You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 13-m-high hill, then descends 18 m to the track's lowest point. You've determined that the spring can be compressed a maximum of 2.5 m and that a loaded car will have a maximum mass of 420 kg. For safety reasons, the spring constant should be 14 % larger than the minimum needed for the car to just make it over the top. A. What spring constant should you specify?
Express your answer to two significant figures and include the appropriate units.

B. What is the maximum speed of a 330 kg car if the spring is compressed the full amount?
Express your answer to two significant figures and include the appropriate units.

5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?

The junction rule describes the conservation of which quantity? note that this rule applies only to circuits that are in a steady state.

What is an electric motor? explain its operation. 2-3 sentence