Question

Finding frictional force given acceleration?

Answer 1

F=u*m*a

Answer 2

a = u m g
u = mg/a ?

Answer 3

I'm really confused as how to do this, could someone help me?

Answer 4

hello @wach i think you need to use both the forms of newtons second law equations i.e. one for translational motion and the other for rotational motion
i'll upload my drawing to show how it goes

Answer 5

Okay, that would be great.

Answer 6

okay ,
i think it goes like this
the plank is being pulled with a constant horizontal force F and the friction between the plank and the cylinders will make the cylinders move and the friction will be static friction as there is no slipping between the plank and the cylinders
next to determine the direction of friction , you need to see the relative motion of the cylinders with respect to the plank
so if friction were absent, then the cylinders would seem to move backwards with respect to a man standing on the plank so the relative motion is backwards so the friction will act in the forward direction
both the cylinders will apply the third law pairs of the friction that the plank offers them in the opposite direction
i'll now post the equations that i get from my analysation

Answer 7

Okay, that makes sense so far.

Answer 8

for the plank
F-2f=Ma
fr=I(alpha) ......(for the cylinder)
fr=I(alpha).........(for the other cylinder)
i think so if you agree we can proceed but i'll check it once more

Answer 9

the equations were not that correct i think so
i'll post a new set of equaitons

Answer 10

what do you think???

Answer 11

Okay. I see that you're using torques.

Answer 12

I understand approximately what you're doing

Answer 13

i'll be there in a few moments will you wait for me??
i'll help you then :)

Answer 14

Sure. :)

Answer 15

it'll take some time but i'll be back in 5 min.

Answer 16

sorry sorry sorry i'm late

Answer 17

what do you think , what will be the correct equations??

Answer 18

No problem, I'm not in a rush and am really thankful you are helping me :)

Answer 19

i've assumed the floor to be a frictionless surface as the question says that it is flat
and it's my pleasure if i'm able to help you

Answer 20

Well, like you said the motion would be impossible without the friction.. Since sum of the forces = ma, I guess if you define the right as the positive direction..
F+2f(-2f? I don't really get this) = ma

Answer 21

torque = I alpha (angular a)
alpha = a/r
so
torque = I a/r? for each cylinder?

Answer 22

yes yo are right the right is the +ve direction.
and as i said that the cylinders will apply the third law(newton's third law) pair on the plank of the friction offered by the plank
and for the torque equation you are totally right but i think it's not right
even though i'm trying to genetate new equations

Answer 23

the acceleration of the plank is given 0.73846(in the figure)
is it right

Answer 24

if we use the equation that i've given, the acceleration of the plank comes out to be 0.6

Answer 25

Yes. 0.73~ is the correct acceleration

Answer 26

if we use the newton's second law equation for the translational motion of the cylinder, we get f=ma1 (the acceleration of the cyl. is not equal to that of the plank so i've rtaken it to be a1)
and if we use the torque equation, then f=ma1/2
so it's not correct

Answer 27

If we take a = 6, how do we find frictional force?

Answer 28

did you understand why did i use the equation F-2f=Ma
if yess, then 6-2f=7 x 0.6
so 2f=1.8
so f=0.9
and f was the frictional force between the cyl and the plank

Answer 29

Yes, because you're finding the sum of the forces.

Answer 30

Thanks for your help!

Answer 31

you're welcome i'm trying to do it

Answer 32

thanks for the medal!!

Answer 33

i'm currently going offline but 'll surely help you i'll be back by 5:00 pm (IST)

Answer 34

sorry

Answer 35

The force is shared between accelerating the plank itself and having the static friction between the plank and the cylinders accelerate the cylinders, using torque to overcome the moments of inertia. A weightless lank would mean all the force goes to accelerating the cylinders. You might look at that case, as the force on the cylinders that provides the torque would be 3 N apiece. the other limit to explore is to have weightless cylinders and put all the 6N into accelerating the plank. Investigating these two limiting cases might prove useful.

Answer 36

@douglaswinslowcooper
you are cool man!
thanks for this post and thanks for correcting me
i tried it doing that way but didn't get the correct answer but i'll try it by using another methods and i want to know that how would you do it please let me know

Answer 37

If you have managed to find the acceleration of the plank, then the second question is easy: simply write Newton's second law for the plank:

F – f = Ma and solve for f.

Answer 38

Tough problem, for which I do not know the correct final answer.

Answer 39

you're right!

Answer 40

@douglaswinslowcooper
What do you mean when you say you "do not know the final answer"?

Final answer is f = F - Ma = 6 - 7 x 0.74 = 0.82 N

Answer 41

hey if the floor is frictionless , then the cylinders cannot do pure rolling
because if we want to make a solid cylinder roll on a firctionless horizontal plane , we need to apply a force at a distance of r/2 from the centre
i can explain you why if you are interested:)

Answer 42

Do you (want to) know how to derive acceleration from m, M, R and F ?