PHYS101L-B1- Group 3-E101 and E102 1Q2021 PDF

Preview

Summary

Download PHYS101L-B1- Group 3-E101 and E102 1Q2021 PDF

Description

E101: NEWTON’S SECOND LAW OF MOTION E102: FRICTION

Group Leader: Group Number: 3 Villamarzo, Trisha Mariel V. Group Members: Abareta, Ian Carlo T. Abueg, Dave Matthew B. Alvarez, Angelo S. Del Prado, Ellison Angelo D.

August 28, 2020

E101: Newton’s Second Law of Motion E102: Friction Results and Discussion Table 1: E101 Part A. Constant Mass and Changing Net Force Mass of cart, 𝑚1 = 0.6161 𝑘𝑔 Distance traveled, 𝑠 = 0.5𝑚 Total Acceleration Acceleration Net Force, Time of Hanging (Accepted (Experimental TRIAL 𝑚2 𝑔 travel, 𝑡 Mass, 𝑚2 Value), 𝑎 Value), 𝑎 1 0.02 0.20 0.31 1.60 0.39 2 0.06 0.59 0.87 0.92 1.19 3 0.10 0.98 1.37 0.78 1.64

Percentage Error 26.71 36.89 19.89

Figure 1. Contrasting Data of 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 and 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑨𝒄𝒄𝒆𝒑𝒕𝒆𝒅 (E101 Part A) Showing the Data of both experimental and accepted shows that as the hanging mass gets heavier it yields a higher acceleration value and higher net force. Another thing to note is the values of 𝑅 2 which indicates that there is a positive linear relationship for both 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 and 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 data. Table 2: E101 Part B. Changing Mass and Constant Net Force Mass of cart, 𝑚2 = 0.1 𝑘𝑔 Net Force, 𝑚2 𝑔 = 0.98 𝑁 Distance traveled, 𝑠 = 0.5𝑚 Mass of cart + Acceleration Time of travel, Acceleration Percentage 𝑡 TRIAL mass added, (Accepted (Experimental Error 𝑚1 Value), 𝑎 Value), 𝑎 1 0.62 1.37 0.81 1.52 10.99 2 0.72 1.20 0.87 1.34 11.27 3 0.92 0.96 0.95 1.10 14.35

Figure 2. Data comparison of 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 and 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑨𝒄𝒄𝒆𝒑𝒕𝒆𝒅 (E101 Part B)

Figure 1.3 shows that if the force is constant both sets of Acceleration Data tend to go downwards which suggests that there is an inverse relationship between the mass and acceleration. Data have shown that in conditions that force is constant as the mass of an object becomes heavier the acceleration of the said object will continue to decrease until it reaches 0. This phenomenon follows the equation that if 𝐹𝑛𝑒𝑡 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑎 =

𝐹𝑛𝑒𝑡 𝑚

𝑤𝑖𝑙𝑙 𝑏𝑒 𝑎 =

1

𝑚

Table 3: E102 Part A. Determining the Coefficient of Friction TABLE 1a. (Large side of the block) TABLE 1b. (Narrow side of the block) (total weight of (total weight of Coefficient of (total weight of (total weight of Coefficient of the block) 𝑊𝑏 the pan) 𝑊𝑝 friction 𝜇 the block) 𝑊𝑏 the pan) 𝑊𝑝 friction 𝜇 141.5 45 0.32 141.5 35 0.25 161.5 50 0.31 161.5 40 0.25 181.5 55 0.30 181.5 45 0.25 201.5 60 0.30 201.5 50 0.25 221.5 65 0.29 221.5 55 0.25 Average coefficient of friction 0.304 Average coefficient of friction 0.25

Figure 3. Data comparison In correlation to the weight of the block the value of the weight of the pan increases. The slope of the line determines the positive steepness of the graph. The slope of the coefficient of the friction is closely proportional. Vertical Height, ℎ 39 Formulas :

Table 3: E102 Part B. Determining the Angle of Repose Horizontal Distance, 𝑏 tan 𝜃 116 0.34 𝐹 = 𝑚𝑎 𝑎𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 =

𝑡2 𝑎𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙−𝑎𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑

%𝐸𝑟𝑟𝑜𝑟 = |

𝑓 = 𝜇𝑛 Sample Computations: Part A Net force (𝑚2 𝑔) = 0.020 kg × 0.98 m/s2 = 0.20 N

(1) (2)

𝑚2 𝑔 𝑚1 +𝑚2 2𝑠

𝑎𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 =

𝑎𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑

𝜃 18.78

(3) | × 100

(4) (5)

0.1960 𝑁 𝑚2 𝑔 = = 0.31 m/s2 𝑚1 +𝑚2 0.6161 𝑘𝑔+0.020 𝑘𝑔 2(0.5 𝑚) 2𝑠 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 = 𝑡 2 = = 0.39 m/s2 (1.6004 𝑠 )2 0.3904 − 0.1960 Experiment Value−Accepted Value | × 100 = | % Error = | | × 100 Accepted Value 0.1960

𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑨𝒄𝒄𝒆𝒑𝒕𝒆𝒅 =

= 26.71 %

Part B 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑨𝒄𝒄𝒆𝒑𝒕𝒆𝒅 =

0.98 𝑁 𝑚2 𝑔 = = 1.37 m/s2 𝑚1 +𝑚2 0.6161 𝑘𝑔+0.100 𝑘𝑔 2𝑠 2(0.5 𝑚) 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝑬𝒙𝒑𝒆𝒓𝒊𝒎𝒆𝒏𝒕𝒂𝒍 = 2 = = 1.52 m/s2 (0.8114 𝑠 )2 𝑡 Experiment Value−Accepted Value 1.5462 − 1.6172

