JSSD

=toc Lab: Moving in a Horizontal Circle= **Group Members:** Nicole, Spencer, Dylan, Jillian **Class Period**: 2 **Date Due:** January 21, 2011

**Objective:** To find the relationships between the maximum velocity and the radius with banked and unbanked angles and to find the relationship between the banking angle and the radius **Objectives for each part:** **A : How does unbanking change the value of the radius at which the maximum velocity is reached? ** **B : How does the presence of banking change the value of the radius at which the maximum velocity is reached? ** **C: How does changing the banking angle change the value of the radius at which the maximum velocity is reached?**

**Hypothesis:** A: Without banking, the radius and maximum velocity have a direct square relationship as seen in the equation v^2=µgR. If you double the radius, the velocity will be four times greater. B: With banking, the radius and the maximum velocity have a direct square relationship as seen in the equation v^2=Rtanø. If you double the radius, the velocity will be four times greater.
 * C:** **As the banking angle increases the radius at which maximum velocity is reached will decrease. With the equation, as seen below, as the angle becomes bigger, the radius will get smaller to reach maximum velocity.**

We tested Part C of this lab.

No Friction Equation:
 * Pre Lab:**

Friction Equation:

**PROCEDURES:**

Materials for **ALL** parts of lab: - Stopwatch - Blocks with different angles - record player - Meter stick - Penny

1. Turn on the record player and use a stopwatch to count the rotations to see if it is truly spinning at the velocity shown on the record player. 2. Put record player on slowest RPM, set a radius to test to see if the penny will stay in a uniform circular motion. 3. Repeat last step and increase the radius until the penny stops moving in a uniform circular path. Record down. This is the maximum radius. 4. Repeat steps 2 and 3 using each speed on the record player and record down maximum radius.
 * Procedure (Part A):**

1. Turn on the record player and use a stopwatch to count the rotations to see if it is truly spinning at the velocity shown on the record player. 2. Place the penny at the desired distance from the center and measure that radius. 3. Turn on the record player and stopwatch. 4. Record the time and penny's position after the circle. 5. Repeat steps 2-4 with the same radius but using the other three speeds. 6. Repeat steps 2-5 with different radii. 4 trials for each radii. 7. Record Data.
 * Procedure (Part B):**


 * Procedure(Part C):**
 * 1.Turn on the record player to 78 rpm and time and count the rotations to see if it is truly spinning 78 rpm **
 * 2. Use a protractor to calculated the angle of the angled block **
 * 3. Attach the block to the record player **
 * 4. Place the penny on the angled block **
 * 5. Start the record player on 78 rpm and see if the penny falls off **
 * 6. If it falls off, lower the penny, do so until the penny does not fall off and record that radius **
 * 7. Repeat steps 2-6 with varying angled blocks **

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 * Data:**

Sample Calculation:
 * Calculations:**

Percent Error: A. Our hypothesis is correct because, as you can see from our data, without banking, as we increased the radius, the velocity increased steadily. When radius was doubled, the velocity was quadrupled. B. Our hypothesis is correct because, as you can see from our data, WITH banking as well, as we increased the radius the velocity increased steadily similarly to in part A. When the radius was doubled, the velocity was quadrupled. C. Our hypothesis is correct because, as you can see from our data, as the angle is getting bigger, the average radius that the penny fell off gets smaller. Radius and angle have an inverse relationship which is shown with our graph.
 * Conclusion:**

We had a .22% error, which means we were pretty accurate. However, there are a lot of places where we could have messed up. First off, its really hard to see exactly where the penny started off and what that radius was. We could have used carbon paper in order to accurately see where the penny slid and be able to measure it. Also, there is a lot of human error involved in this procedure. When one person was counting the rotations and one person was timing, they could have been off. If there was a slow reaction from one person in pressing the start/stop button, then the timing would have been off.

= = =Lab: Maximum/Minimum Tension:=
 * Group Members:** Nicole, Spencer, Dylan, Jillian
 * Class Period**: 2
 * Date Due:** January 11, 2011


 * Objective:** What is the maximum and minimum tension of a string that can maintain centripetal motion?

