Microscopic Interpretation of Entropy

A box is seperated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases are at the same temperature. The partition is punctured, and equilibrium is eventually attained. Assume that the volume of the box is large enough for each gas to undergo a free expansion and not change temperature. What is the probability that the molecules will be found in the same distribution as before the partition was punctured, that is, 500 nitrogen molecules in the left half and 100 oxygen molecules in the right half. I got (1/2)^(100)*(1/2)^500 = 2.41*10^-181, but I think th... click for more

Equilibrium of a Rigid Body

One end of a post weighing 500N and with height h rests on a rough horizontal surface coefficient of static friction equal to .40. The upper end is held by a rope fastened to the surface and making an angle of 37 degrees with the post (see attached figure). A horizontal force F is exerted on the post as show in the attached diagram. a) If the force F is applied at the midpoint of the post, what is the largest value it can have without causing the post to slip? b) How large can the force be, without causing the post to slip, if its point of application is 6/10 of the way from the ground to the top of the post? C) Show that if the point of application of the force is too high, the p... click for more

Collisions

1. During a violent thunderstorm, hail of diameter 1.0 cm falls directly downward at speed of 25m/s. There are estimated to be 120 hailstones per cubic meter of air. (a) what is the mass of each hailstone ( density = 0.92 g/cm^3) ? (b) Assuming that the hail does not bounce fine the magnitude of the average force on a flat roof measuring 10m x 20m due to the impact of the hail. ( Hint : during impact the force on a hailstone from the roof is approximately equal to the net force on the hailstone because the gravitational force on it is small. 2. Figure below shows an approximate plot of force magnitude versus time during the collision of a 58 g Superball with a wall. The initial veloc... click for more

Rotation

1. A wheel has 8 equally spaced spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s ( revolutions per second ). You want to shoot a 20 cm long arrow parallel to this axle and thought the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. (a) What minimum speed must the arrow have ? (s) Does it matter where between the axle and rim of the wheel you aim? If so, what is the best location ? 1. At t=0, a fly wheel has an angular velocity of 4.7 rad/s (radians per second), an angular acceleration of -0.25 rad/s^2 , and a reference line at pheta0 = 0. (a) Through what maximum angle phetamax will the reference line tur... click for more

rotation

1. At t=0, a fly wheel has an angular velocity of 4.7 rad/s (radians per second), an angular acceleration of -0.25 rad/s^2 , and a reference line at pheta0 = 0. (a) Through what maximum angle phetamax will the reference line turn in the positive direction ? At what times t will the reference line be at (b) pheta = 1/2phetamax and (c) pheta = -10.5 rad (consider both positive and negative values of t ) ? 2. (a) What is the angular speed w about the polar axis of a point on Earths surface at a latitude of 40 degrees N ? ( earth rotates about that axis ) (b) What is the linear speed v of the point ? What are (c) w and (d) v for a point at the equator ? 3. A record turntable is rotating ... click for more