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Assign8

# Assign8 - PHY 53 Summer 2010 Duke Marine Laboratory 1 Some...

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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 θ relative to A . b. One requires θ to be the angle between A and B that is no larger than π . Why? 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).] 2. Consider the effects of the gravitational force on the particles of a system. The i th particle, of mass m i at position r i experiences a gravitational force m i g ( r i ) , where g ( r i ) is the gravitational field at that point. If the gravitational field is uniform , then g ( r i ) 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 M g , where M is the total mass. b. The gravitational torque about the CM from the force on the i th particle is τ i = r i × m i g ( r i ) , where r i 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. PHY 53 — Summer 2010 Duke Marine Laboratory 1

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3. Comment on the validity of these statements about forces and torques.
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