In her backyard, Gretchen has a swing set with a rope hanging from it. She fantasizes about running fast enough toward a rope so that she can grab the rope and swing around in a full circle. Gretchen (mass m) swingset frame Rope (length) 278. List at least three simplifying assumptions that need to be made in order to use basic physics models to predict the minimum speed Gretchen must run to make a full circle on the rope. Justify your assumptions. 279. Derive an expression for the minimum speed Gretchen needs at the top of her circular path in order to complete the full circular path. 280. Derive an expression for Gretchen's minimum running speed in order to complete a full circle swing. Pick reasonable values for the variables and use your expression to estimate a value for the minimum running speed. Comment on whether or not this speed is a realistic value for Gretchen. 281. As the child swings in the full circle at the minimum speed condition, at what position will the tension in the rope be the greatest? What is the value of tension there?