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Background: My professor for system dynamics at my university gave us an engineering dynamics concept quiz. A particular question I am interested in presented two figures I have re-drawn below. The pulleys are stated to have no mass or friction. No gravitational accelerations, or mass was given for the left figure.

My professor said (without proof) that the figure with the idealized force (right figure) will accelerate faster. I would like to know why.

I am posting here because my professor could not understand where my confusion was and thus could not answer my question to my satisfaction.

I thought that regardless of the source of force, the accelerations should be the same. How is this possible? Left figure has a mass weighting 50N. Right figure is an idealized force of the same magnitude of 50N

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  • $\begingroup$ First thing: this is a physics question (physics.SE), not engineering. Second, you need to provide some background. Is this a course where you are taking variation of gravitational force with altitude in question? Is your professor a qualified person or just someone brought in for night school? $\endgroup$
    – Carl Witthoft
    Commented Jan 16, 2019 at 20:11
  • $\begingroup$ I'm voting to close this question as off-topic because this belongs on physics.SE $\endgroup$
    – Carl Witthoft
    Commented Jan 16, 2019 at 20:12
  • $\begingroup$ @CarlWitthoft this question arose from an engineering course during an engineering dynamics review. I will provide background information. $\endgroup$
    – Robert Leonillo
    Commented Jan 16, 2019 at 20:29
  • $\begingroup$ @CarlWitthoft there was nothing stated about gravity at all. It was only stated that the pullies are massless and frictionless. Along with the figure shown. $\endgroup$
    – Robert Leonillo
    Commented Jan 16, 2019 at 20:45
  • $\begingroup$ Hint - solve for the tension in the line as a function of gravitational acceleration. $\endgroup$
    – Phil Sweet
    Commented Jan 17, 2019 at 1:42

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The accelerations will not be same. What you do is you reduce the masses as rotational inertia then apply the force as moment.

Since the fïrst drawing has more rotational inerta it will accelerate slower.

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  • $\begingroup$ I'm skeptical - can you justify a mass-based force being different from a mythical "pure force" regardless of the vector to the pulley? $\endgroup$
    – Carl Witthoft
    Commented Jan 17, 2019 at 20:07
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    $\begingroup$ @CarlWitthoft yes, a ideal force does not affect the mass of the system it is coming from outside the system, Moment of inertia determines how fast a rotating system accelerates, more mass means the inertia is is larger thus it takes more time for it to accelerate, all other things being same. So since the only difference in $T/I = \alpha $ is the I then it has a direct affect on acceleration. $\endgroup$
    – joojaa
    Commented Jan 17, 2019 at 20:18

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