Centripetal force Lab PDF

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Section: 012

Experiment Date: 10/17/16 Centripetal Force

Objective/ Description:

The goal of this lab was to further examine and study Newton’s second law of motion, specifically the centripetal force of an object. The Centripetal Force apparatus was attached to the weight hanger and slotted weights, together the equipment was used to determine the centripetal force of the weight on the hanger. Based on the time it took the weight hanger to take 10-20 revolutions, the angular velocity of the weight hanger could be determined, which could then be used to determine the centripetal force. Theory: According to Newton’s second law of motion force=mass x acceleration (F=ma). Since force and acceleration are proportional to each other, the direction of velocity is also parallel to the particle’s path. When an object it moving in a circle, with a constant speed, the force and acceleration are perpendicular to velocity and point to the center of the circle. The force on an object moving in a circle is its centripetal force. It can be calculated using the mass multiplied by the radius and the angular velocity squared. The centripetal force can be calculated when a particle is moving in a circular motion at a constant speed. Procedure: In this lab the task was to determine the centripetal forces of a mass hanging from weight hanger at varying radii of 15,18, and 20 cm. First the mass of the weight (M1) needed to be determined then the mass of another weight attached via a pulley needed to be determined (M2). When connected to the pulley and the spring, the M1 needed to be aligned with the base pointer. Once the mass of M2 was recorded, it was taken off the system, while M1 was still connected to a spring and then spun in a way that its pointer was aligned to the base pointer throughout 10-20 revolutions. The amount of time it took to complete the revolutions was then timed and the centripetal force was calculated based on the amount of revolutions and the times. Data and Calculations: Table 1. Centripetal Force with a radius of 15 cm M1=445.8g M2=350g Period T Angular Trial Time for 20 velocity revolutions(s/1 ω revolution) (radians/s) 1 14 .7 8.98 2 13 .65 9.67 3 15 .75 8.38 T=

seconds revolution

T 1=

M1rw2 (N)

M2g (N)

5.40 6.25 5.21

3.43 3.43 3.43

14 s 13 s 15 s = .7s T2= =.65s T3= = .75s 20 20 20

2Π 2Π 2Π =8.98 radians/ sec =9.67 radians /sec ω1 = ω2 = .7 .65 T 2Π =8.38 radians/ sec ω3 = .75 Fc= M1rw2 Fc1= .4458kg(.15m)(8.98) 2= 5.4N Fc2= .4458g(.15m)(9.67)2=6.25N Fc3= .4458kg(.15m)(8.83)2= 5.21N M2g= .35kg (9.81m/s2)=3.43N Average of Experimental (Fc)= (5.4N+6.25N+5.21N)/3=5.62N ω =

Theoretical−experimental mean ×100 Theoretical 3.43 N −5.62 N × 100=64 % % error= 3.43 N

Error analysis:

Table 2. Centripetal force with a radius of 18cm M1=445.8g M2=800g Trial Time for 20 Period T Angular M1rw2 (N) revolutions(s/1 velocity ω (radians/s) revolution) 1 13 .65s 9.67 7.50 2 14 .7s 8.98 6.74 3 12 .6s 10.47 8.79 12 seconds 13 s 14 s T= T 1= = .65s T2= =.7s T3= = .6s 20 20 20 revolution 2Π 2Π 2Π =9.67 radians /sec =8.98 radians/ sec ω1 = ω2 = ω = .65 .7 T 2Π =10.47 radians/ sec ω3 = .6 Fc= M1rw2 Fc1= .4458kg(.18m)(9.67)2= 7.5N Fc2= .4458kg(.18m)(8.98)2=6.74N Fc3= .4458kg(.18m)(10.47)2= N M2g= .800kg (9.81m/s2)=7.84 N Theoretical−experimental mean ×100 Error analysis: Theoretical Average of Experimental (Fc)= (7.50N+6.74N+8.79N)/3=7.67N 7.84 N −7.67 N ×100=2.2 % %error= 7.84 Table 3. Centripetal Force with a radius of 20cm M1=445.8g M2=970g

M2g (N) 7.84 7.84 7.84

M1rw2 (N) Time for 20 Period T Angular revolutions(s/1 velocity ω revolution) (revolutions/s) 1 18 .7 8.97 7.17 2 19 .65 9.67 8.32 3 17 .75 8.38 6.26 12 seconds 13 s 14 s T 1= = .65s T2= =.7s T3= = .6s T= 20 20 20 revolution 2Π 2 Π =8.97 radians/ sec 2 Π =9.67 radians /sec ω1 = ω2 = ω = .7 .65 T 2Π =10.47 radians/ sec ω3 = .75 Trial

M2g (N) 9.52 9.52 9.52

Fc= M1rw2 Fc1= .4458kg(.20m)(8.97s)2= 7.17N Fc2= .4458g(.20m)(9.67s)2=8.32N Fc3= .4458kg(.20m)(8.38s)2= 6.26N M2g= .970kg (9.81m/s2)=9.52N Average of Experimental (Fc)= (7.17N+8.32N+6.26N)/3=10.40N Theoretical−averageof experimental × 100 Error analysis: Theoretical %error=

9.52 N −10.40 N ×100=9.2 % 9.52 N

Questions: 1. Human error can cause significant random error to the data collected from the lab. For example, if the pointers were misaligned which could have affected the radius, which would affect the system and create an error in calculations. 2. Random error depends on what is done to the system to create errors, while systematic errors are things that are wrong within the system which affect the data. The errors in this lab are random error, for example the aligning of the pointers could cause errors. 3. Yes, the data should enable one to estimate the amount of error, based on the theoretical data of the M2g and the value of the centripetal forces, which should be equal to each other. 4. Yes the data supports Newton’s second law, because the force and acceleration point towards the center of the circle when a mass is moving at a constant speed. 5. The forces involved in the rotation of M1 are the tension force of the string, the centripetal force caused by the spring and force of gravity on M1. Error Analysis: Within this lab, it was evident that there were random errors made. This is most likely due to human error. The error is most likely the result of not counting the revolutions properly, which then affected the times measured. The error could mostly

be due to the aligning of the pointers for each trial. The average of the experimental values differed from the theoretical values, but they were similar to each other. The amount of percent error for each of the different radii was small for the radii of 18 and 20 cm, but the error calculated for the radius of 15cm was larger. This could be due to the not being able to really gauge if the pointers were aligned. Conclusion: In conclusion, the results of the experiment were close to what was supposed to be achieved for most of the lab, based on the percent error. The data supports Newton’s second law is true because the centripetal force on an object moving in a circle is equal to the mass of the object, multiplied by the radius and the angular velocity squared. The experimental and the theoretical values were close to each other. Based to the data, when the radii were smaller, the force of gravity on M2 was smaller and had similar value to the centripetal force. Therefore, it can be concluded that the smaller the radius of a M1, the larger force of gravity is exerted on M2. The centripetal force of M1 was similar throughout the experiment as well as the angular velocity....