A ball of mass m = 2.0 kg is connected to 2 ropes. The two ropes are connected to a pole that is rotating at a constant angular speed ω. The two ropes have an equal tension T. The rope on the bottom makes an angle of 60◦ with the pole and and the rope on the top makes an angle of 60◦ with the horizontal. The ball is going around in a circle at a constant speed v and a radius r = 0.87 m (uniform circular motion).
Problem 1: What is v, the speed of the ball?
Problem 2: What is T, the tension on each of the ropes?

The first law of thermodynamics states that heat added to a system is neither created nor destroyed but is transformed ⇒ as it changes into other forms of energy.

Mutt and jeff are running along a path each pushing a cart loaded with rocks. if mutt's wagon has a mass two times greater than jeff's and they want to stay together, arriving at their destination at the same time, what must happen? a) jeff should slow down so mutt can catch up. b) mutt must use half as much force to push his cart. c) mutt must use twice as much force to push his cart. d) mutt and jeff will use the same force, but mutt will take bigger steps.

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?