E2.4 A laser printer uses a laser beam to print copy rapidly for a computer. The laser is positioned by a control input r(t), so that we have Y(s) = 4(s + 50) R(s) s 2 + 40s + 300 The input r(t) represents the desired position of the laser beam. (a) If r(t) is a unit step input, find the output y(t). (b) What is the final value of y(t)?

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?

Arowboat passenger uses an oar to push the boat off the dock by exerting a force of 40n for 3.0s. what impulse acts on the boat.

Nacidified solution was electrolyzed using copper electrodes. a constant current of 1.18 a caused the anode to lose 0.584 g after 1.52 ✕ 103 s. given that the charge of an electron is 1.6022 ✕ 10−19 c, calculate avogadro's number. assume that copper is oxidized to cu2+ ions.