I would like to thank you all for your generous and patient assistance, and also apologise for the howler above! Anyway, here are the correct equations:
Horizontal Forces on wedge: ##\frac{1}{2}R = \frac{\sqrt{3}}{2}Ma##
Vertical Forces on wedge: ##Mg + R_{m} - \frac{\sqrt{3}}{2}R =...
Talk about embarrassing! Many thanks indeed TSny for revealing my stupid error, which most likely explains the larger coefficient of M mentioned earlier. I'll update the equations and post an update this evening.
Yes, I think the consensus in the thread is that the particle can only move vertically. We just need to show that it's acceleration is:
(M + m)g / 4M + m
I.e. the actual value of the acceleration doesn't matter.
No problem at all! The subject of the question is Introductory Mechanics, specifically using forces represented as vectors to solve for an acceleration.
Hi Rafa_El, thanks for joining the thread. I'm not sure that I quite understand your question - please could you clarify the "it" you refer to? The question text in the original post is copied straight from the book and fully defines the problem. It needs solving using Newton's laws and...
The best I've been able to come up with for now is the following updated equations of motion (where ##R_{m}## is the normal reaction of particle on wedge):
Horizontal Forces on wedge: ##\frac{1}{2}R = \frac{3}{\sqrt{2}}Ma##
Vertical Forces on wedge: ##Mg + R_{m} - \frac{3}{\sqrt{2}}R =...
I haven't solved it yet, but your your reasoning has generated new impetus and I've now gotten closer to the desired result. I'm going to have another try at getting the actual result, but I might have to resume tomorrow evening as I need to be up early tomorrow.
Thank you very much indeed for your response. The equation is definitely printed in the book as being:
(M+m)g / (4M + m),
I.e. M only is multiplied by four in the denominator. The system description preceding the equation is faithfully copied in this post. The book is "Introducing...
Thank you very much for your reply. As all the earlier exercises in the textbook indicated frictionless surfaces, I assume the same applies here and that there's no friction between the wedge and the top particle. Honestly, though, I just don't understand how the system produces an...
Thank you very much for your response and my apologies for not adhering to the template. Based on the problem description (which was not accompanied by an image) I came up with the free body diagram attached.
Does this look correct? As you can probably see, the main problem is that I'm...
I would be very grateful for help with deriving the following equation...
"A smooth fixed plane is inclined at 30 degrees to the horizontal. A wedge of mass M and angle 30 degrees is held on the surface so that its upper face is horizontal, and a particle of mass m rests on this face. The...