Recent content by azure kitsune

Thank you everyone for responding. No, it is definitely "sets." The problem is copied directly from the textbook. (which is Apostol's Mathematical Analysis, chapter 3) No, I have never heard of it before, probably because I'm pretty new to analysis. Wolfram MathWorld tells me that the...

Homework Statement Show that the set of rational numbers in the interval (0, 1) cannot be expressed as the intersection of a countable collection of open sets. Homework Equations The Attempt at a Solution This sounds like something requiring proof by contradiction. There must be...

Thank you! That made the problem a lot clearer!

Thank you for the reply. I got the solutions manual from my teacher. In it, the answer to (b) is given by: \frac{1}{\sqrt{1-0.76^2}} \left[ 3.09 \times 10^{-6} \text{ s} - \frac{(-0.76c)(400 \text{ m})}{c^2} \right] = 6.32 \times 10^{-6} \text{ s} Can someone explain that, or is it a mistake?

Homework Statement A spaceship of proper length Lp = 400 m moves past a transmitting station at a speed of v = 0.76c. At the instant that the nose of the spaceship passes the transmitter, clocks at the transmitter and in the nose of the spaceship are synchronized to t = t' = 0. The instant...

Is this correct? Let v_x and v_y be the x and y components of the velocity of the ball immediately after impact. It's easy to calculate that v_y = \sqrt{2g\alpha h}. Let \Delta t be the time of the impact. During this time, we have \Delta v_y = \sqrt{2gh} + \sqrt{2g\alpha h} =...

Homework Statement You have a solid, homogenous ball with radius R. Before falling to the floor, its center of mass is at rest, but it is spinning with angular velocity \omega_0 about a horizontal axis through its center. The lowest point of the ball is at a height h above the floor. When...

Thank you! Time to mark some corrections into the book!

Homework Statement A 1.00 micro-F capacitor charged to 50.0 V and a 2.00 micro-F capacitor charged to 20.0 V are connected, with the positive plate of each connected to the negative plate of the other. What is the final charge on the 1.00 micro-F capacitor? Homework Equations Q = CV...

Thank you for explaining! I think I understand. Is the following statement correct?: For a charged conducting plate by itself, the charge would be uniformly distributed on the two surfaces because there is no other way for E to be 0 inside. For a capacitor with two dielectrics, the charge is...

Assume you have two parallel plates with charges +q and -q. Now, you fill the space in between with two different dielectrics so that if you were to move straight from one plate to the other, you would be in the same dielectric. (In other words, the two dielectrics do not form "layers.")...

Homework Statement Water flows at 7 m/s in a pipe of radius 5 cm. A plate having an area equal to the cross-sectional area of the pipe is suddenly inserted to stop the flow. Find the force exerted on the plate. Take the speed of sound in water to be 1.4 km/s. (Hint: When the plate is...

That's possible, but I think I may be understanding the problem incorrectly. Maybe the 1 J of work done by the machine is also included in the "joules" that "are removed from the room." (in which case the problem would be asking for QH)

Hi Matt, thanks for your reply. I tried to use the equations you gave for COP, but I still end up with QL = 20.3 J.

Homework Statement A Carnot air conditioner takes energy from the thermal energy of a room at 70 degrees F and transfers it to the outdoors, which is at 96 degrees F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room? Homework...