Work, Energy, and Power in Physics

In a collision between two isolated particles where only conservative forces do work, which quantity must remain constant for both particles together after considering work-energy principles?

What effect would halving both mass and velocity have on an object's kinetic energy?

Which quantity can be calculated by multiplying the net external force acting on an object by the time interval over which it acts?

A pendulum swings from its lowest point (A) up to a maximum height (B), what is the correct relationship between kinetic energy at A and potential energy at B?

A ball is thrown straight up with initial velocity $v$; which new initial velocity will quadruple its maximum height reached?

A wheel rolling without slipping on a flat surface translates kinetic energy into what other type(s) of kinetic energy?

What is the relationship between net work done by external forces and change in kinetic energy of an object according to the work-energy theorem?

In an experiment where two identical masses collide on a horizontal surface with velocities such that their total momentum is zero, how should their individual speeds relate before collision so that post-collision they stick together maximizing thermal energy production?

A cylindrical rod pivoted at one end swings down from rest under gravity and strikes a linear spring perpendicularly compressing it; what maximum compression $x_{ ext{max}}$ does the spring experience given that its stiffness $k$ equals $n$ times the weight $mg$ per unit length $L$ where $n>0$?

A car of mass m accelerates from rest down a hill inclined at angle θ to horizontal; how does increasing θ affect the net work done on it when traveling distance d?