General Physics Lab Department of PHYSICS YONSEI University

Lab Manual (Lite)

Free Fall & Projectile Motion Ver.20180315

Free Fall and Projectile Motion

Experiment 1. Free Fall (1) Set up equipment as below.

(2) Turn on the interface and run Capstone software.

The interface is automatically detected by Capstone. Click [Hardware Setup] in the [Tools] palette to configure the inter-face.

(3) Set up Capstone software (3-1) Add a Photogate. Click the input port which you plugged the Photogate into

and select [Photogate] from the list.

NOTICE This LITE version of manual includes only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual.

Procedure

The Photogate’s icon will be added to the panel and [Timer Setup] icon will appear in the [Tools] palette.

(3-2) Create a timer. Click [Timer Setup] in the [Tools] palette and follow the steps below. ① Select [Pre-Configured Timer] and click [Next].

② Check [Photogate, Ch1] and click [Next].

③ Select [Picket Fence].

④ Make sure [Position] is checked.

⑤ Enter a suitable value in the [Flag Spacing].

You have two kinds of Picket Fences as follows.

Spacing Description

PF#1 0.05m Opaque 0.02m + Transp. 0.03m

PF#2 0.04m Opaque 0.02m + Transp. 0.02m

⑥ Enter any name and finish the timer setup.

(3-3) Create a graph display and a data table. Click and drag the [Graph] icon from the [Displays] palette into the workbook page.

A graph display will appear.

You can select the measurement of each axis by clicking <Select Measurement>. Select [Time(s)] for the 𝑥𝑥-axis and [Position(m)] of the Picket Fence for the 𝑦𝑦-axis.

Click and drag the [Table] icon from the [Displays] palette into the workbook page. Select [Time(s)] for the first column and [Position(m)] for the second column.

You now have two displays in the workbook page.

(4) Begin recording data. Click [Record] in the [Controls] palette. Capstone begins recording all available data.

[Record] button will toggle to [Stop]. You can stop data col-

lection by clicking [Stop].

Collected data are stored in memory and appear in all dis-plays. The data run is listed in the legend for each display. (You can delete any run by clicking [Delete Last Run] or drop-down menu in the [Controls] panel.)

(5) Drop a Picket Fence. Make sure the opaque bands of the Picket Fence block the infrared beam of the Photogate during they pass through the Photogate.

(6) Stop data collection. Click the [Stop] button to stop data collection.

(7) Analyze the data.

Time(s) Position(m)

1 𝑡𝑡1 𝑥𝑥1

2 𝑡𝑡2 𝑥𝑥2

3 𝑡𝑡3 𝑥𝑥3

… … …

Calculate the average speed at each interval, and plot 𝑣𝑣-𝑡𝑡

graph.

𝑡𝑡 𝑣𝑣

1~2 𝑡𝑡1 + 𝑡𝑡2

2

𝑥𝑥2 − 𝑥𝑥1𝑡𝑡2 − 𝑡𝑡1

2~3 𝑡𝑡2 + 𝑡𝑡3

2

𝑥𝑥3 − 𝑥𝑥2𝑡𝑡3 − 𝑡𝑡2

3~4 𝑡𝑡3 + 𝑡𝑡4

2

𝑥𝑥4 − 𝑥𝑥3𝑡𝑡4 − 𝑡𝑡3

… … …

Find the slope of 𝑣𝑣-𝑡𝑡 graph using the method of least

squares (refer to the appendix). The acceleration of the Pick-et Fence is equal to the slope of the 𝑣𝑣-𝑡𝑡 graph. (8) Repeat experiments. ① Repeat measurement with the same Picket Fence (more than three times).

1st 2nd 3rd …

𝑎𝑎result

𝑎𝑎AVG

𝘨𝘨 9.8 m/s

② Repeat measurement using the other Picket Fence. Change [Flag Spacing] parameter. See step (3-2)-⑤. Save the data file with a different name for each Picket

Fence. If you change [Flag Spacing], all premeasured data will be recalculated.

Experiment 2. Projectile Motion

(1) Set up equipment. Attach the Photogate Bracket to the Launcher and attach the Photogate to the Bracket. Align the square nuts of the Bracket with the T-shaped slot

on the bottom of the Launcher barrel and slide the nuts into the slot until the Photogate is as close to the muzzle as pos-sible without blocking the Photogate beam.

