Abowler throws a bowling ball of radius r = 11 cm along a lane. the ball slides on the lane with initial speed vcom,0 = 6.0 m/s and initial angular speed ω0 = 0. the coefficient of kinetic friction between the ball and the lane is 0.35. the kinetic frictional force f with arrowk acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of the ball. when speed vcom has decreased enough and angular speed ω has increased enough, the ball stops sliding and then rolls smoothly.(a) what then isvinterms ofω? (b) during the sliding, what are the ball’s translational and angularacceleration? (c) how far does the ball slide?

How would you place two electrons on a sphere of radius r so that the electrostatic potential energy is minimized. how would you place three electrons to solve the same problem.

Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. so it is no surprise that such clothing has largely replaced thickand heavy old-fashioned coats. (a) consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 w/m·°c) with 1.5-mm-thick air space (k = 0.026 w/m·°c) between the layers. assuming the inner surface temperature of the jacket to be 28°c and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°c and the heat transfer coefficient at the outer surface is 25 w/m2·°c. (b) what would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? what should be the thickness of a wool fabric (k = 0.035 w/m·°c) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a five-layer ski jacket?

If a stone with an original velocity of 0 is falling from a ledgeand takes 8 seconds to hoybthe ground whays the final velocity of the stone