Systems of Particles

Refer to attachment: Find (a) the x coordinate and (b) the y coordinate of the center of mass of the remaining piece. What is h (a) initially and (b) when all the soda has drained (c) What happens to h during the draining of the soda ? (d) If x is the height of the remaining soda at any given instant, find x in terms of M , ...continues

conservation of momentum and kinetic energy

A superball has collisions that are nearly prefectly elastic. A superball of mass M is dropped from rest from a height h (where h >> the size of the superball) together with a smaller marble, of mass m; the marble is initially just a little above the top of the superball and remains right over it throughout the fall. The superba ...continues

Finding the coefficient of friction

A cylinder of mass M and radius R rests on an inclined plane. It is held in place by a horizontal string that is attached to the edge of the cylinder. If the angle that the plane makes with the horizontal is theta, and the coefficient of static friction between the cylinder and the plane is u, what is the smallest value of U tha ...continues

rotational inertia and angular velocity

A solid door of mass M = 20kg and width l= 1m is hit at a right angle by a mud ball of mass m = .5kg, which hits the door at the edge with speed v= 10m/s and sticks. (a) What is the rotational inertia of the door about the hinges? (b) What is the angular velocity of the door after having been struck? (c) What fraction of the ini ...continues

gravity

a mass of 100kg weighs 980.6N at sea level. estimate the weight of this body at the top of a mountain 5km high. assume that the mean diameter of the earth is 12742km

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 b ...continues

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 di ...continues

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 ...continues

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 mini ...continues

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 an ...continues