The system below consists of a particle P' (mass 5m) and a dumbbell B comprised of...

 

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The system below consists of a particle P' (mass 5m) and a dumbbell B comprised of two particles each of mass m. The relative positions of P' and B remain fixed and the length of the rod is L. Let the direction from P' to the cm ben. (a) Determine the exact gravity force on B due to P'. Use this exact force and locate the c.g. Add both the c.m. and the c.g. to the sketch in their relative locations. (b) Add the exact gravity force to the sketch and its line of action. What moment M acts about the c.m. due to the exact gravity force? (c) Let the rod be disturbed and placed at an angle 60 (dashed line) with respect to the line connecting P' and the c.m. as seen below. How will the line of action, corresponding to the resultant gravity force, shift? (Determine the angle of the line of action relative to n.) Now compute the moment about the c.m. (magnitude and direction). Discuss how such a moment tends to rotate the rod from its original orientation? Is the original orientation stable or unstable? 0.75 L P' P' 60 The system below consists of a particle P' (mass 5m) and a dumbbell B comprised of two particles each of mass m. The relative positions of P' and B remain fixed and the length of the rod is L. Let the direction from P' to the cm ben. (a) Determine the exact gravity force on B due to P'. Use this exact force and locate the c.g. Add both the c.m. and the c.g. to the sketch in their relative locations. (b) Add the exact gravity force to the sketch and its line of action. What moment M acts about the c.m. due to the exact gravity force? (c) Let the rod be disturbed and placed at an angle 60 (dashed line) with respect to the line connecting P' and the c.m. as seen below. How will the line of action, corresponding to the resultant gravity force, shift? (Determine the angle of the line of action relative to n.) Now compute the moment about the c.m. (magnitude and direction). Discuss how such a moment tends to rotate the rod from its original orientation? Is the original orientation stable or unstable? 0.75 L P' P' 60