16-Sept-2014: Circular Motion

Purpose
The purpose of this lab is for students to experience with rotational motion. Students are to find and calculate certain measurements with given information about the rotating object.
Apparatus
There are two part to this lab: the first is a rotating disk and the second is a motor that rotates a hanging object from a string that is attached onto a stick. The first part was done as a class, several students timed the period of each rotation, and the actual speed was measured by LoggerPro. The second part was done in groups and each group measured the time of each period as the professor monitored the motor and the speed of the rotation. To measure the angle, we used a stand with a piece of paper attached onto a bar. Students were to find the height of the stand, the distance of the stick from center, and the length of the string.

Explanation
The first part was to rotate a solid disk, which was spun by the professor, and the time was recorded by several students. As a class, we resulted with several different times, similar but different, and we averaged the time. With the average of the time, we then found the acceleration for the five trial rotations. Then we graphed an omega vs. acceleration plot chart and found that the correlation was close to the value of 1.

Before starting the second part of the lab, we solved for an equation that shows the relationship between omega and angle; as angle becomes larger, so does the omega. Each group were to find the time it took for a number of revolutions, and the class found the height of the hanging mass was measured from one student in the class. With the height of the hanging object, we were able to find the angle created from the string and hanging object. With the distance of the stick, the length of the string, and the angle, we measured omega with our equation. Comparing the measured omega and the actual omega, we get a correlation of 0.9851, and the percent error were below 4%.

Conclusion
Circular motion deals with omega and period, which are measurable. For period, we measured the time it takes for one revolution. For omega, it took a little more effort to find an equation that gives omega. We calculated an equation of omega depending on the angle, so we concluded from the equation that if the angle grows larger so does the omega.

18-Sept-2014: Modeling Friction Forces

Purpose:
The purpose of this lab is to explore with static and kinetic friction by applying force in a few different ways.
Apparatus:
There are five parts to this lab, and each part is different from each other in terms of which friction we are dealing with and how we use certain materials to find the coefficient of friction.
Part 1: We placed a wooden block with felt, on one side of the face of the block, facing down on the table to give friction between the table and the block. We tied a string to the block and over a pulley at the edge of the table. At the other end of the string is a cup with a paperclip use to hold up the cup. With this setup, we added water into the cup until the block starts to move, which then we can measure the mass of the cup and block. We repeat this step while adding an extra block on top of the original, until the 4th block.

Part 2: We connect the force sensor to logger pro and opened up the file Coefficient of Kinetic Friction.cmbl to set up sensor. Then, calibrated the force sensor using a 500-g hanging mass. Afterwards, we placed the force sensor on the table and Zero the force sensor. We measured the mass of the block. We tied a string to connect the force sensor and wooden block with felt underneath, and started collecting data. The data collect a force from us pulling on the force sensor at a constant force. Repeat this step with one extra block each time, until 3rd block is added.

Part 3: In this part of this lab, we needed to find static friction. We placed the block with the felt side faced down on a ramp, and then we slowly lifted the ramp until the block starts to move. At that angle, we can calculate what the static friction.

Part 4: For this part of the lab, we needed to find kinetic friction. Same as Part 3, we placed the block with the felt side facing down on the ramp, but the ramp is at an angle larger than the angle from Part 3. With Logger Pro, we can record the data of the block accelerating toward a sensor at the bottom of the ramp. With the velocity vs time graph, we can find the acceleration by plotting a fit line.

Part 5: With the same step up as Part 4, we added a pulley at the top end of the ramp, and tied a string to the block and a mass weight to the other end. By dropping to mass weight, we see the block accelerate towards the top of the ramp.With the kinetic friction, we can find the theoretical acceleration, and compare the actual to the theoretical.

Explanation

Part 1: For Part 1 of this lab, we did four different trials, adding an extra block with each trial. With the mass of the blocks and the mass of the cup and water, we came up with the normal force between the block and the track and the static friction between the block and the track. 

Number of blocks on the track	Total mass of blocks on traks (kg)	Mass of water+cup when the blocks just started to move (kg)	Normal force between the block and the track (N)	Maximun static friction force between the block and the track (N)
1	0.1474	0.0607	1.44452	0.411804613
2	0.245	0.0909	2.401	0.371020408
3	0.3929	0.1473	3.85042	0.374904556
4	0.5311	0.1795	5.20478	0.337977782

Part 2: We pulled the force sensors, that was tied to a string on one end and the other end to the block with a felt side faced down, with a constant force that gives us a data plot, from Logger Pro, showing a rigid horizontal line. We did four different trials, starting with one block and adding another block with each trial, giving us four different results. We plotted a graph of Kinetic friction vs. Normal.