When the ball passes the Photogate, the initial speed of the

ball is calculated as

Speed =Moving distance (= diameter)of the ball

Time interval the ball blocks the Photogate

Thus, make sure the Photogate beam is exactly on the path of the center of the ball. Tighten the Bracket thumbscrew to secure the Photogate in place. (The Photogate could be slightly shifted on impact. Whenever you shoot the ball, make sure the Photogate is in position.) Using the table clamps, clamp the Launcher to the left end of the table. Connect the Photogate to the interface.

(2) Measure the diameter of the ball.

CAUTION NEVER LOOK INTO THE MUZZLE of the Projectile

Launcher when it is loaded. Accidental shooting could cause blindness or serious loss of vision.

NOTE

① 22 mm is to the immediate left of the zero on the ver-nier scale. Hence, the main scale reading is 22 mm. ② Look closely for and alignment of the scale lines of the main scale and vernier scale. In the figure, the aligned (13th) line corresponds to 0.65 mm (= 0.05 × 13). ③ The final measurement is given by the sum of the two readings. This gives 22.65 mm (= 22 + 0.65).

(3) Add a Photogate. Click the port which you plugged the Photogate into and se-

lect [Photogate] from the list.

(4) Create and configure a timer. Click [Timer Setup] in the [Tools] palette and follow the steps below to create a timer. ③ Select [One Photogate (Single Flag)] for the type of timer. ④ Make sure [Speed] is checked. ⑤ Enter the measured diameter of the ball for [Flag Width].

(5) Create and configure a digital meter. Click and drag the [Digits] icon from the [Displays] palette

into the workbook page. Select [Speed(m/s)] for <Select Measurement>.

(6) Load the launcher. Place the GREEN ball in the muzzle of the launcher. And then push the ball down the barrel with the ramrod until the trigger catches the MEDIUM RANGE setting of the piston. (The trigger will click into place.) You can use a different range setting, if required. If you cannot coke the piston due to a structural problem, pull and return the trigger while you are pushing the ramrod.

NOTE The Launcher has three range settings. The reference lines of the ramrod show the positions of each setting. Remember, if you cock the piston with a ball in the pis-

ton, the piston is in the MEDIUM RANGE position when the first (left) line (not the middle line) of the ramrod reaches near the entrance of the muzzle,

CAUTION NEVER LOOK INTO THE MUZZLE of the launcher when it is loaded. Accidental shooting can cause blind-ness or serious loss of vision.

(7) Measure the initial speed of the ball. ① Click [Record] in the [Controls] palette. ② Shoot the ball by pulling straight up the trigger.

③ Click [Stop] and record the speed of the ball. ④ Repeat more than 3 times with the same range setting. ⑤ Find the average speed of the ball. The average repre-sents the initial speed 𝑣𝑣0 of the projectile.

1st 2nd 3rd …

𝑣𝑣result

𝑣𝑣AVG 𝑣𝑣0 = ___________(m/s)

(8) Adjust the height and the angle of the Launcher. The height and angle of inclination above the horizontal is adjusted by loosening the two thumbscrews and rotating the Launcher barrel to the desired angle. Use the plumb bob and the protractor on the label to select the angle. Tighten both thumbscrews when the angle is set.

(9) Place white paper and carbon paper on the box. ① Fire a test shot to locate where the ball hits. ② Put a piece of white paper on the box at this location. ③ Put a piece of carbon paper (carbon-side down) on top of the white paper. When the ball hits the carbon paper, it will leave a mark on

the white paper underneath.

(10) Begin experiment. ① Fire three shots with the same range setting of step (7). ② Carefully remove the carbon paper. ③ Use a measuring tape to measure the horizontal distance 𝑅𝑅 from the muzzle to the dots. ④ Repeat measuring 𝑅𝑅 for angles below.

𝛼𝛼0 𝑅𝑅

1st 2nd 3rd AVG

15°

30°

45°

60°

75°

⑤ Calculate the error between the theoretical distance and the actual average distance for all angles.

𝑅𝑅 = (𝑣𝑣0 cos𝛼𝛼0)𝑡𝑡1 =2𝑣𝑣02 sin𝛼𝛼0 cos𝛼𝛼0

𝘨𝘨 =𝑣𝑣02

𝘨𝘨 sin 2𝛼𝛼0 (16)

Q What angle give the maximum range of 𝑅𝑅? What pairs of angles have a common range?

A

Please put your equipment in order as shown below.

□ Delete your data files from your lab computer. □ Turn off the Computer and the Interface. □ Clamp the Projectile Launcher to the left end of the table. □ Keep the Photogate Bracket assembled to the Photogate. □ Keep the Carbon Paper in the plastic bag.

End of LAB Checklist