Lab: Collisions in two dimensions

Lab: Collisions in two dimensions

Purpose:
Look at a two-dimensional collision and determine if momentum and energy are conserved.

Experiment:
1. Set up the apparatus as pictures show.
2. Connect the camera and follow the instruction to set up.
3. Gently set the stationary ball on the leveled glass table. Aim the rolling ball so that it his the side of the stationary ball. The balls should ideally roll off at some decent angle from one another.
4. Input the video in LogPro and add point series following the motion of the balls.
5. After adding two series, set the origin at the point the rolling ball left my hand. And rotate the axes to be the same direction as the ball rolled.
6. Click linear fit for each portion of the graph to get the slopes.
7. Based on the value of slope, record the initial velocity and final velocity of the rolling ball and stationary ball.
8. Calculate the momentum and energy before and after the collision.

Data and analysis:
Steel ball and marble:
m(steel ball 1)=0.0671kg  m(marble)=0.0053kg

Two steel balls:
m(steel ball 1)=0.0671kg   m(steel ball 2)=0.0603kg

Result:
Steel ball and marble:

Two steel balls:

Calculation:

Conclusion:

Based on the graph, within acceptable error, the momentum and energy are both conserved in the collision in two dimensions.

Verification the relationship of Impulse and momentum

Verification the relationship of Impulse and momentum

Purpose: 
Through the bounce of the cart, verify the relationship of Impulse and change of momentum.

Eqiupment:
track, cart, force sensor, motion sensor, and mass.

Experiment:
Part One:
1. Set up the apparatus as the pictures show.
2. Measure the weight of the cart and the force sensor.
3. Give the cart with the force sensor a initial velocity and let the force sensor bounce upon the other cart.
4. Record the motion and the force.
5 Integrate the force that the cart received and examine the velocity right before the collision and after the collision.

 Part Two:
1. Set up the apparatus as the pictures show.
2. Measure the weight of the cart with the force sensor and the mass.
3. Give the cart with the force sensor a initial velocity and let the force sensor bounce upon the other cart.
4. Record the motion and the force.
5 Integrate the force that the cart received and examine the velocity right before the collision and after the collision.

 Part Three:
1. Set up the apparatus as the pictures show.
2. Put a nail in front of the cart and stick a clay at the same height of the nail on the other side of the track.
3. Measure the weight of the cart with the force sensor and the nail.
3. Give the cart with the force sensor a initial velocity and let the force sensor bounce upon the other cart.
4. Record the motion and the force.
5 Integrate the force that the cart received and examine the velocity right before the collision and after the collision.

Result:

Conclusion:
We verify the relationship of Impulse and change of momentum J=F*t=delta p= m(Vf-Vi)

Lab: Conservation of energy 2

Lab: Conservation of energy 2

Purpose:
Verify the conservation of energy using air track.

Equipment:
Air track, cart, ruler, air source, and motion sensor.

Experiment:
1.  Set up the apparatus as the pictures show.
2. Turn on the air source and lift up the air track with certain angel so that the cart slide down.
3. Measure the distance of two magnet, and write down the angle and the distance.
4. Repeat step two and three with different angles.
5. Calculate the force acting on the cart by the formula F=mgsin(deta).
6. Enter the data into the logPro and click curve fit with power model to get the relationship between the distance and the force.
7. Integrate the force to get the formula of the work done by the force. Take the opposite of the work as the potential energy of the cart.
8. Turn on the air source, give the cart an initial velocity, and record the motion of the cart.
9. Get a new calculated column of the Kinetic Energy of the cart, Potential Energy of the cart, and the total energy of the cart.

Result:

F=0.0003785*x^-1.792

Conclusion:

Within the a certain error, the total energy of the cart is conserved. Therefore, it verify the law of conservation of energy.

Lab: Verification of conservation of energy

Lab: Verification of Conservation of Energy

Purpose: 
Use the spring and hanging mass to verify the conservation of energy.

Equipment: Spring, Hanging Mass, motion sensor

Experiment:
1. Set up the apparatus as pictures show
2. Measure the length of the spring without hanging mass Lo.
3. Hang a known mass on the spring, measure the length of springL.
4. Calculate the spring constant k by the equation mg=k(L-Lo).
5. Derive the formula for the kinetic energy of mass, gravitational potential energy of mass, elastic potential energy of the spring, gravitational potential energy of the spring, and kinetic energy of the spring.
6. Pull down the mass with certain distance, release the mass and record the motion of the mass.
7. Add new calculated column for kinetic energy of mass, gravitational potential energy of mass, elastic potential energy of the spring, gravitational potential energy of the spring, and kinetic energy of the spring.
8. Add new calculated column named total energy as the sum of all calculated energy.
9. Graph all calculated energy and total energy in the same graph.
Apparatus

 Formulas:

Results:

Conclusion:
The total energy is around a constant, therefore the energy of the system is conserved.

