- We Will Measure The Acceleration A G 9 80 M S 980 Cm S Due To Gravity By Observing The Distance An Object Fall 1 (111.5 KiB) Viewed 42 times
- We Will Measure The Acceleration A G 9 80 M S 980 Cm S Due To Gravity By Observing The Distance An Object Fall 2 (107.33 KiB) Viewed 42 times
- We Will Measure The Acceleration A G 9 80 M S 980 Cm S Due To Gravity By Observing The Distance An Object Fall 3 (120.04 KiB) Viewed 42 times
- We Will Measure The Acceleration A G 9 80 M S 980 Cm S Due To Gravity By Observing The Distance An Object Fall 4 (63.09 KiB) Viewed 42 times
how to continue from there.
We will measure the acceleration (a = g = 9.80 m/s² = 980 cm/s²) due to gravity by observing the distance an object falls during a very short interval of time. The falling object will be an ordinary meter stick, and the time interval during which we will allow it to fall is your personal "reaction time". We saw in the lecture that even for a short time interval of 1 s, an object falling from rest will drop about 5 m 16 ft. Therefore, if we are to observe a falling object within the confines of a lecture room whose ceiling is only about 3 m above the floor, we need a means for measuring very short intervals of time. A common stopwatch seems to be a good choice. However, using a stopwatch to measure short time intervals is complicated by the fact that the human operator has a reaction time that is about 20 times longer than the 0.01 s resolution of the instrument. Therefore, our body's physiology limits the shortest time interval one can measure with his/her fingertips to about 0.2 s. In the first part of this experiment, you will use the stopwatch to approximate your personal reaction time Atr. In the second part of the experiment, you will measure how far a meterstick falls during a time interval equal to your reaction time. We recall that the distance Ay [m] that an object falls in Atr [s] is given by the formula 1 Ay = = a^t² Here, a, is the acceleration the falling object experiences, namely the acceleration due to gravity
Therefore, the above formula can be rearranged to express g in terms of the measured quantities Δy and Δt, : 24y g= (eqn. 1) At² Procedure: 1. Determining reaction time Atr. a. Reaction time is how long it takes you to respond to an observed change in your environment. For example, after you see your classmate drop a meterstick between your outstretched fingertips, there is a time delay before you are able to close your fingers to catch the stick. This delay is your reaction time. You can use a stopwatch to obtain a crude estimate of your reaction time. Namely, it is easy to measure the shortest time interval you can record on a stopwatch. All that you need to do is "zero" the stopwatch and then click the "start/stop" button twice in succession as quickly as you can. (If you do not have a stop watch, you can use your phone's stopwatch). Doing this four times and taking the average of the readings will indicate how quickly you can physically move your finger tips. Let us call this finger reaction time Atf. Record your measurements in column 2 of table 1 beside the times labeled Atr.1, Atr2, Atr3 and Atf4 respectively. Take the average of these and write it beside Atrave in column 2 of table 1. b. The above measurements do not include the time it takes your brain to process a given observed information. I suspect that this extra time is approximately the same as Atrave (Note: This approximation is probably the largest source of error in the experiment.) In other words, your personal reaction time Atr is about twice your fastest finger movement time Atrave - Record your reaction time 4t, in column 2 of table 1.
2. Determining fall distance Ay. a. Have someone (family member, friend or classmate) hold a ruler with cm scale top (near the 12 cm mark) so that it is oriented vertically. Locate your thumb and index finger on opposite sides of the ruler about the 1 cm mark, without touching the ruler. (You can make a mark or attach a masking tape you can see the top of your fingers will align with the 1 cm mark). Without warning, your friend will release the ruler or meterstick. The stick will fall several centimeters before you are able to catch it between your fingers. Take note of the cm mark at which your fingers catch the stick. From this, determine Ay (Subtract 1 cm from this mark). Take four trials and record your data in column 3 of table 1. Take the average Ayave. Using equation 1, and using your measured Atrave and Ayave (column 2 and 3) determine g and record your result in column 4 of table 1. 3. Repeat above procedure, asking a family member or friend, and tabulate your results in table 1 for person # 2 and # 3. Table 1: Data Sheet Student # Reaction time Atr (s) Fall distance Ay (cm) Measured acceleration g :(cm/s²) (Person #) 1 Avi= 10 Av2= 8 Ay3= 8 AV4= Average Ay: Measured g by student #1: Ay = g= Ay₁= a Ay2=O Ay3 = 7 Ay4= 8 Average Ay: Measured g by student # 2: Ay= g= Ayı = 8 Ay2= 9 Ay3 = Ay4= 8 Average Ay: Measured g by student # 3: Ay = g= 2 3 Atr=0lbs Atr2 = 0.205 Atra= 0.175 Atr.4=16s Average: Atfave = 0.1725 Reaction time: Atr=2*(Attuve) = Atr=07 Atr.2 0.17 Atr=0-18 Atr=0-18 Average: Atfave = Reaction time: Atr=2*(Atfave) = Atr=7 Atr=0. Atr3= 0.17 Atr4 0.16 Average: Atfave = Reaction time: Af=2* (Atfave) =
4. Find the average value of g measured by your group by taking the average of g obtained by each member of your group from the table above. Average g measured by your group: [cm/s²] gave = 5. Percent error Calculate the percent discrepancy between this experimental value and the accepted value of 980 cm/s². % discrepancy = experimental value - accepted value accepted value x 100% Record your answer here: % discrepancy=