Write down the total energy (potential and elastic) of a hanging cable made up of three weightless springs connecting two objects of mass m1 and m2 the end points of the cable are (x0, , 1) and (x3, y3) = (3,1). the masses are located at (x1, y1) and (x2, y2). the springs have hooke's constants k01, k12, k23 and natural lengths l01, l12 and l23. the equilibrium position of the cable is obtained by minimising the total energy of the system. formulate the problem mathematically to solve for the equilibrium position (x, y).

An electron and a proton have the same kinetic energy upon entering a region of constant magnetic field and their velocity vectors are perpendicular to the magnetic field. suppose the magnetic field is strong enough to allow the particles to circle in the field. note: you'll need to look up the masses for an electron and proton. 1) what is the ratio of the radii of their circular paths rp/re?

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?

Which features on mars point to the possibility of liquid water on the planet? impact craters with sharp rims volcanic cones with craters gullies and stream-like channels mountain ranges with faults