Determining the acceleration of freefall experimentally Determining the

Determining the acceleration of free-fall experimentally

Determining the acceleration of free-fall experimentally Consider the multiflash image of an apple and a feather falling in a vacuum: If we choose a convenient spot on the apple, and mark its position, we get a series of marks like so:

Determining the acceleration of free-fall experimentally Now we SCALE our data. Given that the apple is 8 cm in horizontal diameter we can superimpose this scale on our photograph. 0 cm Then we can estimate the position in cm of each image. -9 cm -22 cm -37 cm -55 cm

Determining the acceleration of free-fall experimentally Suppose we know that the time between images is 0. 056 s. 0 cm We make a table starting with the raw data columns of t and y. We then make calculations columns in t, y and v (processed data). -9 cm t(s). 000 y(cm) t -22 cm y vv 0 -37 cm -161. 056 -9 -161 -9. 056 -9 To find t you need to subtract TWO t's. Therefore the first entry for t is BLANK. . 112 -13 -232 -22. 056 -13 -232 To find t you need to subtract TWO t's. To find y you need to subtract TWO y's. To find v you need to divide y by t. CURRENT t MINUS PREVIOUS t. CURRENT y MINUS PREVIOUS y. Same thing for the first y. . 168 -15 -268 -37. 056 -15 -268 Since v = y / t, . 224 -18 -321 -55. 056 -18 -321 -55 cm the first v entry is also BLANK.

Determining the acceleration of free-fall experimentally Now we plot v vs. t on a graph VELOCITY / cm sec-1 v 0 -50 -100 -150 -200 -250 -300 . 000 t(s) y(cm) t y v . 000 0 . 056 -9 -161 . 112 -22 . 056 -13 -232 . 168 -37 . 056 -15 -268 . 224 -55 . 056 -18 -321 . 056 TIME / sec. 112 . 168 . 224 t

Determining the acceleration of free-fall experimentally 0 -50 -100 -150 -200 -250 -300 . 056 . 112 t = 0. 224 s TIME (sec). 224. 168 t / s v = -220 cm/s VELOCITY (cm/sec) v Finally, the acceleration is the slope of the v vs. t graph: The graph v vs. t is linear. Thus a is constant. The y-intercept (the initial velocity of the apple) is not zero. But this just means we don’t have all of the images of the apple

Graphs of free fall motion u = 0 m/s v = 10 t x = 5 t 2 time speed distance (s) (m/s) (m) 0 0 1 10 5 2 20 3 30 45 4 40 80 Velocity vs. time Distance vs. time 80 Distance (m) velocity (m/s) 40 30 20 10 0 1 2 3 4 5 Time (s) constant slope → constant acceleration 60 40 20 0 0 1 2 3 4 5 Time (s) changing slope – changing speed → acceleration

Qualitatively describing the effect of fluid resistance on falling objects or projectiles, including reaching terminal speed -Students should know what is meant by terminal speed. -This is when the drag force exactly balances the weight

"A female Blue Whale weighing 190 metric tonnes y (418, 877 lb) and measuring 27. 6 m (90 ft 5 in) in At first, v = 0. length suddenly materialized above the Southern Ocean on 20 March 1947. " Guinness World Records. Falkland Islands Philatelic Bureau. 2 March 2002. Suppose a blue whale suddenly materializes high above the ground. The drag force D is proportional to the speed squared for high speeds. For low speeds it is proportional to speed. W Then, as v increases, so y does D. D Thus, as the whale picks up speed, the drag force increases Once the drag force equals the whale’s weight, the whale will stop accelerating. v v reaches a maximum value, called terminal speed. D = W. W D It has reached terminal speed. vterminal W

If air resistance can not be neglected, there is additional force (drag force) acting on the body in the direction opposite to velocity.

Comparison of free fall with no air resistance and with air resistance time velocity displaceme nt In air velocity displaceme nt In vacuum Acceleration is getting smaller due to air resistance time and eventually becomes zero. When the force of the air resistance equals gravity, the object will stop accelerating and maintain the same time speed. acceleration time terminal velocity is maximum velocity an object can reach in air/any fluid. time It is different for different bodies. time

Comparison of free fall with no air resistance and with air resistance time velocity displaceme nt In air velocity displaceme nt In vacuum Acceleration is getting smaller due to air resistance time and eventually becomes zero. When the force of the air resistance equals gravity, the object will stop accelerating and maintain the same time speed. acceleration time terminal velocity is maximum velocity an object can reach in air/any fluid. time It is different for different bodies. time

Air drag and terminal speed If a raindrops start in a cloud at a height h = 1200 m above the surface of the earth they hit us at 340 mi/h; serious damage would result if they did. Luckily: there is an air resistance preventing the raindrops from accelerating beyond certain speed called terminal speed…. How fast is a raindrop traveling when it hits the ground? It travels at 7 m/s (17 mi/h) after falling approximately only 6 m. This is a much “kinder and gentler” speed and is far less damaging than the 340 mi/h calculated without drag. The terminal speed for a skydiver is about 60 m/s (pretty terminal if you hit the deck)