Question

Table 6 and Table 7 and Table 8 Calculations Please!

oni a auns ayeu oj seg on aup uo syans sped ojaA al o suousod ap snipe os paau no x between two balls although they look like sticking together, but the timers count them separately aery ut aun1. un ep an i ( Table 1 Data of the balls' mass, dimension and position. m (kg) d (m) d, (m) d, (m) h, (m) 031S 03I Ol05 O01135 O L h, (m) h=h.-h (m) 128 Software setup Turn on PASCO 850 Interface and computer. Log in computer using Password: phy2048 Kinetic energy conservation in Measurement #1 ( elastic collision) kinetic energy before collision (J) .102 Table 6 % Is the kinetic energy conserved? kinetic energy difference after collision () Ball # 17 yes LO 2 total Momentum conservation Measurement # 2 ( nelastic collision) momentum before Table 7 Is the momentum % momentum after collision (kg m/s) conserved? collision (kg m/s) difference Ball #1 Ball #2 total MivI yes Imi+m)v Kinetic energies in Measurement # 2 ( inelastic collision) kinetic energy before collision (J) Table 8 s the kinetic energy kinetic energy after collision (J) conserved? difference V/2mvi Ball #1 Ball #2 total no Cm,+m2v Lab report on Experiment 6 1Your lab report should be in the required format described in the "Introduction" of the lab manual. 2 Graph Page # 1 should be included in your lab report. 3. Tables 1 to 8 should be included in your lab report. 4 It is required that the answers or solutions to the questions (see below) should be included in your lab report 5 You can tear those pages out of the lab manual as a part of your lab report, which contain measured (raw) data and analyzed data, answers to questions. The data sheets must be checked and signed by your lab TA Questions and exercises AstroBlaster the Multiple Collision Accelerator (This toy is available in the lab, play it before you answer the following questions). 1. Take the smallest ball (red) out of the AstroBlaster and hold it at arm's length from your body, then drop it at height h. The ball will be bounced upward after it hits the ground and reaches a height h, -Smallest ball (red) Use the energy and momentum conservation laws to prove that h, sh Figure 4. AstroBlaster Table 1 Data of the balls' mass, dimension and position. m (kg) d (m) d, (m) d, (m) h (m) h, (m) h=h,-h (m) 828 0315.0310 Software setup 1. Turn on PASCO 850 Interface and computer. Log in computer using Password: phy2048 Table 6 Kinetic energy conservation in Measurement # 1 ( elastic collision) kinetic energy after collision (J) kinetic energy before collision (J) T02 Is the kinetic energy difference conserved? Ball #1 Ball # 2 2mv L47 yes total LO 2 Momentum conservation Measurement # 2 ( inelastic collision) momentum before collision (kg m/s) Table 7 momentum after % Is the momentum collision (kg m/s) difference conserved? Ball #1 MIVI Ball #2 yes total Imi+m2)v Table 8 Kinetic energies in Measurement #2 ( inelastic collision) kinetic energy before collision (J) kinetic energy after collision (J) Is the kinetic energy % difference conserved? /2mM Ball #1 Ball #2 total Cm,+m2)v Lab report on Experiment 6 1. Your lab report should be in the required format described in the "Introduction" of the lab manual. 2. Graph Page #1 should be included in your lab report. 3. Tables 1 to 8 should be included in your lab report. 4. It is required that the answers or solutions to the questions (see below) should be included in vour lab report. 5. You can tear those pages out of the lab manual as a part of your lab report, which contain measured (raw) data and analyzed data, answers to questions. The data sheets must be checked and signed by your lab TA. Kinetic energy conservation in Measurement # 1 ( elastic collision) kinetic energy hefore collision (J) 102 Table 6 Is the kinetic energy kinetic energy after collision (J) % difference conserved? /2mN,2 Ball #1 15/ yes Ball #2 102 total Momentum conservation Measurement # 2 (inelastic collision) momentum before collision (kg m/s) Table 7 momentum after collision (kg m/s) Is the momentum conserved? difference Ball #1 Ball # 2 MIVI yes total Imitm)v Kinetic energies in Measurement # 2 ( inelastic collision) kinetic energy before collision (J) Table 8 Is the kinetic energy conserved? kinetic energy after collision (J) difference Ball #1 Ball #2 no total Cm,+ m2)v Lab report on Experiment 6 1. Your lab report should be in the required format described in the "Introduction" of the lab manual. 2. Graph Page # 1 should be included in your lab report. 3. Tables 1 to 8 should be included in your lab report. 4. It is required that the answers or solutions to the questions (see below) should be included in your lab report. 5. You can tear those pages out of the lab manual as a part of your lab report, which contain measured (raw) data and analyzed data, answers to questions. The data sheets must be checked and signed by hi Apparatus setup The sketch of PASCO 850 interface is given in the "Introduction" of this lab manual. 1. Connect the photogate1 to Port 1 and the photogate 2 to Port 2 of the Digital Inputs on 850 Interface respectively (Fig. 2). 2. Measure the mass m and the diameter d of the steel ball. Record the data in Table 1. Stick a velcro pad to a steel ball and measure its dimension d,- d+ the thickness of one velcro pad. 3. Record the data in Table 1. Stick a velero pad to each of two balls and stick them together, then measure the dimension of the 2- ball system d, -2d + thickness of two velcro pads. Record the data in Table 1. 4 5. Unscrew and pull out the guide bar outward until the center of the ball #1 at position A is just touch the mark h, on the guide bar as shown in Fig. 2. Measure and record h, and h, accurately using a 15 cm ruler and record h= h,-h, in Table 1. 6, Table 1 Data of the balls' mass, dimension and position. h=h,-h (m) h, (m) m (kg) d (m) h, (m) d, (m) d, (m) OloSOOI 135 0315. 0310 Software setup Turn on PASCO 850 Interface and computer. Log in computer using Password: phy2048 1. 2. Start PASCO Capstone by double clicking the symbol on computer. The Workbook Page appears. 3. Hardware Setup on the Workbook Page In the Tools Palette, click on the "Hardware Setup" icon, the Hardware Setup panel appears with a picture of the PASCO 850 Interface. (a) Click "Port 1" on the "Digital Inputs", in the pop-up select "Photogate (b) Click "Port 2" on the "Digital Inputs", in the pop-up select "Photogate" (c) Click on "Hardware Setup" icon to close the Hardware Setup panel. 4. Setup "Timer" by clicking "Timer Setup" icon, and make the following selections: (a) select "Pre-Confiqured Timer", click "Next", (b) check "Photogate, chl", "Photogate, ch2", click "Next" (c) select "Collision (Single Flag)", click "Next", (d) check both "Time in Gate 1" and "Timer in Gate 2", uncheck all others since they are not used in this experiment. (e) select "Flag Length" 0.1 m, (f) select "Collision (Single Flag)", click "Finish". (g) Click on "Timer Setup" icon to close Timer Setup. 5 In the Controls Palette (at the bottom of the Workbook Page), select "Keep Mode" and set sampling rate to 10 Hz Setup Table on Page #1 6. (a) Double click the Table icon in the Displays palette to create a Table on Page #1 (b) In the 1* column of the Table, elick "Select measurement", in the pop-up select *"Time in Gate 1", units "s" (c) In the 2*d column of the Table, click "Select measurement", in the pop-up select "Time in Gate 2", unit "s" (d) You may reduce the size of the Table by dragging a comer of the blue frame. (e) You can move the Table around by clicking on and dragging one of the four sides (blue frame) to where you want to place it. an arrow cursor () along the diagonal from 53 Experiment 6 Collision Purpose 1. Verify energy conservation law when the potential energy of a ball is converted to its kinetic energy. 2. Study elastic and inelastic collisions between two balls. Equipment A pair of metal balls, a pair of velcro pads, two photogates (PASCO Assembly No 0003-06268), vernier calipers, 15 cm ruler, balance, 850 Universal Interface, computer, AstroBlaster. Theory Two identical steel balls with mass m and diameter d are suspended by two massless, non-stretchable strings (m m). The separation of the two strings at their equilibrium (vertical) positions is d, so the two balls just barely touch each other when both of them at their equilibrium (vertical) positions. By convention, level B is chosen as the reference of gravitational potential enersgy (U), at which both ball # 1 and #2 string have zero potential energy, i.e., U, -U,, =0. Pull ball #1 from its equilibrium position (level B) to a height h (level A) as shown in Fig. 1, thus, ball #1 gains a potential energy U T mgh. Now release ball #1 from rest, it will gain a maximum velocity U,, therefore, a maximum kinetic energy K, =½ mu, and maximum linear momentum p, = mu just before hits ball # 2. The direction of v, is to the left and the - A B magnitude of v, is given by the energy conservation law: mg mgh=2 mu (1) Figure 1 y="n Before collision ball # 2 is at rest, hence D, 0-> p, = 0 Consider balls # 1 and # 2 as a system which has the following total momentum and kinetic energy before collision: K, 0. and (2) K K+K,% mu Pe=P=mu, beore 1. Elastic collision If both the momentum and kinetic energy of the two-ball system are conserved before and after collision. i.e.. P P Upon elastic collision ball #1 stops and ball # 2 swings to left, i.e., ball #1 loses its velocity. momentum and kinetic energy while ball #2 gains the same velocity, momentum and kinetic energy from then it is called an elastic collision. and K Kd hofine afier s be the velocities of balls #1 and # 2 respectively after collision, and we have ball #1. et (3) or In the upcoming measurement of elastic collision, U, and U are determined by and (4) where d is the diameter of the steel ball, , is the time that takes ball #1 to pass through photogate #1 and t, is the time that takes ball # 2 to pass through photogate # 2 ( see Fig. 2). 51

Answer 1

For the case of inelastic collision, the two balls will stick together and move along.

table 7 will be similar to table 6 as momentum is conserved in an inelastic collision.

In the case of table 8, the kinetic energy of the combined mass after the collision will be much lower than kinetic energy of ball one, there will be a huge percentage difference.