Timeline for What is physically changing from velocity or acceleration to force and their vector components?
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9 events
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| Apr 4, 2021 at 19:53 | history | edited | kbakshi314 | CC BY-SA 4.0 |
edited text for better explanation
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| Apr 4, 2021 at 19:49 | comment | added | kbakshi314 | The answer above alludes to the proof by contradiction by indicating that the shifting of the $\cos\theta$ factor is what enables consistency in the mathematics of the related principles of geometry $-$ Newton's laws $-$ conservation of energy. In the comments above, we observe that an erroneous geometric, and thus kinematic, relationship between the velocities of the masses and rope lead to a contradiction to the Newton's second law of motion. The only case in which this contradiction is resolved is in the case that $v':=u=\frac{v}{\cos\theta}$. | |
| Apr 4, 2021 at 19:43 | comment | added | kbakshi314 | @UV0 the idea in the explanation above is proof by contradiction. If we assume, for instance, the wrong kinematic $v'\cos\theta=v$ (instead of the accurate kinematic) and apply the law of conservation of mechanical energy to the point mass system and the $\text{pint mass}\cup\text{rope and pulleys}$ respectively, we obtain $F'=mg$ and $2Fv-mgv'=2Fv-mgv\cos\theta=0$ so that $F=\frac{mg}{2}\cos\theta$ which implies that $F'=2F\cdot\frac{1}{\cos\theta}$. The final expression obtained contradicts Newton's second law $F'=2F\cos\theta$. Therefore the assumption $v'\cos\theta=v$ is incorrect. (2/2) | |
| Apr 4, 2021 at 19:36 | history | edited | kbakshi314 | CC BY-SA 4.0 |
edited text for better explanation
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| Apr 4, 2021 at 19:31 | history | edited | kbakshi314 | CC BY-SA 4.0 |
edited text for better explanation
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| Apr 4, 2021 at 19:19 | history | edited | kbakshi314 | CC BY-SA 4.0 |
edited text for better explanation
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| Apr 4, 2021 at 19:12 | comment | added | kbakshi314 | @UV0 let us assume that in both situations the mass moves at constant velocity. Denoting $v':=u$ for clarity, the relationships $v'=u=\frac{v}{cos\theta}$ is derived by geometry (and then kinematics) and $F'=2F\cos\theta$ derived from Newton's laws are true in both situations depicted in the pictures in the OP. We observe that the factor $\cos\theta$ has flipped sides or gets applied to the tension in the rope in one equation and the velocity of the mass in the other. (1/2) | |
| Apr 3, 2021 at 14:16 | comment | added | UV0 | I still dont get it, | |
| Mar 29, 2021 at 14:39 | history | answered | kbakshi314 | CC BY-SA 4.0 |