A friend is going to make two skateboard runs down a long ramp with your help. First run: you hold her in place until she's ready, then just let go. She rolls down the ramp and then along a level sidewalk until she collides with a huge, well-padded horizontal spring. The spring compresses some distance before momentarily stopping your friend. We'll consider friend + skateboard + spring all together as the system being analyzed. Since the speeds involved will be low, drag (air resistance) should be ignored. And since the skateboard has wheels, friction should also be ignored, until such time as friction may be assigned to you in the second run. (1) Make a sketch of the first run as described above, showing the ramp, sidewalk, and spring, with your friend pictured at the beginning and end, as well as somewhere in-between. (2) RNG Your friend is 4.56m above the sidewalk when released, the spring compresses 65.4 cm while stopping her, and her mass is m = 89.3 kg (including skateboard). Calculate the spring's force constant k, assuming the mechanical energy of the system is conserved. For credit, start from Ei = Ef, show all steps (including cancellation of qtys that are zero) and maintain i/f (initial/final) subscripts until numerical values are substituted. The rest of the assignment is entirely about the second run. Second run: Next, you'll either push your friend for a few meters from rest at the same starting point, OR you'll let her go as before, but one wheel will get briefly stuck after she reaches the bottom of the ramp, causing it to skid for a few meters along the sidewalk until the wheel starts rolling again, all before she hits the spring. (3) MVQ, RNG You push (if the next-to-last digit of you phone number is odd) Choose the force of the push (Fp = 397 N) or friction (FK = 351 N), and how far (x = 3.95 m) either you push before losing contact or the stuck wheel skids. If pushing, assume you push downhill, in the same direction she rolls. State your version, list your randoms, then calculate how much work is done on the system by either your push or friction. (4) Calculate how far the spring compresses in the second run. For credit, start with WNC,net = Ef - Ei and show work as in #2. Check: should the spring be compressed more or less than before? (5) MVQ Next, you're going to calculate your friend's speed at the instant before she hits the spring. Choose the interval you're going to analyze, then describe it here in one sentence: when does the interval begin and end? The choice is entirely up to you, but of course the interval must either begin or end at some instant before she hits the spring. (6) Starting from either Ei = Ef or WNC,net = Ef - Ei , depending on the interval you described, calculate your friend's speed just before she hits the spring. Show all steps.