# Square Hole, Exploding Shell, Rotating Molecule, and Atwood's Machine

1. Nov 3, 2008

### quidditch

1. A uniform square plate 7.2 m on a side has had a square piece 3.9 m on a side cut out of it. The center of the missing piece is at x = 1.65 m, y = 0. The center of the square plate is at x = y = 0. What is the x-coordinate of the center-of-mass of the remaining piece?

2.

3. I really don't know what to do. I know that the square piece that was cut out needs to be subtracted, but that's all I can figure out.

1. A shell is fired from a gun with a muzzle velocity of 52.0 m/s, at an angle of 32.0 degrees with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass. One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming level terrain and negligible air drag?

2.

3. I really have absolutely no idea where to even begin. I always have problems with finding the equations to use.

1. The oxygen molecule, O2, has a total mass of 5.30×10-26 kg and a rotational inertia of 1.94×10-46 kg-m2 about an axis perpendicular to the center of the line joining the atoms. Suppose that such a molecule in a gas has a speed of 1.52×103 m/s and that its rotational kinetic energy is two-thirds (2/3) of its translational kinetic energy.
Find its angular velocity.

2. Again, I have no clue what to do for this problem!

1. In an Atwood's machine, one block has a mass of 540.0 g, and the other a mass of 695.0 g. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.10 cm. When released from rest, the heavier block is observed to fall 86.2 cm in 2.64 s (without the string slipping on the pulley).
What is the change in the potential energy of the system after 2.64 s?

2. There are seven parts to this problem and I did get the first six right:

What is the acceleration of the 540.0-g block? 2.4700×10-1 m/s^2
What is the acceleration of the 695.0-g block? 2.4700×10-1 m/s^2
What is the tension in the part of the cord that supports the 540.0-g block? 5.4308 N
What is the tension in the part of the cord that supports the 695.0-g block? 6.6463 N
What is the angular acceleration of the pulley? 4.8430
What is the rotational inertia of the pulley? 1.2800×10-2 kg*m^2

But now i can't figure out how to do the last one, which is the change in potential energy of the system.

I am pretty sure I can figure these out if I have the correct equations, I just can never seem to use the right ones. So even the littlest thing might help. Thanks so much!

2. Nov 4, 2008

### tiny-tim

Welcome to PF!

Hi quidditch! Welcome to PF!

1. How would you solve it if there was no hole, but an extra square plate was added?

ok, use the same method, but with negative mass.

2. Use conservation of energy to find the height, and then conservation of momentum to find the initial velocity.

3. How is rotational inertia related to rotational kinetic energy?