Consider the rigid object in the figure below. Four masses lie at the points sho
ID: 1297888 • Letter: C
Question
Consider the rigid object in the figure below. Four masses lie at the points shown on a rigid isosceles right triangle with hypotenuse length 4a. The mass at the right angle is 3m, and the other three masses are m. Label them A, B, C, D, as shown. Assume that the object is floating freely in outer space. Mass C is struck with a quick blow, directed into the page. Let the impulse have magnitude Integral of Fdt=P. What are the velocities of all the masses immediately after the blow?
http://imgur.com/ucqixyy <---image here
Explanation / Answer
k so let position of the CM be R and lets work in the x y z coordinate system
Then R=[m(0,0,0)+m(2a,0,0)+m(4a,0,0)+3m(2a,2a,0)]/6m
which simplifies to
R=((4/3)a,(1/3)a,0)
Then using the equation Impulse=(mtotal)(vcm) we can write:
P=(6m)(vcm)
vcm=p/6m
Now to find the initial angular velocity ? I can write:
vcm=? r
for r though do I use the distance from the cm to mass C?
In that case I would have:
P/6m=? (a/3)(?65) and so
?=P/(2(?65)a m)