Chapter 7, Problem 7.79P

DATA A single conservative force F(x) acts on a small sphere of mass m while the sphere moves along the .v-axis. You release the sphere from rest at x = 1.50 m. As the sphere moves, you measure its velocity as a function of position. You use the velocity data to calculate the kinetic energy K; Fig. P7.79 shows your data, (a) Let U(x) be the potential-energy function for F(x). Is U(x) symmetric about x = 0? [If so, then U(x) = U(−x). (b) If you set U = 0 at x = 0, what is the value of U at x = -1.50 m? (c) Sketch U(x). (d) At what values of x (if any) is F = 0? (e) For what range of values of x between x = −1.50 m and x = +1.50 m is F positive? Negative? (f) If you release the sphere from rest at x = −1.30 m. what is the largest value of x that it reaches during its motion? The largest value of kinetic energy that it has during its motion?