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The figure here shows a plot of potential energy U versus position x of a 0.900 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA = 15.0 J, Up = 35.0 J and Uc = 45.0 J. The particle is released at x = 4.50 m with an initial speed of 7.96 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.00 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.50 m at speed 7.96 m/s. (d) If the particle can reach x = 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x = 5.00 m? UC UA 2 4 6 x (m) (a) Number Unit (b) Number Unit V (c) (d) Number Unit (e) Number Unit V (f )The potential energy of a diatomic molecule (a two-atom system like Hg or 02) is given by U: T12 T63 where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential energy is associated with the force that binds the two atoms together. NOTE: Espress your answers in terms of the variables given. (a) Find the equilibrium separation - that is, the distance between the atoms at which the force on each atom is zero. (b) Is the force repulsive (the atoms are pushed apart) or attractive (they are pulled together) if their separation is smaller than the equilibrium separation? Choose one v c Is the force re ulsive the atoms are ushed a art or attractive P P P (they are pulled together) if their separation is larger than the equilibrium separation? Choose one v A rope is used to pull a 2.59 kg block at constant speed 6.87 m along a horizontal floor. The force on the block from the rope is 7.77 N and directed 10.70 above the horizontal. What are (a) the work done by the rope's force, (b) the increase in thermal energy of the block-floor system, and (c) the coefficient of kinetic friction between the block and floor? (a) Number i Units (b) Number i Units (c) Number UnitsIn the figure, a block of mass m = 1.30 kg slides head on into a spring of spring constant k = 260 N/m. When the block stops, it has compressed the spring by 12.0 cm. The coefficient of kinetic friction between block and floor is 0.280. While the block is in contact with the spring and being brought to rest, what are (a) the work done by the spring force and (b) the increase in thermal energy of the block-floor system? (c) What is the block's speed just as the block reaches the spring? (a) Number Units (b) Number Units (c) Number i UnitsIn the figure, a 3.9 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is vo = 5.2 m/s, the height difference is h = 1.0 m, and MK = 0.648. Find d. U=0 Number Units