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As the title suggests, I have a physics final tomorrow and have been doing questions from past finals to prepare. I've tried to solve these independently since that is what will be expected of me on the test, but there are a couple that have me stumped.

1:

The problem statement: http://imageshack.us/a/img688/6753/screenshot20121212at619.png [Broken]

Here's what I've tried for this one. I broke up the situation into 3 stages, each of which is pictured in the diagram.

Stage 1 - the wheel has kinetic energy KE = 1/2 Iω^2 + 1/2 mv^2. Using the substitution v = rω, the expression came out to be 3/4 mr^2 ω^2.

Stage 2 - Next, since this was an elastic collision, KE was conserved, so I said that 1/2 Iω^2 - 1/2 mv^2 = 1/2 Iω^2 + 1/2 mv^2 because ω is still going in the same direction, but v is going in the opposite direction. But this gave me 0 = mv^2, which doesn't make much sense to me. I also think I should draw a free-body diagram showing the effects of static friction here, but I don't know how to start.

EDIT: Apparently forgot the carat (^) sign to denote exponents... oops.

2:

The problem statement: http://imageshack.us/a/img641/6753/screenshot20121212at619.png [Broken]

I tried solving this as a static equilibrium problem. I had T = (2.5)(-0.732 * 9.8) + (5)(25 * 9.8), but didn't manage to get much farther than that.

For the second part, I used the fundamental frequency expression f1 = v/2L, and the wave speed v = sqrt(T/μ). Obviously I'll have to use the value for T I attempted to find above, but I don't know whether that value is correct to begin with.

Any tips would be appreciated - thanks a ton!

1:

The problem statement: http://imageshack.us/a/img688/6753/screenshot20121212at619.png [Broken]

Here's what I've tried for this one. I broke up the situation into 3 stages, each of which is pictured in the diagram.

Stage 1 - the wheel has kinetic energy KE = 1/2 Iω^2 + 1/2 mv^2. Using the substitution v = rω, the expression came out to be 3/4 mr^2 ω^2.

Stage 2 - Next, since this was an elastic collision, KE was conserved, so I said that 1/2 Iω^2 - 1/2 mv^2 = 1/2 Iω^2 + 1/2 mv^2 because ω is still going in the same direction, but v is going in the opposite direction. But this gave me 0 = mv^2, which doesn't make much sense to me. I also think I should draw a free-body diagram showing the effects of static friction here, but I don't know how to start.

EDIT: Apparently forgot the carat (^) sign to denote exponents... oops.

2:

The problem statement: http://imageshack.us/a/img641/6753/screenshot20121212at619.png [Broken]

I tried solving this as a static equilibrium problem. I had T = (2.5)(-0.732 * 9.8) + (5)(25 * 9.8), but didn't manage to get much farther than that.

For the second part, I used the fundamental frequency expression f1 = v/2L, and the wave speed v = sqrt(T/μ). Obviously I'll have to use the value for T I attempted to find above, but I don't know whether that value is correct to begin with.

Any tips would be appreciated - thanks a ton!

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