Jing has 1200 ft2 of roof in his home in pittsburgh, pa (hdd = 6,000). he is considering upgrading the insulation from r-16 to r-22. the estimate from the contractor was $554. his home is heated with natural gas. last year, the average price he paid for natural gas was $14.6/mcf. assuming an afue of 84.1%, how long will it take jing to recover his investment?

Aboxcar traveling at 12 m/s approaches a string of 5 identical boxcars sitting stationary on the track. the moving boxcar collides and links with the stationary cars and they all move off together along the track. what is the final speed of the cars immediately after the collision? (you may take the mass of each boxcar to be 18,537 kg.)

The percent efficiency of a machine can never be 100% (or greater), because in the real world some energy is always converted into a. heat b. work c. input force d. output force

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.