53 Replies
hey! Can you share an attempt?
Yes I will write it here
Here's what I did
Energy conservation from A to B to get velocity of sphere just before it lands on the plank
FBD of sphere and plank
Equations of motion on sphere and plank
We got time t where it starts pure rolling
distance travelled by plank in time t is now known
and thus work = F.s
most probably I wont get a reply but thats okay :)
bruh for this I will learn this concept and respond to you. Thanks hah for the effort.
What is the q though? work done by frcitonal force btw ground and plank
uff rotational xD
That would be OP sir
Yes rotational + nlm
I am not able to find a flaw in my method, but my answer is not matching
Could you share your equations here?
sure
energy conservation --> mgh = 1/2 m v^2 ( no rotational KE as no frictional force on the incline)
on sphere N1= mg upwards and on plan 2Mg = N2
On sphere F1 in left direction that is mu * mg
and on plank F1 in right direction mu * mg and F2 in left direction mu/4 * mg
and from eqns of motion we can get time t
Gimme a few minutes so I can get near a pen and some paper
phew thanks dude. the one thing i dread more than oc is rbd 😛
Sure man
RBD is the final boss for me
So far so good
What have you done after that?
You'll have torque equations from friction
yes
I got alpha from that
and w
but my answer is not matching
What were the torque equations you used?
wait i never really used it
alpha = mu mg r
go on
We have force and torque equations
and we have w as well
How did you find omega?
wait i messed up here
torque = rF= I alpha from center of sphere
from here we get alpha
and from eqn of motion we get omega at time t
is this correct?
Yep
Good
and now moving onto plank we can find its velocity at t time
and then we apply condn for pure rolling that is velocity at pt of contact = 0
so
velocity of sphere + omega * r = velocity of plank
omega is inside the plane
so w cross R and sphere velocity in same direction
and plank velocity in opposite direction
right?
This is the constraint to find v_final and then time
Did you use it to find t?
yes
is this not correct?
It should work but there's calculation too
if your calculation and equations are right then it'll work
yes they are right ig
Ok let's try this
I'll provide a solution tomorrow (it's late today), try matching yours with that
if it matches then it should work
Would that be ok?
Yeah sure
Thanks man
Great
@Comrade Rock Astley
Hi
I'm back now
So we have vcm - Rw = vp
where v cm is the velocity of centre of mass of the sphere
vp is the velocity of plank
Comrade Rock Astley
This is the constraint for pure rolling
and
Comrade Rock Astley
I guess that's the one thing you missed
where friction between the plank and ground uses a mass of 2m not m
And we also have v=at
so
we have a
we just need to figure out t
As you said you can use the torque equation to figure out alpha, and omega = alpha times t
Well...I'll leave the rest to you since the equations are already there
You just need to figure out how to manipulate them
Lmk if you've gotten a result or if you're stuck somewhere
I will write down my solution and you tell me where am i going wrong
is that good
sure go ahead
man i will surely send you my soln today
@Comrade Rock Astley
@Xyphoes
Sorry, was sick
Comrade Rock Astley
Comrade Rock Astley
So your time calculation varies
but everything upto that is fine
oh gws
yeah but ans at the back isnt matching
Did you try it with this equation?
for plank initial velocity is 0
and net accn on plank is mug/2
yes
But the time is v_0/4 mu g
isnt it v0/3 mu g
omega times r is vcm - vplank, and from there you should get this
Then v0/4 mu g
I think you missed the mu g t term here
omega is inside
so at ICOR w cross R is in +ve x
Vplank and V sphere in same direction
so wr= v pl + v sphere
omega is inside the plane
brb
It’s just that v sphere is v0 - mu g t not v0
In the final step in the first page
got my mistake
thanks man
+solved
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