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Learning Objectives. Know the comparison to register the drag power on an item because of air frictionApply Newton\'s Second Law and the relationship between quickening, speed and position to take care of a two-dimensional shot issue, including the influences of drag.Prepare an Excel spreadsheet to actualize answer for two-dimensional shot with drag..

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Shot Motion (Two Dimensional) Accounting for Drag

Learning Objectives Know the condition to register the drag constrain on a question because of air grating Apply Newton\'s Second Law and the relationship between speeding up, speed and position to take care of a two-dimensional shot issue, including the effects of drag. Set up an Excel spreadsheet to actualize answer for two-dimensional shot with drag.

Projectile Problem - No Drag V 0 y Position: q x Velocity: Acceleration: V x = V o cos( q ) a x = 0 V y = V o sin( q ) - g t a y = - g

Projectile Problem - Drag All shots are liable to the impacts of drag. Drag brought on via air is huge . Drag is a component of the properties of the air (consistency, thickness), shot shape and shot speed.

General Drag Force The drag FORCE following up on the shot causes it to decelerate as per Newton\'s Law: a D = F D/m where: F D = drag compel m = mass of shot

Drag Force Due to Air The drag constrain because of wind (air) following up on a question can be found by: F D = 0.00256 C D V 2 A where: F D = drag drive (lb f ) C D = drag coefficient (no units) V = speed of protest (mph) A = anticipated region (ft 2 )

Pairs Exercise 1 As a couple, take 3 minutes to change over the proportionality figure the drag drive condition on the past slide if the units of speed are ft/s, and the units of territory are in 2

Drag Coefficient: C D The drag coefficient is a component of the state of the question (see Table 10.4). For a circular shape the drag coefficient ranges from 0.1 to 300, contingent on Reynolds Number (see next slide). For the shot speeds contemplated in this course, drag coefficients from 0.6 to 1.2 are sensible.

Drag Coefficient for Spheres

q Projectile Problem - Drag Consider the shot, measuring W, and going at speed V, at an edge q . The drag constrain acts inverse to the speed vector, V .

q Projectile Problem - Drag The three strengths following up on the shot are: the heaviness of the shot the drag compel in the x-heading the drag constrain in the y-bearing

Drag Forces The aggregate drag drive can be figured by: F D = 8.264 x 10 - 6 (C D V 2 A) where: |V 2 |= V x 2 + V y 2

Drag Forces The X and Y segments of the drag drive can be registered by: F Dx = - F D cos( q ) F Dy = - F D sin( q ) where: q = arctan(V y/V x )

Pair Exercise 2 Derive conditions for a x and a y from F Dx and F Dy . Expecting a x and a y are steady amid a short moment of time, infer conditions for V x and V y at time t i knowing V x and V y at time t i-1 . Accepting V x and V y are steady amid a short moment of time, infer conditions for x and y at time t i knowing x and y at time t i-1 .

PAIRS EXERCISE 3 Develop an Excel spreadsheet that depicts the movement of a softball shot: 1) disregarding drag and 2) including drag More

PAIRS EXERCISE 3 (con\'t) Plot the direction of the softball (Y versus X) expecting no drag accepting drag Answer the accompanying for each case : max. stature of ball level separation at contact with the ground More

Data for Pairs Exercise 3 Assume the shot is a softball with the accompanying parameters: W = 0.400 lb f m = 0.400 lb m Diameter = 3.80 in Initial Velocity = 100 ft/s at 30 o C D = 0.6 g = 32.174 ft/s 2 (yes, expect you are on planet Earth) More

Hints for Pairs Exercise 3 Reminder for the AES: F = m a/g c where g c = 32.174 (lb m ft)/(lb f s 2 ) The conditions of speeding up for this issue are: a x = (F Dx )g c/m a y = (F Dy - W)g c/m More

Considerations for Pairs Exercise 3 What is a sensible D t ? What happens to the heading of the drag compel after the shot achieves most extreme stature? More

Sample Excel Spreadsheet

Sample Chart