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a complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations among them. this information is needed to solve oscillation problems of this type.

the position of a 45 g oscillating mass is given by x(t)=(2.0cm)cos(10t), where t is in seconds.

a

determine the velocity at t=0.40s.

express your answer in meters per second to two significant figures.

b

assume that the oscillating mass described in part a is attached to a spring. what would the spring constant k of this spring be?

express your answer in newtons per meter to two significant figures.

c

what is the total energy e of the mass described in the previous parts?

express your answer in joules to two significant figures.

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?

Which atomic model was proposed as a result of j. j. thomson’s work?

The mantle is made up of which structural zones?