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?

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?

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?

A system has potential energy U(x)=(10 J)[1−sin((3.14 rad/m)x)] as a particle moves over the range 0 m≤x≤3 m b. For each, is it a point of stable or unstable equilibrium?

A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is (delta)U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?

CALC The potential energy for a particle that can move along the x -axis is U=Ax²+B sin(πx/L) , where A , B , and L are constants. What is the force on the particle at (a) x=0 , (b) x=L/2 , and (c) x=L?

In FIGURE EX10.27, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0mm and x = 8.0 mm