# Assignment 8

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## Assignment 8

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Problems/Exams

- Pages:
- 4
- School:
- Duke University
- Course:
- Phy 053l - General Physics I

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PHY 53 Summer 2010 Duke Marine Laboratory Assignment 8 1 Some questions about the vector product C A B a Prove the rules given in the notes for the magnitude and direction of C from the definition in terms of components Let A and B lie in the x y plane with A along the x axis and B having direction with angle relative to A b One requires to be the angle between A and B that is no larger than Why 2 c What are the rules for the vector products of the unit vectors i j k d Prove directly from the definition in terms of components that A B B A Use the situation in a Consider the effects of the gravitational force on the particles of a system The ith particle of mass mi at position ri experiences a gravitational force mig ri where g ri is the gravitational field at that point If the gravitational field is uniform then g ri is the same at the location of all the particles Call it g a If the gravitational field is uniform show that the total gravitational force on the system is simply Mg where M is the total mass b The gravitational torque about the CM from the force on the ith particle is i ri mig ri where ri is the position of the particle relative to the CM Show that if the gravitational field is uniform the total gravitational torque about the CM is zero 1 PHY 53 Summer 2010 3 Duke Marine Laboratory Comment on the validity of these statements about forces and torques a If two forces obey F1 F2 0 then they give zero torque about any point b If the total force on a body is zero and the total torque from those forces is zero about some point then the total torque from those forces is zero about all points c Two forces acting along two separate parallel lines obey F1 F2 0 There is a point between those lines about which the total torque is zero d If F1 F2 0 and the forces both act along the same line then they give zero total torque about any point 4 An object with a circular cross section of radius R and moment of inertia about its symmetry axis I mR 2 is rolling down an

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