In lab you submerge 100 g of iron nails at 40 0C in 100 g of water at 20 0 C. Specific heat of iron is 0.12 cal/g∙0C. Equate the heat gained by water to the heat lost by nails and show that the final temperature of water becomes 22.1 0C.

An input force of 7 n is applied to a machine with a mechanical advantage of 1.75. what is the maximum the machine could lift? 12.25 n7n7.25 n26.2 n

Consider an ordinary, helium-filled party balloon with a volume of 2.2 ft3. the lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. using this fact, we can derive archimedes’ principle, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. assuming that the balloon is at sea level, where the air density is 0.002377 slug/ft3, calculate the maximum weight that can be lifted by the balloon. note: the molecular weight of air is 28.8 and that of helium is 4.

You are given two vectors a⃗ =−3.00ι^ 5.00j^ and b⃗ =5.00ι^ 2.00j^. let the counterclockwise angles be positive.