Recent content by TSny

Yes. I see your point. For this problem, a sketch shows that the rod's diameter would have to be very small to cause a problem. Here is a diagram that I tried to draw to scale. Each small square has a side of 1 cm. The object is given to be only 0.18 cm tall. But I drew it 1 cm tall to...

Yes. I think either interpretation would yield the same answer. The top figure has the full hemispheres. The bottom figure is a cylinder cut out of the top figure. The height of the object is small compared to the radii of the hemispheres, and we assume paraxial rays. So, the rays...

Interesting. I did not interpret the problem this way. But I see now that the problem does state "hemispherical." @rogue_system : Make the sign correction mentioned above in post #8 and see if you get the expected answer.

Review the sign conventions associated with the equation ##\frac{n_1}{s} + \frac {n_2} {s'} = \frac{n_2 - n_1}{R}##. Yes, that's right. Check that this is correct for both ##S' < L## and ##S' > L##. You'll need to know the sign conventions.

Here, you are dealing only with the "electrical" free energy ##F_{\rm elec}## associated with the work done by the battery. In the term ##T \frac{\partial F_{\rm elec}}{\partial T}##, it’s important to know which variables are to be held constant in the partial derivative. According to a couple...

See post #5. When an object is in contact with a flat surface, the friction force that the surface exerts on the object is parallel to the surface. The normal force that the surface exerts on the object is perpendicular to the surface. Apply this to the person in your problem. Construct a...

Good point.

Refer to: Note that ##\phi## is measured from the ##z##-axis. So, all elements of the ring with positive ##z## coordinate should be depicted with positive charge. Elements with negative ##z## coordinate should be depicted with negative charge.

Yes, good. That's what I get. If @akapm90 is OK with this argument, then they can proceed onward and ignore post #5. Very good point. I agree that the question must be asking for the initial acceleration of M.

@Steve4Physics: Your post made me think of an easier way to see how ##a_y## is related to ##A_x## and ##A_y##. Imagine that the block is lifted vertically upward so that it only has a vertical acceleration ##A_y##. Consider how ##a_y## is related to ##A_y## when the string is still...

I'm not seeing this. If ##\alpha = 0##, so the upper section of the string remains horizontal, then ##a_y = -A_x##. But this is not true for general ##\alpha##.

Even though it starts at rest, we can still consider the configuration after the block has moved some distance. Of course, the block might move down the slope instead of up the slope, but the sign of ##S## handles both directions. (The block might even remain at rest for certain values of the...

The pulley moves with the block ##M##. If the block moves a distance ##S## up the slope, then the pulley moves parallel to the slope the same distance ##S##. Let ##l_{1,0}## represent the initial length of the portion of the string from the pulley ##P## to the fixed point ##A##. Let...

OK. I see now that you already brought up this ambiguity in your first post. Thanks.

I'm wondering if the question is asking for the acceleration ##a## and tension ##T## as functions of time, or if it is asking only for the values of ##a## and ##T## immediately after the system is released (while the upper portion of the string is horizontal)?