Number of blocks on the track	Total mass of blocks on tracks (kg)	Normal force between the block and the track (N)	Average kinetic friction force between the block and the track (N)
1	0.1427	1.39846	0.6043
2	0.2807	2.75086	0.6748
3	0.4287	4.20126	1.221
4	0.5314	5.20772	1.43

Part 3: As we lifted the ramp higher, we came to a stop at 14 degrees and a height of .29m. With the angle, we were able to conclude that the kinetic friction was 0.249.

Part 4: We raised the ramp at a angle of 25 degree, which is obviously larger than the angle in Part 3. With this angle we see a definite acceleration from the block with the felt on one side of the block. We calculated the kinetic friction to be 0.546 and the acceleration was 0.7106m/s².

Part 5: With the same setup as Part 4, we added a pulley at the top end of the ramp, and a 0.3kg mass weight at one end of the string and the other end of the string was tied to the block which had a mass of 0.25kg; the angle is 25 degrees again. Once the apparatus was put into motion, Logger Pro recorded the motion across a period of time and gave us an acceleration of 1.579 m/s². The theoretical acceleration was 1.259m/s², which gives us a 20% error. The percent error was quite large, but this was due to the small measurements that we took, like the angle and the mass of the block and hanging weight.

Conclusion

To find the static friction and kinetic friction, students must understand the concept of how friction applies. In this lab, we learned that static friction can be measured by using two objects with forces that goes against each other, while the whole apparatus stays completely motionless. Furthermore, kinetic friction can be measured by either the object moving from a force that applies, putting the object in motion, or by two objects with forces that goes against each other, but objects are in motion. This lab required several different methods to measure both static and kinetic friction, and with those measurements, we graphed force applied vs. friction. We also calculated theoretical acceleration, giving us a large percent error. The large percent error was due to inaccurate measurements of the angle or the masses or both.

12-Sept-2014: Determination of Unknown mass

Purpose
The purpose of this lab is for students to experience with tension and figure out the mass of an object with the tensions.
Apparatus
With a object with an unknown mass held up by spring scales that are tied to long rods each. The spring scales should be suspend at an angle. Measure the angle and record the scale readings. Estimate the uncertainty in the angle readings and scale readings. Use the measured values to determine the mass of the unknown mass. Propagate uncertainty in the calculated values of your mass.

Explanation
With the spring scales reading 4N at an angle of 48 degree above the horizontal and 3.2N at an angle of 42 degree above the horizontal. The uncertainty of the objects are listed: spring scales are 0.025N and the angles are π/180. After calculating the mass of the unknown mass, we came up with a mass of .522kg and an uncertainty of 0.03858kg.

Conclusion
The spring scales were placed at an angle above the horizontal, which were enough for students to find the mass of the unknown object. After measuring all the spring scales and angles we came up with a mass and uncertainty, which gave us a 7.4% leeway of what the exact mass is.

4-Sept-2014: Non-Constant Acceleration Problem (Activity)

Purpose:
The purpose of this activity was to experience non-constant acceleration from a kinematics problem. This activity will use different equations that will help solve for acceleration, velocity, and position when the object accelerates for a short amount of time. Also, to use excel to check our answer.
Apparatus:
The situation is "A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a rocket mounted on the elephant's back generates a constant 8000N thrust opposite the elephant's direction of motion. The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the m(t) = 1500-20 kg/s*t. The question is asking to find how far the elephant goes before coming to rest.
Explanation:
First we need to find the equation for acceleration with every mass totaled together, so it would be Fnet/m(t).

With the acceleration as a function with respect to time, we can then find velocity as another function with respect to time.

With the velocity as a function with respect to time, we can find position as a function with respect to time.

To find how far the elephant goes before stopping completely, we need to find when final velocity reaches zero. When we set the velocity function to zero, we find that time is 19.7 seconds. Then we plug in time into the position function, which gets us around 250 meters. 

After finding the distance, we used excel to check our answers. The first column input is time, where the time interval is 1/20th of a second. The second column is acceleration function and the third column is the average of the acceleration of the previous 1/20th of a second. The fourth column is change in velocity and the fifth column is the instant velocity at that specific time. The last two columns consists of change in distance and the total distance travel by the elephant with the rocket. According to excel, the time the elephant took to come to a complete stop was around 19.7 seconds, and the distanced traveled was 248.7 meters. The percent difference was 0.53%.

Conclusion:

The activity required the use of formulas of non-constant acceleration and excel inputs. The calculations weren't that different from excels answers. With this being said, we can further use excel in future lab and lecture activities, instead of calculating everything by hand.

12-Sept-2014: Measuring the Density of Metal Cylinders

Purpose:
The purpose of this lab is to determine the density of a metal cylinder and to experience with calipers and micrometers. We will be propagating uncertainty in this lab.

