- #1
lastguymade
- 8
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Homework Statement
Hi guys! I'm having trouble with this Problem. A thin uniform rectangular sign hangs vertically above the door of a shop. The sign is hinged to a stationary horizontal rod along its top edge. The mass of the sign is 2.40kg and its vertical dimension is 50.0cm. The sign is swinging without friction, becoming a tempting target for children armed with snowballs. The maximum angular displacement of the sign is 25.0 degrees on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 400g, traveling horizontally with a velocity of 160cm/s to the right strikes perpendicularly the lower edge of the sign and sticks there. (a) Calculate the angular speed of the sign immediately before the impact. (b) Calculate its angular speed immediately after the impact. (c) The spattered sign will swing up through what maximum angle?
Homework Equations
for part (a) I'm not sure if I'm supposed to use conservation of mechanical energy or if I should do the vector product of the sign at the maximum angle (since its swinging without friction) multiplied by the vector of the sign at the origin.
for part (b) I know momentum is conserved but I really don't understand how linear momentum converts to angular momentum or vice versa. I am also confused as to how get the moment of inertias for both the sign and snowball before impact and the combined moment of inertia after.
for part (c) I'm completely lost
The Attempt at a Solution
Ok so for (a) if I use conservation of kinetic energy I get mgh=.5mw^2
if I take height as h=.5cos25 I get w=2.98
If I do it the second way I mentioned I get w=L/I = 1.892
(I got the moment of Inertia by looking on this forum where someone mentioned it but I don't know how they got it.)
for (b) I got the angular momentum of the sign by multiplying I=.2 *w (2.98)=.596 (This would be wrong if my first calculation was wrong) and then I added it with the momentum of the ball to get the total momentum which is conserved after to get L(total)=-.044
I then divided that number by the new I (.2+.1) and got w=-.146
(c) I don't know at all.
I'm sorry guys, I'm really confused by angular momentum but I figured this would be the best place to look. If my basic understanding is too flawed then just tell me and I'll go back to the books but any tips would be appreciated.
Cheers!