When the mass m of a body is changing with time, Newton’s second law of motion becomes
where F is the net force acting on the body and mv is it momentum. Use (17) in Problems 21 and 22.
A small single-stage rocket is launched vertically as shown in Figure 1.3.19. Once launched, the rocket consumes its fuel, and so its total mass m(t) varies with time t > 0. If it is assumed that the positive direction is upward, air resistance is proportional to the instantaneous velocity v of the rocket, and R is the upward thrust or force generated by the propulsion system, then construct a mathematical model for the velocity v(t) of the rocket. [Hint: See (14) in Section 1.3.]
(reference problem 14)
The right-circular conical tank shown in Figure 1.3.13 loses water out of a circular hole at its bottom. Determine a differential equation for the height of the water h at time t > 0. The radius of the hole is 2 in., g = 32 ft/s2, and the friction/contraction factor introduced in Problem 13 is c = 0.6.
(reference problem 13)
Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to is an empirical constant. Determine a differential equation for the height h of water at time t for the cubical tank shown in Figure 1.3.12. The radius of the hole is 2 in., and g =32 ft/s2.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.