Application of Newton’s 2nd Law of Motion on Atwood’s machine

Application of Newton’s 2nd Law of Motion on Atwood’s machine

This is an experiment dealing with ideal measurementreal Atwood’s Machines. In this machine, there is friction, and the pulley’s revolution has an impact on mass acceleration. Besides, an assumption of a frictionless and massless pulley is made. Therefore, the lighter object(m2) moves towards down, and the heavy object (m1) moves towards up, and the pulley does not revolve. Downward movement direction is positive, thus resulting in a tension force (T) of every mass and upwards movement of rope (similar for every mass) having a forced weight (mg) impacting downwards in addition to accelerations (a) of every mass. Application of 2nd Newton’s law (F=ma) for mass 1, resulting in T=m1g-m1a equation and T=m2g+m2a as the second mass equation and acceleration magnitude is equal for each mass just like friction. However, there is a movement of these two masses in the opposite direction instead of the tension force. The use of the following equation acceleration of masses on linear length: a=(m1-m2) */(m2+m1); this is obtained by elimination of tension and solving for (a) in every mass. During the experiment m1 and m2, values will be set, and measurement of linear velocity is done, and finally, linear acceleration of masses obtained from the sloping curve. A comparison of calculated and obtained values from the given masses is then used to solve equation a.

Apparatus and Method of Experiment:

The task requirements include 120cm rod, pulley system (ME-6838A)/Photogate, table clamp, Thread, PASCO 850 interface, Mass and Hanger set, and computer.

Method:

1. The Pulley system is connected to Digital inputs’ port one at interface 850.
2. They set up software done by opening up the computer, then starting PASCO Capstone software, and selecting port one at the digital input section. Pulley Ch1 photogates are chosen.
3. Timer set up is done by selecting timer settings and clicking on initial configuration timer, photogate ch1 is checked. Linear speed alone is checked on photogate with a pulley. Spoke Angle set to 36o, and large spoke arc to 0.015m. Timers’ specification name is done like on photogate having pulley then select finish.
4. Select the continuous mode in the controls palette, and the rate of sampling should be set at 200 Hz.
5. Graph and table are set by clicking its icon, remove column option are selected to remove one of the columns. Click measurement selections and pick linear speed (m/s) in the remaining column.
6. Linear speed is selected on the y-axis section in the graph’s measurement. Then measurement on the x-axis and time selections.
7. Thread is placed correctly over a pulley and appropriately set masses on weight hangers to current measurement.

1st measurement: m1=0.060kg, m2=0.50kg

2nd measurement: m1=0.60kg, m2=0.040kg

3rd measurement: m1=0.055kg, m2=0.045kg

4th measurement: m1= 0.065kg, m2=0.035kg

8. Movement of masses starting at rest commence. A partner must hold m1 to the pulley with the hanging of m2 close to the floor.

1. One partner does the click of the record, and the other partner does the release of m2.
2. The partner on the computer should select stop before m1 hits the floor, and the other should catch up m2 before it collides with the pulley.
3. Click the highlight range tool and highlight your linear data to fit the curve. Click apply on a chosen curve fit and select linear and record the slope. Masses used is renamed.
4. Repetition of 7-11 steps is done after completion of measurement one, two through four.

Comparison of results and Error analysis

The acceleration result of 0.812m/s2 is obtained from 1st measurement and 0.891m/s2 from calculated acceleration with an error of 8.86%. For 2nd measurement, the acceleration result is 1.83m/s2, and the calculated acceleration is 1.96m/s2 with a 6.63% error. For 3rd measurement acceleration results is 0.874m/s2 and the acceleration results is 0.980m/s2 with an error of 10.81% e. For measurement four, the experimental acceleration is 2.76m/s2, and the calculated acceleration is 2.94m/s2 with a 6.12% error.

Measurement three had the most significant percent error (10.81%), while the other measures all have a percent error under 10%. Percent error varies slightly for each measurement, so this is likely due to random errors when trying to properly coordinate when one lab partner clicks stop and when the other catches m2 before it hits the pulley. 4th measurement had the highest acceleration and 2nd measurement, having the lowest acceleration. The acceleration values were similar for 1st and 3rd measurements.

Conclusions:

1st and 2nd Measurements had an equal mass for m1, but m2 had a greater mass in 1st measurement than in measurement two, and measurement two had a much higher acceleration (1.83m/s2) than measurement one (0.812m/s2). Variations between m1 and m2 masses were more considerable in 2nd measurement, so there was less weight force exerted in the downward direction by m2, allowing it to accelerate upward more quickly and thus for m1 to accelerate downward a higher rate. From this, the bigger variations of mass amongst m1 and m2 caused a higher rate of acceleration in 2nd measurement. The sum of 3rd and 4th measurement masses’ (m1 and m2) were the same, but 4th measurement had a greater acceleration. The 1st and 2nd measurements sum of m1 and m2 were equal and similar values of acceleration (0.812m/s2 and 0.874m/s2). The difference between m1 and m2 in 4th measurement being the most magnificent (0.03kg) and the acceleration was the greatest of all four measurements (2.76m/s2). From these results, I can conclude that m1 and m2 differences had a more significant effect on the linear acceleration than the addition of m1 and m2. Also, an increase in the mass difference between m1 and m2, the linear acceleration will increase, and the decrease indifference, the acceleration will also decrease.