wwwww 5.0 m d X = = (a) 2.0 m, (b) 4.0 m, (c) 10.0 m, (d) Does the particle turn around at some point and head back toward the origin? (e) Repeat part (d) if v=2.0 m/s at x = 0. F(x)(N) 10.0+ 5.0+ 0 2.0 4.0 6.0 8.0 x(m) -5.0 -10.0+ 44 A small ball is tied to a string and set rotating with negligible friction in a vertical ball moves over the top of the circle slowest possible speed (so tha cle. If the on in the string is negligible), what is the tension in the string at the bottom of the circle, assuming there is no additional energy added to the ball during rotation? 3.4 Potential Energy Diagrams and Stability 45. A mysterious constant force of 10 N acts horizontally on everything. The direction of the force is found to be always pointed toward a wall in a big hall. Find the potential energy of a particle due to this force when it is at a distance x from the wall, assuming the potential energy at the wall to be zero. A single force F(x)=-4.0x (in newtons) acts on a 1.0-kg body. When x = 3.5 m, the speed of the body is 4.0 m/s. What is its speed at x = 2.0 m? 47. A particle of mass 4.0 kg is along the x-axis under F(x)=-x particle's spe m/s. Wha to move 50. A particle of mass 0.50 kg moves along the x-axis with a potential energy whose dependence on x is shown below. (a) What particle at x=2.0, 5.0, 8.0, and 12 mechanical energy E of the particle is -6.0 J, what are the minimum and maximum positions of the (c) What are these positions if E = 2.0 J? 16 J, what are the speeds of the particle at ons listed in part (a)? 4.0 -8.01 -12.0+ 4.0 8.0 12.0 16.0 20.0 x(m) 51. (a) Sketch a graph of the potential energy function U (x)=kx+12+ Ae¯x, where k, A, and a are constants. (b) What is the force corresponding to this potential energy? (c) Suppose a particle of mass m moving with this potential energy has a velocity va when its x=a. Show that the particle does through the origin unless AS mua² + ka² e-aa2 49. A 4.0-kg particle moving along the x-axis is acted upon by the force whose functional form appears below. The velocity of the particle at x = 0 is v = 6.0 m/s. Find the particle's speed at of Energy cartoon movie Pocahontas openstax.org/1/21pocahontclip), tas runs to the edge of a cliff and jumps casing the fun side of her personality. is running at 3.0 m/ bre jumping iff and she hits the water at the bottom cliff at 20.0 m/s, how high is the cliff?