A falling body will approach its terminal velocity when the drag force becomes n

Question

A falling body will approach its terminal velocity when the drag force becomes nearly equal and opposite to gravitational force. suppose that a scientific instrument for deep water sounding is enclosed ina 10 cm diameter spherical shell an has a net gravitational force in water (actual water minus its buoyancy force) equal to 2.30 x 10^5 dynes. Determine its terminal velocity. (Note: you must assume a force law, calculate a velocity and then check it the asociated Reynolds number is consistent with the assumed force law.)

Explanation / Answer

I'll cover this topic as cleanly as possible! Wikipedia comments that, '... A free falling object achieves its terminal velocity when the downward force of gravity (Fg) equals the upward force of drag (Fd). This causes the net force on the object to be zero, resulting in an acceleration of zero. Mathematically an object asymptotically approaches and can never reach its terminal velocity. As the object accelerates (usually downwards due to gravity), the drag force acting on the object increases. At a particular speed, the drag force produced will equal the object's weight (mg). Eventually, it plummets at a constant speed called terminal velocity (also called settling velocity). Terminal velocity varies directly with the ratio of drag to weight. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity. An object moving downward with greater than terminal velocity (for example because it was affected by a downward force or it fell from a thinner part of the atmosphere or it changed shape) will slow until it reaches terminal velocity. ...' Wikipedia further adds, '... Based on wind resistance, for example, the terminal velocity of a skydiver in a free-fall position with a semi-closed parachute is about 195 km/h (120 mph or 55m/s). This velocity is the asymptotic limiting value of the acceleration process, since the effective forces on the body more and more closely balance each other as the terminal velocity is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on. Higher speeds can be attained if the skydiver pulls in his limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s), which is also the terminal velocity of the peregrine falcon diving down on its prey,. And the same terminal velocity is reached for a typical 150 grain bullet travelling in the downward vertical direction — when it is returning to earth having been fired upwards, or perhaps just dropped from a tower — according to a 1920 U.S. Army Ordnance study. Competition speed skydivers fly in the head down position reaching even higher speeds. The current world record is 614 mph (988 km/h) by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag. An object falling toward the surface of the Earth will fall 9.81 meters per second faster every second (an acceleration of 9.81 m/s²). The reason an object reaches a terminal velocity is that the drag force resisting motion is directly proportional to the square of its speed. At low speeds, the drag is much less than the gravitational force and so the object accelerates. As it accelerates, the drag increases, until it equals the weight. Drag also depends on the projected area. This is why things with a large projected area, such as parachutes, have a lower terminal velocity than small objects such as cannon balls. Mathematically, terminal velocity, without considering the buoyancy effects, is given by Vt = v(2.m.g/?.A.Cd) where Vt = terminal velocity, m = mass of the falling object, g = gravitational acceleration, Cd = drag coefficient, ? = density of the fluid through which the object is falling, and A = projected area of the object. On Earth, the terminal velocity of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area. For objects falling through the atmosphere, air density increases with decreasing altitude, ca. 1% per 80 m. Therefore, for every 160 m of falling, the terminal velocity decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal velocity. ...'

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.