Conservation of linear and Angular Momentum

Conservation of linear and Angular Momentum

Introduction:

We already do lots of different lab about inertia, then this one we set up like this 

We will find the speed when the ball come out from the ramp

then calculate the angular speed should and see the experiment 

Date and calculation: 

First of all, we find the speed when it come out from the ramp

those are the date we measure and we do the calculate the the speed speed be and actually be.

we get 1.14m/s in the experiment and 1.657m/s from calculation

they are lots of different because the friction do too much work on the ball.

and then we use Vo=1.14m/s to find the angular speed it should be 

we get 1.74 rad/s for the final angular speed 

and 1.572rad/s from the logger pro as the figure 

Conclusion:

The error between experiment and calculation is 9.6%

The result is close enough to said that the angular momentum from ball and the final momentum

is the same 

Ruler with clay collision

Ruler with clay collision

Introduction:

In this lab we let the meter stick collision with the clay and see how high it go and calculate it find if they have the same result

Calculation:

we capture the video and find the final height is 0.08m

We do calculate like this 

we do it by part 

first we find the speed when it just hit the clay

then want though the momentum calculation as the figure

We came so far then we get the final high is 0.108m

Conclusion:

the experiment height is 0.08m

the calculation high is 0.108m

we have an error about 25%

It is quite different, but we can say that there might be lots of friction between the clay and the supporting stick. 

I think the result is reasonable. 

Moment of Inertia

Moment of Inertia

Introduction:

First of all, we get a pulley and cart in this lab. what we try to do is calculate the date we have and expect the experiment result. We find the pulley inertia then that it hang our cart. We calculate when the cart go 1 m far and do the experiment.

pulley

collect the date

 

we capture the video and find x and y axis speed

and this is what we get

find the total speed and use the logger pro to find our changing angular speed

that is how we find the angular acceleration= 2.385 rad/s^2

then now we calculate the inertia =0.021 kg*m^2

after we get those date we are able to calculate time which cart go  1m

Calculate:

use inertia and angular acceleration find torque =0.005

so that we get 9.247s in our calculation 

WE ARE READY TO GO !!

in our experiment we do three time and our final average time is 9.3 s

Is amazing! we do it almost the same result 

Conclusion:

so the error we have is about 0.5% 

our experiment is really success and make us understand how to calculate the inertia stuff 

#15 Collisions in two dimensions

Collisions in two dimensions

Introduction:

We learn how two do the momentum stuff in one dimension, then now we are trying to collision balls in two dimensions.  In this lab, we set up ours experiment on the leveled glass table, and roll our balls but not hit straight to the other ball. Also, we do it twice that one is metal ball the metal ball, another is marvel to metal ball.

Experiment:

We set up the video capture right above the glass table.

1)
using two metal balls with same mass which is 67.2g
and this is what we get

and this is our calculate 

In x and y axis 

we see that the momentum before and after are almost same 

then we find the relationship in KE 

find the error is 2%

2)using two ball 

the rolling ball is 19.6g    another is 67.3g

this is what we get

this is our calculation 

In x and y axis 

we see that the momentum before and after are almost same 

then we find the relationship in KE 

the error is 9%


conclusion:

after two experiment can tell that how the energy and the momentum relate before and after two balls do collision
we calculate both and just get a smell error which is lower than 10%
It is close to what we expect.

#14 Impulse-Momentum Activity

Impulse - Momentum Activity

Introduction:

 This activity is trying to measure the Impulse Momentum by two different way
1) the changing momentum which is come from changing velocity
2) integral of the force by time  =Fdt

we set up motion sensor, force senor, and cart like this: (but we actually hit on the force senor instead of magnetic)

we did take the photo so i found this here 

( http://teacher.nsrl.rochester.edu/PhyInq/Experiments/P14/P14_Collision_Impulse.html)

In this activity we do 3 part 

1) normal one, the cart with nothing 

2) we put 50g mass on the cart

3) we make it hit the sensor and stop there 

Experiment:

So here we start the experiment,  we use the motion sensor and force sensor get the date like this 

Part 1

We give cart speed and then hit on the force senor see how the impulse work on the car

Found that our impulse

by force sensor    = integral of force = 0.8925

by motion sensor  =  0.523+0.475=0.998 

the error is about 10% 

Part 2

 Then add mass

We give cart speed,mass and then hit on the force senor see how the impulse work on the car

Found that our impulse

by force sensor    = integral of force =1.115

by motion sensor  =  1.223 

the error is about 8.8% 

Part3

Put clay in front of the cart

Found that our impulse (we miss one pic of the integral but I have this date)

by force sensor    = integral of force =0.312

by motion sensor  =  0.331

the error is about 5%

Conclusion:

Look back the date we collect and calculate we can see that we impulse momentum can use two different way as the changing momentum and the integral of the force

and we also can say that whatever the cart go, this two way to find the impulse momentum can both find the same result

#13 Magnetic Potential Energy Lab

Magnetic Potential Energy Lab

Introduction:

To verify that conservation of energy in this system, we set up the air track as the frictionless surface. First, we find the magnetic repulsion force between two magnetic. Then verify conservation of energy.

Experiment:

First of all, we raise one side of the air track then use logger pro to calculate the magnetic repulsion by different angle with the  different distance it make. By the way, we download some app to phone that can make us measure the angle easily

                                  

We collect 8 distance from 8 different angle we set up

To find magnetic repulsion force 

F= mass of the air track glider *g*sin(angle)

R, Force relationship date 

then we do the linear fit in the logger pro  = Ar^B

And now we are able to verify the conservation of energy.

We put on the motion sensor and set it up to record 30 measurement per second, and also attach the aluminum on the air track glider for senor to collect the date.

Let the air track horizontally and push it slowly run to the motion senor but do not tough the magnetic at the closest point to the magnetic.

Then we get time, velocity, and acc 

and we are able to calculate our KE U and Total Energy

then we graph it

Conclusion:

In the first part of the experiment shows that the relationship between the distance and the magnetic repulsion force. It perfectly fit in the linear fit of Ax^B

 In second experiment, we except the total energy stay same, but the few graph we make early shows that it is a little be different then we keep fix it and get this final result. It still seem that the total energy have change when the cart close to the magnetic. We think that there might have some error when the experiment going or there are some other force doing in the system.

#12 Spring

Energy of the Spring

Introduction:

In this lab we use the spring and the hanging mass to calculate the total energy which include our mass kinetic energy, elastic potential energy, gravitational potential energy to find that the total energy stay same when our mass go bouncing. We use logger pro to collect date from our experiment.

We set up like this figure. We put a piece of paper on it that the motion sensor can easily collect our date from the experiment.

Calculation:

This is the date we collect from the motion sensor. We get time, position, velocity, and accelerate. 

Then now we can write the energy calculation on the logger pro.

All we need is Kinetic Energy of mass, Elastic potential energy, Gravitational Potential Energy of mass, Kinetic Energy of spring, Gravitational Potential Energy of spring.

KE= 1/2*m*v^2                                      KES= 1/2*(1/3mass of spring)*( v of spring)^2

GPE= m*g*h( position of mass)           GPEs= (1/2 mass of spring)*g*(position of the center mass of the spring)

EPE= 1/2*k*x^2

this is our date

add it all and we get the total energy

Conclusion:

By our experiment, we can see our total energy is bounding around +and- 0.0125 which mean without the error we can say that the total energy stay the same value about 0.482J.
Beside, we see that the total energy decreasing slowly which mean the system may have some other resistance like air resistance doing work on it.