When the mass m of a body moving through a force field is variable, Newton’s second law...

When the mass m of a body moving through a force field is variable, Newton’s second law takes on the form: If the net force acting on a body is not zero, then the net force F is equal to the time rate of change of momentum of the body. That is,

where mv is momentum. Use this formulation of Newton’s second law in Problems 21 and 22.

A uniform chain of length L, measured in feet, is held vertically so that the lower end just touches the floor as shown in FIGURE 1.3.19. The chain weighs 2 lb/ft. The upper end that is held is released from rest at t = 0 and the chain falls straight down. Ignore air resistance, assume that the positive direction is downward, and let x(t) denote the length of the chain on the floor at time t. Use the fact that the net force F in (18) acting on the chain at time t ≥ 0 is the constant 2L to show that a differential equation for x(t) is