PHYS171_f11_lecture_supp_10(1) - attachment to each mass...

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PHYS171 Fall 2010 Prof. Arthur La Porta Is Tension a scalar or a vector? The question is, is the tension in a string a scalar or a vector, and if it is a vector why can the direction of the same tension be different in different locations along the string? You can consider the tension in a string to be a scalar. However, to have tension the string must be attached at both ends, and the force that the string exerts on each attachment point is a vector. The tension always acts along the direction defined by the string, and is always directed away from the attachment point (i.e., a string can only pull, it can’t push). Since the string exerts equal and opposite forces on both ends there is no net force on a segment of string. 1 m m T 2 T 4 T 3 T 1 F In the example above a single string is draped over a pulley has a scalar tension T. At the
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Unformatted text preview: attachment to each mass this the tension would manifest itself as a vector force which is directed vertically upward. Where the string makes contact with the wheel the scalar tension manifests itself as a downward force (as though the string were attached to the wheel at this point). At each mass we would write y ma mg T a m F = = r r T is in positive y direction because the tension produces an upward force. Since the pulley does not move the sum of forces on the pulley would be written as = = T T F a m F r r where T is in the negative y direction because the force due to tension acts downward. 1 This is true in the limit of a light string. If the string has substantial mass a net force would be required to accelerate the string and assumption that the net force is zero would fail....
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PHYS171_f11_lecture_supp_10(1) - attachment to each mass...

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