{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
3. Comment on the validity of these statements about forces and torques.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}