Apparatus:
First we start by obtaining three different metal cylinders, a caliper, and a small scale. Then we measure the height, diameter, and the mass of the cylinders. To use a caliper, one must understand how a caliper works. calipers measure to the millimeters, which are the increments that moves along with the outside large jaw, called the vernier scale. The vernier scale measures the mm, and to find out which increment to look at, you must match up the increments on the both scales. Wherever the increments match up is where you would read the measured value. To calculate density we need to take the mass and divide by the volume (m/v). The volume of a cylinder is Πr²h. To calculate uncertainty, we use partial derivatives. Partial derivatives is where you derive a single variable and leave the rest as constants for every variable. In other words, partial derivatives can be seen as deriving a function of F(x,y,z,...).

Uncertainty Formula

the caliper with the three different metal cylinders

Measuring the height of the brass cylinder with the caliper

Measuring the diameter of the brass cylinder

The scale that was used to measure the weight of the 

Explanation:
We started by taking measurements of everything necessary with a caliper and a small scale, which measures in centimeters and grams.  The uncertainty of the mass was 0.1g, which was given, and the uncertainty for the length was 0.005, which is half the smallest increment on the caliper. Then we took those values and calculated the density of each cylinder. One cylinder showed quite a small value for density in comparison to the other two cylinders. We measured uncertainty for each of the rod which gave us a percentage of around 1.8%. The first cylinder had a density of 7.69g/cm³±0.1444, the second cylinder had a density of 8.94g/cm³±0.16546, and the last cylinder had a density of 2.819g/cm³±0.04888.

The measured values of the different cylinders.

Calculating density with the values we found.

Calculating uncertainty for first cylinder.

Calculating uncertainty for second cylinder.

Calculating uncertainty for third cylinder.

Conclusion:
To find density of an object, we must first find the volume and mass of the object, then divide the mass by the volume. Although, finding density of an object using calculations isn't always correct, therefore we must find uncertainty to estimate the value we calculated. For uncertainty, we decided to use partial derivatives, which is deriving each variable separately while treating the other variables like a constant.

4-Sept-2014: Free Fall Lab

Purpose:
The purpose of this lab was to experience an object in free fall motion, and to see the object accelerate at 9.8 m/s², due to gravity.
Apparatus:
Students will use a sturdy column with an electromagnet at the top of the column. Hanging on the magnet will be a wooden cylinder with a metal ring around it, and a spark-sensitive tape attached to the column. With the cylinder at the top, the magnet will release the cylinder and the spark generator will spark at 60 Hz, which leaves dots on the tape. Each dot is 1/60th of a second apart.

Explanation:

Once we received our tape with dots marked on every 1/60th of a second, we measured the distance of about 15 consecutive dots. We use excel to plot the data and came up with a distance vs. time graph. Then found the differences of each 2 consecutive dots and divided each differences by 1/60; this gives us the velocity of the wooden cylinder it passes each dot. Using the velocity vs. time graph, we find the acceleration to be 9.47 m/s². (Every distance is measured in centimeter, and I am referring to every increment as meters.)

 With eight groups in the class, we took the acceleration of each group, and found the average and standard deviation. This allows us to draw the bell shape curve and see if majority falls within a certain region and to spot any outliers.

Conclusion

Gravity has been measure to have an acceleration of 9.8 m/s². Although, in reality, objects on Earth don't accelerate at that speed due to lots of factors that we need to take into account, like air resistance. In this lab, we experienced that gravity was a little under the actual, where our results put acceleration to be 9.47m/s², and other groups reached somewhere around that value.

9-Sept-2014: Trjectories

Purpose:
To experience and better understand projectile motion and to predict where an object might land.

Apparatus:

The set up, on the left, is for part 1 of the lab which was to make a ramp out of aluminum v-channel" that gave the velocity to the steel ball. The ball shoots out of the ramp and lands somewhere on the carbon paper which was on the floor.

The set up on the right is for part 2 of the lab, which has the same set up but we added a board that rests on the table at one end and the other end rests on the floor which results in a diagonal position. A piece of carbon paper was placed somewhere on the board to see if the landings are correct according to the prediction.

Explanation:
The first part was to find the initial velocity by shooting the steel ball out of the ramp 5 times and landing on the carbon paper that was placed on the floor. With the results of 5 different landings, we took the average, measured the height of the table, and calculated initial velocity to be 1.73m/s. With the initial velocity, we were able to predict where the ball will land if the board was in place (Part 2 of this lab). The board was placed at a 48 degree angle above the horizontal. We solved symbolically for the distance of where the ball will land and plugged in numbers, and the result was around 1.01m. We, then, rolled the ball off the ramp five more times and the distance was between 0.94 to 0.98 meters, giving us a 2.97 to 7.45% error.

finding initial velocity and distance

continuation of finding distance

Conclusion:
In this lab experiment, we explored projectile motion and measured distance of where the steel ball might land. We first found initial velocity by rolling the ball off the ramp to see how far the ball will travel, and measured the height of the table. Then we predicted the distance where the steel ball will land if the board was placed in front of the ramp. We average a 5.21% error, which is considerable acceptable.