FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0m. (b) What is the particle's maximum speed? At what position does it have this speed?

A system in which only one particle moves has the potential energy shown in FIGURE EX10.31. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?

In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?

FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. (a) Where are the particle's turning points?

FIGURE EX10.24 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle's speeds at B, C, and D?

CALC A clever engineer designs a 'sprong' that obeys the force law Fx=−q(x−xeq)³ , where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we'll let xeq=0 m .Then Fx=−qx³.b. Find an expression for the potential energy of a stretched or compressed sprong.

A particle moving along the y-axis is in a system with potential energy U = 4y^3 J, where y is in m. What is the -component of the force on the particle at y = 0 m, 1 m, and 2 m?

CALC A particle that can move along the x -axis is part of a system with potential energy U(x)= A/x2 − B/x where A and B are positive constants.a. Where are the particle's equilibrium positions?