2. (Rationale: Tension is at its greatest when it reaches maximum speed because it reaches its maximum speed at the bottom of the circle path it is traveling.The equation, T-mg=m(v^2/r) uses maximum tension, and can solve for maximum velocity, or the maximum speed the string can withstand while still traveling in a circle. The maximum tension of the string will not change if the radius stays constant, and neither will gravity. By changing the masses the velocity must get smaller in order to keep the right side = to the left. We tested this by adding more mass to the same radius and seeing what the maximum speed the string could move before it broke.)
 * Hypothesis:** As the mass increases, velocity will stay the same at its minimum speed.
 * 1) (Rationale: Because tension will theoretically be 0 when the mass reached its minimum velocity it can withstand while still traveling in a circle, Velocity is only affected by gravity and the radius of the circle. Look at it using the equation T+w =m(v^2/r). Since T=0 when it reached minimum speed, the equation can also be rewritten like this: mg=m(v^2/r). You can divide both sides by m, which then makes the equation, g=(v^2/r). This shows mass has no affect on the velocity, which is why we decided to test it to make sure.)
 * Hypothesis:** As the mass increases, velocity will decrease when it reaches its maximum speed.


 * Materials:**
 * - Meter Stick**
 * - String**
 * - Washers**
 * - Stopper**
 * - Masses**
 * - Stopwatch**
 * - Tape (if desired)**

1. By using a meter stick and string, choose a radius that will stay constant throughout all of the trials, (.235m). 2. Weigh the stopper, (.01190kg) and the washers (1 washer = .00578kg). 3. By using the equation, 0 +mg =m(v^2/r), find the minimum theoretical velocity, 1.518m/s. 4. Then with the excel worksheet find out how long 10 rotations should take for the minimum speed. 5. With a stopwatch, time 10 rotations 4 times for each mass before adding another washer. 6. Record data into excel worksheet and find the average velocity. 7. Repeat steps 1-6 two other times with two different masses (.02924kg, and .03502kg.) 8. Analyze data, velocities should be the same and unchanged.
 * Procedures:**
 * Procedure for Hypothesis 1, (As the mass increases, velocity will stay the same at its minimum speed.)**

1. Measure the string to find a radius that should stay constant for the trials. (.225m) 2. Add weights until string breaks record the weight right before it broke and then when it did. 3. Do three trials with the same radius, average out weight and find maximum tension using the equation T-mg=0
 * Procedure for Finding Maximum Tension:**

1. By using a meter stirck and string, choose a radius that will stay constant throughout all of the trials. (.268m) 2. Weigh the stopper (.1190kg) and the washers (1 washer = .00578kg). 3. By using the equation T-mg=(v^2/r) plug in the maximum tension found in the procedure before and the mass and radius to find maximum theoretical velocity, 2.043m/s. 4. Then with the excel worksheet find out how long 10 rotations should take for the maximum speed. 5. With a stopwatch, time 10 rotations 4 times for each mass before adding another washer. 6. Record data into excel worksheet and find the average velocity. 7. Repeat steps 1-6 two other times with two different masses, (.02924kg and .03502kg) 8. Analyze data. Velocities should decrease as the mass increases.
 * Procedure for Hypothesis 2 (As the mass increases, velocity will decrease when it reaches its maximum speed.)**

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 * Data:**



Both of our hypotheses proved to be correct. As mass increased the velocity remained the same at minimum speed. When mass increased, velocity decreased after it reached its maximum speed. From our data in the first trial, there were three different masses with the same radius, and all with the same approximately the same average velocity. In our second experiment, the masses went up and our average velocity went down. The error in these experiments were when we were timing the rotations to have the right velocity. There is human error when using the stopwatch and counting the different rotations.
 * Calculations:**

Maximum Speed: Minimum Speed: Percent Error for Maximum and Minimum Speed:


 * Conclusion:**

Both of our hypotheses proved to be correct. As mass increased the velocity remained the same at minimum speed. When mass increased, velocity decreased after it reached its maximum speed. From our data in the first trial, there were three different masses with the same radius, and all with the same approximately the same average velocity. In our second experiment, the masses went up and our average velocity went down. The error in these experiments were when we were timing the rotations to have the right velocity. There is human error when using the stopwatch and counting the different rotations.

