m, and g.) of m, must be --Select--- v the magnitude of the acceleration of m,. (3) a,- Categorize The objects in the Atwood machine are subject to the gravitational force as well as to the forces exerted by the strings connected to them. Therefore, we can categorize this problem as one involving two particles ---Select--- Analyze The free-body diagrams for the two objects are shown in figure (b). Two forces act on each object: the upward force T exerted by the string and the downward gravitational force. In problems such as this one in which the pulley is modeled as massless and frictionless, the tension in the string on both sides of the pulley is ---Select--- v. If the pulley has mass or is subject to friction, the tensions on either side are not the same and the situation requires techniques we will learn in a later chapter. Substitute Equation (3) into Equation (1) to find T. (Use the following as necessary: m, m2, and g): (4) T- m,(g + a,) = We must be very careful with signs in problems such as this one. In figure (a), notice that if object 1 accelerates upward, object 2 accelerates downward. Therefore, for consistency with signs, if we define the upward direction as positive for object 1, we must define the downward direction as positive for object 2. With this sign convention, both objects accelerate in ---Select--- v as defined by the choice of sign. Furthermore, according to this Finalize The acceleration given by Equation (3) can be interpreted as the ratio of the magnitude of the unbalanced force on the system (m, - m,)g to the total mass of the system (m, + m,), as expected from Newton's second law.
Notice that the sign of the acceleration depends on the relative masses of the two objects. For which case will the acceleration be negative? O m, > m2 O m, < m2 m1 = m2 EXERCISE Suppose that in the same Atwood setup another string is attached to the bottom of m, and a constant force f is applied, retarding the upward motion of m,. If m, = 6.60 kg and m, = 10.00 kg, what value of f (in N) will reduce the acceleration of the system by 52%? Hint N Need Help? Read It
Transcribed Image Text:Notice that the sign of the acceleration depends on the relative masses of the two objects. For which case will the acceleration be negative? O m, > m2 O m, < m2 m1 = m2 EXERCISE Suppose that in the same Atwood setup another string is attached to the bottom of m, and a constant force f is applied, retarding the upward motion of m,. If m, = 6.60 kg and m, = 10.00 kg, what value of f (in N) will reduce the acceleration of the system by 52%? Hint N Need Help? Read It
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