Conservation of momentum in two dimension

Recore the collsion on the top of the equirement as shown.

     before

during

after 

Set the initial velocity as the +x-direction.

 Find the slopes (velocitise) of each part of the lines.

x-axis
   pix=M1*v 1i=0.622m/s*0.0668kg=0.044 Ns
   p1x=M1*v 1fx=0.451m/s*0.0668kg=0.03 Ns
   p2x=M2*v 2fx=0.593m/s*0.0198kg=0.012 Ns
   p1x+p2x=0.42 Ns Approximate to pix 0.044Ns

y-axis
   piy=0
   p1y=M1*v 1fy=-0.009m/s*0.0668kg=-4.2x10^-3 Ns
   p2y=M2*v 2fy=0.161m/s*0.0198kg=3.2*10^-3 Ns
   p1y+p2y=-1*10^-3 Ns approximate to zero.

conform the conservation of momentum in both x and y axis.

Data 2

The x axis initial momentum is 0.039kg*m/s which is approximat to final momentum 0.036kg*m/s.

The y axis initial momentun is 0. the final momentum is 0.001.

Those values can conform the conservation of momentum in both x and y axis.

Impulse and the change of momentum conservation

Set up the equirement as shown.

1.Level the track.

2.Calibrate the force sensor.

3.Turn force sensor horizontal and zero sensor.

4.motion sensor

Measured the mass of the cart is 0.434kg. The the mass of the block is 0.084kg.

Compare mv*=-0.764 N*s and the intergration of the force by time which is -0.6706 N*s.
those nubmers are colsed.

Elstic collsion.
Add a block on the cart and redo this experiment.

Compare mv*=-0.303 N*s and the intergration of the force by time which is -0.2723 N*s.
those nubmers are colsed.

Use a plasticene instead of the red car so that change it to be a inelstic cllosion.

Compare mv*=-0.203 N*s and the intergration of the force by time which is -0.235 N*s.
those nubmers are colsed.

Through this experiment, we can conform the impluse is the change of the mementum.

Deterning the mangetic energy/ conform the conversion of the energy in magnetic system

Part 1. Determent the relationship between the magnetic force and distance

Set up the equriment as shown.

1.Put one book under one end of the air track. Turn on the air source. Find a position makes equalibrium. Measure the distance between the two magents. Measure the angle between  the track and horizontal.

2. Repeat last step with two books under the track.

3.Adding one book each times until we got 5 groups of data.

4. Measure the mass of the cart.

5.Enter those data to Log Pro.

6.Calculate the force in each position. F=sin(angle)mg

7.Use Log Pro power fit the Force Vs. Distance graph.

F=A*d^B

A=0.002036

B=-1.388

F=0.002036*d^-1.388

Part2. Conform the conversion of energy in this magnetic system.

1.Set a motion sensor on the end of the track.

2.level the air track.

3.Turn on the air track.

4.Record the date while the cart moving toward the magent and the motion it repels by the magnet.

5.Measure the distance between the stationaly magnet and the motion sensor.(L=0.043m)

6.Add a new calculation column named KE (kinetic energy) = 0.5*mass of the cart*"velocity"^2

7.Add a new calculation column named PE （Potential energy）= the intergation of the force by distance=(A/B+1)*(x-L)^(B+1)

8.Add a new calculation column named Total energy=KE+PE

Garph the total energy.

the graph shows the total energy is constant that could conform the conversion of energy threom

Conservation of energy

work your d to something from defined zero GPE to somewhere else.
Elastic PE = work you did to stetch the spring from unstreched.

verify conservation of energy in mass-spring system.
things for measure.
1. KE of mass get v from motion sensor.
2. GPE of the mass get mass
3.Elastic PE of the spring =1/2k(stretch)^2
 k= hang a mass get streach
4/ GPE of the spring (uniform spring)

GPE of spring is constant +mgy/2

5. KE of spring choose respresent piece of mass

d(KE) of the bit=(dm/2)v^2=(1/2)*dm((g/L)*Vend)^2=(1/2)(M/L)*dy*((y/L)Vend)^2

take the intergal of the d(KE) form 0 to L.

KE=(1/6)M*Vend^2.

Set up the equirement as showen

Measure the mass of the spring is 64g and hanging a mass of 300g.

as the sping is stretched 0.24m find out the sring consitant is 16.33N/m.

Recored the y as the spring hanging the mass with no motion

Recored the data when you lease the mass from a stretched positon.

Add new calculation coulumn named "KE m"

=0.5+0.3*"velocity"^2

Add new calculation coulumn named "GPE m"

=0.3*9.8*"position"

Add new calculation coulumn named "PE of the spring"

=0.5*0.064*9.8*"position"

Add new calculation coulumn named "GPE of the spring"

=(1/6)*0.064*"velocity"^2

Add new calculation coulumn named "KE of spring"

=0.5*0.064*"velocity"^2

Add new calculation coulumn named Total energy

="KE m"+"GPE m"+"PE of the spring"+"GPE of the spring"+"KE of spring"

 Add the Total energy in the graph
As it shown below it looks like a horizontal line which can verify the total energy is conserved.

Work kinetic energy theorem

1. calibrate force sensor and zero froce secsor.

Set up the equirement as showen.

2. zero reverse the dircetion on the motion sensor.
3. change the date collection to 30 pts/sec.
5. cart with extra mass.
Data collection:
Setetch the cart to position and click the "collect" button on the screen, then release the cart.
Data annlysis:
Add a new calculation coulumn named KE: =0.5*mass of the cart*"velocity"^2
take off all the data has a negative position value.

Intergate the force graph and find out the area of the force has the same value of the KE value.

2-oct-2014Relationship between angular speed (ω) and angle of the string above the vertical (θ) for a particular rotating apparatus.

1.Set up the equirement as showen.

2. Measure the hight and lengh of the arm and the lengh of the string.

3.As the hanging mass is spining. Measure the time uses to spin ten periods.

The measurement and angular speed and the angle of the srting above the vertical is 

5.Use excel to do the preditcition of the angular speed and compare with the actural angular speed.

 

 

Comparing the  E and J columns, we can find the angular speed we predicted are very colse to the angular speed we measured. So this formular is correct.