During this lab, our objective was satisfied and our experimental results validated our thesis. We hypothesized that as mass increased, the velocity at maximum tension would remain at minimum speed. First, we found maximum tension by hanging as much mass from the string as it could hold until it broke. Because velocity was 0, the entire first term of the equation cancelled out and the tension in the string equalled the mass. Our string broke when we added .0467 kg, which told us that the maximum tension in our string was .0467 N. We then used this value of maximum tension to find the relationship between mass and velocity at maximum tension. Our results indicated that as mass increased, velocity remained at its minimum velocity. We know our results are for the most part accurate because they are very close to our theoretical velocity. Based on the statistics in our chart above, we can conclude that our hypothesis was correct; as mass increased, velocity remained at its minimum. Although our experimental results seem accurate compared to our theoretical results, there were still many sources of error in our experiment. Inaccurate timing is possible to have contributed to our error. It was difficult to start timing exactly when we reached a //constant// max or min velocity, and also to record the time fast enough before the string broke. If our numbers for time were off a little bit, we are likely to have error in our results. Also, there was no way for us to tell if we were moving at exactly maximum or minimum speed during the experiment. We could only make observations and guess. If we weren't spinning at exactly the right velocity, our results would be somewhat off.

**Lab: Circular Motion**
Group Members: Nicole, Spencer, Jillian, Dylan Due Date: January 7, 2011


 * Objective:**Does the radius affect the force pulling to the center of a circle?
 * Purpose**: We are trying to determine the relationship between the radius and the tension of the string while it is in circular motion by keeping the speed and mass of the object constant.


 * Hypothesis**: The radius will be inversely proportional to the force. This is because as the radius increases the velocity decreases making the force decrease as seen in the equation F=m(v^2/R).

**Materials:**

- Stopwatch - Centripetal Force Apparatus - Meter Stick - String - Rubber stopper (mass) - Force sensor - Tape

**Procedure**:
 * 1) Set up lab
 * 2) Measure the mass of the object (stopper, 11.84g)
 * 3) Measure 1st radius
 * 4) Spin in a circular motion 10 seconds to find the constant speed. (22.6 periods in 10 seconds)
 * 5) After finding the time it takes per rotation and the radius, you can find the velocity. This should be the velocity for all of the trials. (Even when the radius changes.)
 * 6) Do three trials and find the mean of the runs (find the force)
 * 7) After 3 trials change the radius keeping the mass and speed constant.
 * 8) Use the velocity and radius to figure out how long it takes for 10 periods.
 * 9) Do three trials and find the mean of the runs (find the force)
 * 10) Repeat steps 7,8,9 until you have data for 3 different radii.
 * 11) Create and graph and analyze results.

**Graph**: Our Graph: F vs r

Roshni, Erica, and Amanda's Graph: F vs m

Sam, Evan, and Ryan's Graph: F vs v

**Data**: [|rotation.xls]

Radius= 0.195 m



Radius= 0.341m

Radius =0.421m

Circumference Calculation: Sample Velocity Calculation: Tension Calculation:
 * Calculations**:

Our purpose was satisfied because we created a graph showing the relationship between radius and tension. This was an inverse relationship, making our hypothesis correct. Because our R squared value is pretty low (94%) our findings aren't that precise. There was a lot of error in our experiment. For one thing, our actual radius was really less than what we wrote it down to be. We weren't able to spin our mass exactly horizontal and there was a slight angle. In addition, it was difficult to keep the velocity constant and what we wanted it to be. For the future, we would determine the real radius and try to keep it more constant.
 * conclusion**: