A small ball swings in a horizontal circle at the end of a cord of length l1, which forms an angle θ1 with the vertical. The cord is then slowly drawn through the support at O until the length of the free end is l2. (a) Derive a relation among l1, l2, θ1, and θ2. (b) If the ball is set in motion so that initially l1 5 0.8 m and θ1 5 35°, determine the angle θ2 when l2 5 0.6 m.

Ateam of astronauts is on a mission to land on and explore a large asteroid. in addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. with what minimum initial speed vesc will the rocks need to be thrown in order for them never to "fall" back to the asteroid? assume that the asteroid is approximately spherical, with an average density p 3.84 x108 g/m3 and volume v 2.17 x 1012 m3 recall that the universal gravitational constant is g 6.67 x 10-11 n m2/kg2

Argon is adiabatically compressed from an initial volume of 16 liters to a final volume of 2 liters. by what factor do the following quantities change? do they increase or decrease? (a) the rms speed (b) the thermal energy of the gas (c) the molar specific heat cv (d) the pressure

Quantum mechanics applies to subatomic, atomic, nanometer-size, and micrometer-size systems. nanometer, micrometer, and kilometer-size systems. atomic, nanometer-size, and micrometer-size systems. subatomic, atomic, and nanometer-size systems.