2. Determining the acceleration of free-fall experimentally

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

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

5. Suppose we know that the time between images is 0.056 s. Determining the acceleration of free-fall experimentally We make a table starting with the raw data columns of t and y. 0 cm -9 cm -22 cm -37 cm -55 cm t(s).056 y(cm) 0 tt yy v -9 -22 -37 -55.112.168.224.000 To find  t you need to subtract TWO t's. Therefore the first entry for  t is BLANK. Same thing for the first  y. Since v =  y /  t, the first v entry is also BLANK..056 To find  t you need to subtract TWO t's. CURRENT t MINUS PREVIOUS t. -9 -13 -15 -18 To find  y you need to subtract TWO y's. CURRENT y MINUS PREVIOUS y. -161 -232 -268 -321 To find v you need to divide  y by  t. t(s).056 y(cm) 0 tt yy v -9 -22 -37 -55.112.168.224.000.056 -9 -13 -15 -18 -161 -232 -268 -321 We then make calculations columns in  t,  y and v (processed data).

6. t(s).056 y(cm) 0 tt yy v -9 -22 -37 -55.112.168.224.000.056 -9 -13 -15 -18 -161 -232 -268 -321 VELOCITY / cm sec -1 v 0 -50 -100 -150 -200 -250 -300 t TIME / sec.000.056.112.168.224 Now we plot v vs. t on a graph Determining the acceleration of free-fall experimentally

7. VELOCITY (cm/sec) v 0 -50 -100 -150 -200 -250 -300 t / s TIME (sec).000.056.112.168.224  v = -220 cm/s  t = 0.224 s Determining the acceleration of free-fall experimentally 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 Finally, the acceleration is the slope of the v vs. t graph:

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

9. 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

10. "A female Blue Whale weighing 190 metric tonnes (418,877lb) and measuring 27.6m (90ft 5in) in length suddenly materialized above the Southern Ocean on 20 March 1947." Guinness World RecordsGuinness 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. y W At first, v = 0. y W D Then, as v increases, so does D. v 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. W D v reaches a maximum value, called terminal speed. D = W. v terminal It has reached terminal speed.

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

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

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

14. If a raindrops start in a cloud at a height h = 1200m above the surface of the earth they hit us at 340mi/h; serious damage would result if they did. If a raindrops start in a cloud at a height h = 1200m above the surface of the earth they hit us at 340mi/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 7m/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 340mi/h calculated without drag. The terminal speed for a skydiver is about 60 m/s (pretty terminal if you hit the deck) Air drag and terminal speed