% Error = |

| × 100 = |

Accepted Value

1.6172

| × 100 = 10.99 %

Table 1a. (large side of the block) 𝑊𝑏 = 141.5 𝑔 𝑊𝑝 = 45 𝑔 𝜇=

𝑚2 𝑔

𝑚1 +𝑚2

=

𝑊𝑝 𝑊𝑏

=

45

141.5

Average Coefficient of Friction: 𝜇 =

= 0.32 𝜇𝑡𝑜𝑡𝑎𝑙 5

=

0.3180 + 0.3096 + 0.3030 + 0.2978 + 0.2935

= 𝟎. 𝟑𝟎𝟒

=

80.2473 + 0.2477 + 0.2479 + 0.241 + 0.2483 5

= 𝟎. 𝟐𝟓

5

Table 1b. (narrow side of the block) 𝑊𝑏 = 141.5 𝑔 𝑊𝑝 = 45 𝑔

𝜇=

𝑚2 𝑔 𝑚1 +𝑚2

=

𝑊𝑝

𝑊𝑏

=

45 𝑔 141.5 𝑔

= 0.3180

Average Coefficient of Friction: 𝜇 =

𝜇𝑡𝑜𝑡𝑎𝑙 5

Discussion In E101, graphs A and B were able to show the relationship of each variable in Newton’s second law which is often stated as equation (1). Acceleration is directly proportional to the Net force which means when one variable increases, the other variable also increases, whereas it is inversely proportional to its mass because the heavier the object, when applied a given force, will decrease its acceleration. The cart’s mass (𝑚1 ) affects the string’s horizontal force or the tension and the cart’s acceleration whereas the hanging mass (𝑚2 ) affects the string’s vertical force and the cart’s acceleration. Equations (2) and (3) are needed to obtain the % Error (4) to know how close the experimental value is to the true value (accepted value) and will be the basis for this experiment’s success. In E102, it shows that the area of contact does not affect the coefficient of friction because of the equation (5) where Frictional force equals to the coefficient of 𝜇 times the normal force N. The graphs shown also illustrates the relationship of the Frictional force and Normal force which is directly proportional. Observing uniform motion is a must to be able to maintain a constant kinetic friction and will also help avoid errors in the experiment. Conclusion In E101 the data have shown the conditions and validity of Newton’s Second Law of Motion which explains the nature of mass, acceleration, and force with each other. The experiment was able to prove that the acceleration is directly proportional to the applied force and inversely proportional to the mass. In E102, it was stated above on the relationship of the frictional force and Normal force on which it has been said that it is proportional. In addition, it has been concluded that if the angle of repose increases, the coefficient of friction also decreases based on the group’s calculations. This would mean that if the incline is higher,

the body can slide more smoothly. The errors found in the experiments were kept to a minimum and that the experimental values are quite close to the accepted value which concludes the validity of the experiments. The data obtained were quite near to each other which is why we were able to come up with an accurate measurement and interpretation of data. The concepts from these experiments can be and is being applied in different fields of expertise. The concept of E101 can be used in creating fuel for aircraft which prioritizes for higher octane rating which is more stable fuel that will provide a higher amount of acceleration thus, allowing the aircraft to fly. In the mechanical engineering field, the second law of Newton is one of the core principles everyone in the field should know for the interaction of a machine, and the forces acting upon it should be seen for the efficiency and safety of the said machine should be highlighted. Friction is important in mechanical engineering. When dealing with machine friction, wear lubrication, and bearing design go hand in hand to maintain and make the machine more efficient (Brain, 2000). References: Blau, P. J. (2001). The significance and use of the friction coefficient. Tribology International, 34(9), 585– 591. doi:10.1016/s0301-679x(01)00050-0 Brain, M. (2000, April 01). What Does Octane Mean? Retrieved from https://auto.howstuffworks.com/fuelefficiency/fuel-consumption/question90.html

Group Interaction (50%) Group No. 3

Experiment No. 101 & 102

Date: August 28, 2020

Member’s Name and Rating DESCRIPTION

Del Alvarez Prado

Abareta

Abueg

10

10

9

10

10

10

7

10

ATTITUDE TOWARDS OTHERS. Definitely friendly, cooperative, considerate and understanding. 1 – 3 Rare 4–5 Sometimes 6 – 8 Oftentimes 9 – 10 Always

10

10

8

10

DEPENDABILITY AND RESPONSIVENESS. Always reliable, dependable, and complete works as requested without confusion. 1 – 3 Rare 4–5 Sometimes 6 – 8 Oftentimes 9 – 10 Always

10

10

7

10

PUNCTUALITY AND ATTENDANCE. Exceptionally punctual; always the first to come to class in your group. 1 – 3 Rare 4–5 Sometimes 6 – 8 Oftentimes 9 – 10 Always

10

10

8

10

Total

50

50

39

50

QUALITY AND VOLUME OF WORK. Quality and thoroughness generally above requirements; works exceptionally accurate, neat, and complete 1 – 3 Rare 4–5 Sometimes 6 – 8 Oftentimes 9 – 10 Always INITIATIVE. Consistently searches for ideas; prompt in taking actions; not easily put off by obstacles.

Villamarzo...