Solve Snowball Question: Physics for Scientists and Engineers

[xoombot]

We got this homework question out of the Physics for Scientists and Engineers book and I came up with some answers but am not sure if they are correct. It's a pretty confusing one and I'm not expecting anyone to answer this before the assignment is due -- it would be nice to see how to solve it before an exam though. Here's the question:

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.

 

[OlderDan]

What did you assume to do part a? There is not enough information given. Did the sign start swinging from the maximum angle?

 

[xoombot]

I think "The maximum angular displacement of the sign is 25.0° on both sides of the vertical" and "The sign is swinging without friction" imply that the sign starts 25 degrees above the vertical and goes back and forth forever.

By the way, as far as the not enough information given argument, I didn't post the question we were assigned after this but it has a huge typo where angular momentum is measured in seconds (unless I misunderstood the question) :O.

 

[OlderDan]

I think "The maximum angular displacement of the sign is 25.0° on both sides of the vertical" and "The sign is swinging without friction" imply that the sign starts 25 degrees above the vertical and goes back and forth forever.

By the way, as far as the not enough information given argument, I didn't post the question we were assigned after this but it has a huge typo where angular momentum is measured in seconds (unless I misunderstood the question) :O.

Your part b and your very incorrect part c makes me wonder if you are using linear momentum or angular momentum. You did not say anything about moment of inertia. Are you using angular momentum and rotational energy for this?

 

[xoombot]

Angular momentum.

Edit -- I just worked the problem again and ended up with an angle of 18.46 degrees above the vertical. Does anyone know if that's what I should have ended up with?

 

[OlderDan]

Angular momentum.

Edit -- I just worked the problem again and ended up with an angle of 18.46 degrees above the vertical. Does anyone know if that's what I should have ended up with?

I found different answers for everything. It's an easy problem to make an Algebra mistake, so it's entirely possible I made one. Obviously, one of us did. See if we agree on any of these

I_sign = 0.2kgm^2
I_ball = 0.1kgm^2 when it splats onto the sign
ω_i = 2.347rad/sec
L_sign = .4694kgm^2/s before impact
L_ball = -.32kgm^2/s before impact
L_total = .1494kgm^2/s before and after impact
ω_i = 0.498rad/sec (no reversal of sign direction)
θ_f = 5.58degrees.

 

[xoombot]

I'm not sure since I already turned the assignment in but when I get it back, if it's wrong, I'll post what I got for those to figure out where the mistake was.