Lab: Verify the integral of the force with respect to the distance is equal to kinetic energy of the block

 Lab: Verify the integral of the force with respect to the distance is equal to kinetic energy of the block

Purpose:
Through the motion of the block pulled by the spring to verify the integral of the force with respect to the distance is equal to kinetic energy of the block.

Equipment:
track, block, spring, motion sensor, force sensor.

Experiment:
1. Set up the apparatus as the pictures show.
2. Calibrate the force sensor, and zero it.
3. Stretch the block and the spring to a certain length.
4. Release the block and record the position and force.
5. Add calculated column of Kinetic Energy.
6. Do the integral of the force.
7. Click examine and move the mouse along the Kinetic Energy curve with the same portion of the integral of the force. Record the value of the integral of the force and Kinetic Energy.
8. Change the range of the integral and record the value in two other different place.

Result:

Number one: 
Integral: 0.8197m*N
Kinetic Energy: 0.636J

Number second: 
Integral: 1.203m*N
Kinetic Energy: 1.164J


Number three: 
Integral: 1.556m*N
Kinetic Energy: 1.331J


Conclusion:
 Within a certain error, the integral of the force with respect to the distance is equal to kinetic energy of the block. The work done by the force convert into the Kinetic Energy of the block.

Lab: Finding the power of the work

Lab: Finding the power of the work

Purpose:
Learn about how to calculate the work and power by measuring the force, distance and time.

Equipment:
Mass, pulley, string, timer

Experiment:
Part 1:
1. Each person walk and run up the stairs and measure both the time t to get to the second floor.
2. Count how many stairs are there.
3. Measure how high is each stair.
4. Calculate the height that the person travel.
5. Use W= mgh to calculate the work done by person against the gravity.
6. Use P=W/t to calculate the power of the work.

Part 2:
1. Set up the pulley system on the second floor.
2. One person stands on the first floor and pull the backpack with a mass, the other person stand on the second floor and record the time it takes for the backpack being pulled up to the second floor.
3. Record the weight of the mass.
4. Use W= mgh to calculate the work done by the person against the gravity.
5. Use P=W/t to calculate the power of the work.

Calculation:

Result:

Part 1: 

W=3032.12J, Pwalk=216.27W, Prun=489W

Part 2:

W=389.87J, P=97.46W

Conclusion:

We learn about how to calculate the work and power by measuring the force, distance and time.

relationship between angular speed (ω) and angle of the string above the vertical (θ) for a particular rotating apparatus

relationship between angular speed (ω) and angle of the string 

above the vertical (θ) for a particular rotating apparatus

Purpose:

Through modeling the circular motion with different angular speed, to find the relationship between angular speed (ω) and angle of  the string above the vertical (θ) for a particular rotating  apparatus.

Equipment:

Tripod, rod, string, mass, meter stick, timer

Experiment:

1. Set up tripod with a rod horizontally at the top of tripod, attach a string to one end of the rod with a mass on the other end.

2. Measure the height of the tripod h=211 cm and the length of the rod l=61.5 cm.

3. Measure the time of 10 rotations.

4. Measure the height of the hanging  mass h2 (with a certain angle) by slowly raising a piece of paper, which was attached to a sturdy pole.

5. Repeat step 3 and 4 with different angular speed.

Data:

1) 37 sec. and 49 cm.

2) 30 sec. and 72 cm.

3) 26 sec. and 92 cm.

4) 25 sec. and 104.5 cm.

5) 23 sec. and 119 cm.

6) 21 sec. and 132 cm.

7) 19 sec. and 147 cm.

8) 17 sec. and 157 cm.

Data analysis:

1. Divide the time by ten to get the period T.

2. Calculate the angel θ by height of the tripod h , the height of the mass h2, and the length of the string l.

3. Open an excel and input the data of period T, the height of the mass h2, and the angel θ.

4. In Cell D2, input the formula for calculated angular speed ω in terms of g, θ, d, and l.
5. In Cell E2, input the formula for measured angular speed ω in terms of T.
6. Drag down the column and get the calculated angular speed ω and measured angular speed ω for all other experiments.
7. Copy the column of calculated angular speed ω and measured angular speed ω, and paste it in Logger Pro.
8. Click Linear Fit to get the graph and equation between calculated angular speed ω and measured angular speed ω.

Result:

Conclusion:

We find the relationship between angular speed (ω) and angle of  the string above the vertical (θ) for a particular rotating apparatus. And we verify it through ω=2pi/T.