- #1

xoombot

- 5

- 0

P38. 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 2.40 kg and its vertical dimension is 50.0 cm. 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° on both sides of the vertical. At a moment when the sign is vertical and moving to the left, a snowball of mass 400 g, traveling horizontally with a velocity of 160 cm/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 the angular speed immediately after the impact. (c) The spattered sign will swing up through what maximum angle?

To save time, I'm not going to type out all the algebra I used to come up with my answers. Here's a short version of how I solved it (after loads of help).

For part a, mechanical energy is conserved. I got 1.916 rad/s.

For part b, momentum is conserved. I got -1.643 rad/s.

For part c, Use the same thing as part a except do it backwards to find the angle. I ended up with 86.05 degrees, which is definitely incorrect.

I'll probably take a look at the problem again before attending class. I hate asking for help on forums like this but it'd be a lot more convenient for me to get a response online instead of having to skip a class to go to a help center's hours. Thanks in advance.