Ass 1 f12-11 report engineering dynamics problems
Download as DOCX, PDF0 likes628 views
The document analyzes the motion of a bicyclist traveling 40 meters. It relates the bicyclist's velocity to distance traveled as V=0.25*s. It then plots graphs of acceleration, velocity, and distance over time. The motion depicts an unrealistic rapid increase in velocity and acceleration that could only be possible for an Olympic cyclist over a short distance.
Ass 1 f12-11 report engineering dynamics problems
- 1. ABSTRACT: To analyze the motion of a bicyclist as described in the above problem. I will be making explicit relation of time with the given velocity-distance relation, and plotting the acceleration, velocity and distance against time. ANALYSIS: S=0 to 40 meters: Velocity is dependent on distance as follows: V=0.25*s 푑푠 푑푡 = 0.25 ∗ 푠, => 1 0.25 ∫ 푑푠 푠 푡 푡0 = ∫ 푑푡 푠 푠0 t-t0 = 1 0.25 (ln(s)-ln(s0)) s-s0 =0.25*(푒푡 − 푒푡0 ) =>> @s0=0, t0 t=4*ln(s) S=0.25*푒푡 − 0.25 푑푠 푑푡 = 0.25*et =V 푑^2푠 푑푡^2 =0.25*et =a
- 2. To get the time for bicyclist to travel 40 meters : t40=4*(ln(40)) t40=14.755 sec GRAPH: 15 10 5 0 v-s 0 10 20 30 40 50 velocity distance Series1 800000 600000 400000 200000 0 v-t(s) -5 0 5 10 15 20 -200000 velocity time Series1
- 3. 30 25 20 15 10 5 0 a-s 0 10 20 30 40 50 700000 600000 500000 400000 300000 200000 100000 0 a-t(s) -5 0 5 10 15 20 Observations: Here the distance of very infinitesimal range is being covered before the infinitesimal time interval. The motion of this bicyclist seems to be recorded as a sudden motion due to which the time factor is defined at the velocity of 0.25m/s not when the distance was one meter. This motion depicts the motion with variable velocity and acceleration at some time t and some distance s. The motion is depicting a very rapid increase of velocity and acceleration which seems impossible for a human to ride or even a robot cannot run a cycle with this characteristics. This motion can be valid for limited time and short distance, as then it could depict the motion of an Olympian cyclist competing in the event. acceleration distance Series1 -100000 acceleration time Series1
- 4. Conclusion: This data might be related to some Olympic game researcher or a hypothetical over plotting of the bicyclist who has a jerky start in the beginning of his ride. ANNEXURE: TABLE 1: s t(s) v(t) a(t) a(s) v(s) 0 #NUM! #NUM! #NUM! 0 0 1 0 0.25 0.25 0.625 0.25 2 2.772589 4 4 1.25 0.5 3 4.394449 20.25 20.25 1.875 0.75 4 5.545177 64 64 2.5 1 5 6.437752 156.25 156.25 3.125 1.25 6 7.167038 324 324 3.75 1.5 7 7.783641 600.25 600.25 4.375 1.75 8 8.317766 1024 1024 5 2 9 8.788898 1640.25 1640.25 5.625 2.25 10 9.21034 2500 2500 6.25 2.5 11 9.591581 3660.25 3660.25 6.875 2.75 12 9.939627 5184 5184 7.5 3 13 10.2598 7140.25 7140.25 8.125 3.25 14 10.55623 9604 9604 8.75 3.5 15 10.8322 12656.25 12656.25 9.375 3.75 16 11.09035 16384 16384 10 4 17 11.33285 20880.25 20880.25 10.625 4.25 18 11.56149 26244 26244 11.25 4.5 19 11.77776 32580.25 32580.25 11.875 4.75 20 11.98293 40000 40000 12.5 5 21 12.17809 48620.25 48620.25 13.125 5.25 22 12.36417 58564 58564 13.75 5.5 23 12.54198 69960.25 69960.25 14.375 5.75 24 12.71222 82944 82944 15 6 25 12.8755 97656.25 97656.25 15.625 6.25 26 13.03239 114244 114244 16.25 6.5 27 13.18335 132860.3 132860.3 16.875 6.75 28 13.32882 153664 153664 17.5 7 29 13.46918 176820.3 176820.3 18.125 7.25 30 13.60479 202500 202500 18.75 7.5 31 13.73595 230880.3 230880.3 19.375 7.75 32 13.86294 262144 262144 20 8 33 13.98603 296480.3 296480.3 20.625 8.25 34 14.10544 334084 334084 21.25 8.5
- 5. 35 14.22139 375156.3 375156.3 21.875 8.75 36 14.33408 419904 419904 22.5 9 37 14.44367 468540.3 468540.3 23.125 9.25 38 14.55034 521284 521284 23.75 9.5 39 14.65425 578360.3 578360.3 24.375 9.75 40 14.75552 640000 640000 25 10