@haruspex Solved it. If ##\mu=1## the additional torque needed is
$$\vec{\tau^\text{ext}}=\frac{1}{\sqrt{2}}mgR$$.
In general
$$\vec{\tau^\text{ext}}=\frac{\mu}{1+\mu^2}mgR\sqrt{2}$$
... which respects the particular situation of ##\mu=1##.
I got these relations from the translational equilibrium:
$$\frac{N_1}{N_2}=\frac{1+\mu}{1-\mu}$$
$$(1+\mu)N_1+(1-\mu)N_2=mg\sqrt{2}$$
Solving for ##N_1,N_2##:
$$N_1=\frac{1+\mu}{2+\mu^2}mg\sqrt{2}$$
$$N_2=\frac{1-\mu}{2+\mu^2}mg\sqrt{2}$$
Torque from frictions:
$$\vec{\tau_{f_1}}=-R(\mu...
It actually is!
This is their drawing, but they did not specify in the problem.
By the way, I have got ##\vec{\tau^\text{ext}}=\frac{2\mu^2}{2+\mu^2}mgR\sqrt{2}\hat{k}##
Hope it's good!
A sincere thanks for being along in my Newtonian physics journey @haruspex! You are an awesome man. Got...
I am confused because according to my solution the disk is already rotating at constant angular velocity.
I have written the translational equilibrium on the horizontal and vertical component:
##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
How I like to solve this kind of problems:
Suppose we have two particles colliding perfectly elastic, knowing their initial speeds and the fact that the mass of the second particles is much greater than the mass of the first particle.
$$m_1,~\vec{v_{1,i}}$$
$$m_2\gg m_1,~\vec{v_{2,i}}$$
Then...
Exactly, so after all the formula ##P_{ave}=\vec{F}\cdot\vec{V_{ave}}## only works for constant direction. This is what intrigued me, because they did not specify it. Thanks.
(This is somewhat explainable because at the level of the book students are not supposed to know calculus so nor how to...
I did not omit the delta. This is what says in my book. However I agree with the delta.
As of what I know, we can only integrate if we are working with infinitesimal quantities, whereas ##\Delta{\vec{r}}## and ##\Delta{t}## are finite quantities as described in my book.
When the potential is increasing (positive derivative) the force is negative (points to the left) and when the potential is decereasing (negative derivative) the force is positive (points to the right). Related to that, one analogy that we can make is that the graph metaphorically represents the...
Thanks!
Just a quick off-topic question pleaase
In my physics book it states that "Power is the ratio between work ##W## done by a force during a time interval ##\Delta{t}## and the time interval. Hence ##P_{ave}=\frac{W}{\Delta{t}}=\vec{F}\cdot\vec{v_{ave}}##."
My attempt to prove...
It is my second "energy state diagram problem" and I would want to know if I am thinking correctly.
First I have done some function analysis to get a glimpse of the plot:
- no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0##
- y interception: ##U(0)=-U_0##
- even...
You are right, I have corrected it.
I have done these late night and taking into account that I haven't slept I think I am so mentally disabled right now making these errors. Excuse my inattention and impatience.