An experiment was conducted with a hoop spring attached to a force probe, both of which were mounted to a low friction dynamics cart. The compression of a hoop spring may be modeled as a Hookean spring. The system was placed on a horizontal track with a motion encoder to measure the displacement of the cart. The following graph shows the experimental force vs. displacement for a black hoop (steeper line) and a white hoop, each tested separately. The white hoop/probe/cart mass is 0.500 kg and the black hoop/probe/cart mass is 1.000 kg. Spring Force (N) Hoop Spring Force vs. Displacement 3 Linear Fit for:Black Hoop I Spring Force Force =mx+b m (Slope): 78 N/m b (Y-Intercept):0.096 N Correlation: 1.0 RMSE: 0.056 N 2 0 0.00 Linear Fit for:White Hoop I Spring Force Force =mx+b m (Slope): 30 N/m b (Y-Intercept):0.015 N Correlation: 1.0 RMSE: 0.021 N 0.02 0.04 Displacement (m) 0.06 237. The carts experience a head-on collision such that the hoops compress between them. If the white hoop compresses a total distance of 5.0 cm, what is the compression distance of the black hoop? 238. If the cart with the black hoop is pushed against a wall and compresses spring 5.0 cm, how fast will it be released? the 239. How far must the white cart's hoop be compressed against the wall for it to leave at the same speed as the black-hoop cart moved in the previous question?