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December 18, 2014

December 18, 2014

Posted by **Andy** on Monday, December 9, 2013 at 3:08am.

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 5:56amHey, look there is a limit to the number of times that I am going to respond to the same 8.01 question.

If you are taking 8.01 you are capable of reading, at least we could in 1955. Scroll and stop spamming.

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 6:13amexcept that no one is helping on the last two parts.

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 6:34amLook at what Mum posted below my first response:

Classical Mechanics Physics - Urgent help please - Mum, Monday, December 9, 2013 at 2:52am

I don't want you to cheat so I am giving some hints - not full solution. As for part b - Damon gave you everything in his geometrical approach. Look at the equations for forces - you need x and y (Damon calls it x and z) component of acceleration a of the center of mass. You have the equations for them given by Damon in his geometrical appoach. In these equations you have the angle - you know it, then you have the angular velocity - you just calculated it, at last you have there angular acceleratin - get that either from the torque equation (taking pivot point as origin gets rid of the contact force). Then you can solve. Or if you have a nice equation for omega from part a), take a derivative to get the acceleration.

As for part c): F_x=0 therefore a_x=0 - play with the equations for a_x and a_y and omega from part a).

Sorry for my grammar :-).

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 6:47amNote, when you use the pivot point at the floor for torques be sure to use (1/3)m L^2 instead of (1/12)m L^2 as I did for the origin at the CG.

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 6:49ambut how do you find alpha?

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 6:56amalpha is d^2T/dt^2

quoting Mum:

".....Then you can solve. Or if you have a nice equation for omega from part a), take a derivative to get the acceleration. ....."

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 7:02amthis is what i have.

dT/dt=sqrt(3g*(1-cos(30))/L)

dt^2/dt=sqrt(3)*g*sin(30)/2L*sqrt(10*(1-cos(30))/L)

however i do not know how to continue.

I know you gave some equations but they are not yielding answers, if you could pls help out?

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 7:25amF = m A

Fz(.075)sin T -Fx(.075)cos T = 1.88*10^-4 alpha

.981 - Fz = .1 az

Fx = .1 ax

ax =

-.075 sin T (dT/dt)^2 + .075 cos T alpha

az =

-.075 cosT (dT/dt)^2 -.075 sin T alpha

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 7:36amhow did you get -0.075?

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 7:50amI am taking moments about the cg.

The length of the rod is .15

so half of it is .075

==========================

Harder way

---------------------------

Force up from floor = Fz

Force down from gravity = m g = .1*9.81 = .981 Newtons

so

.981 - Fz = .1 az

where az is acceleration of CG down

Force horizontal out from wall = Fx

acceleration of cg out from wall = ax

so

Fx = .1 ax

Torques about cg = I alpha

Fz(.075)sin T -Fx(.075)cos T = 1.88*10^-4 alpha

Now geometry, relate angular acceleration to linear acceleration components at cg

x = .075 sin T

dx/dt = .075 cos T (dT/dt)

ax = d^2x/dt^2 =-.075 sin T (dT/dt)^2 + .075 cos T alpha

{{note - because alpha = ang accel = d^2T/dt^2}}

y = .075 cos T

dy/dt = -.075 sin T dT/dt

az = d^2y/dt^2 = -.075 cosT (dT/dt)^2 -.075 sin T alpha

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 7:58amshould these forces end up as a negative value?

- physics(URGENT!!!!!) -
**Anonymous**, Monday, December 9, 2013 at 8:39amand it also seems your equations are wrong

- physics(URGENT!!!!!) -
**Anoninho**, Monday, December 9, 2013 at 10:58amSorry Damon,

I'm trying to make by myself, and your notes are beeing really helpful, but I could't understand 1 thing, at here:

ax = d^2x/dt^2 =-.075 sin T (dT/dt)^2 + .075 cos T alpha

I see that a_x it's the second derivative of x = (l/2)*sin(theta)... But really, where did that (l/2*cos(theta)*alpha) came from, I just can't see it... Could you tell me this? I would appreciate, my math isn't the best. \:

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 11:31amdx/dt = .075 cos T (dT/dt)

is:

[ .075 cos T ] {dT/dt)

BOTH of those are changing with time

form is

f(t) = a(t) b(t)

so

f'(t) = a db/dt + b da/dt

so

d/dt(dx/dt) = [ .075 cos T ]d^2T/dt^2 +{dT/dt) [- .075 sin T ] (dT/dt)

or

ax = what is said

- physics(URGENT!!!!!) -
**MegaM**, Monday, December 9, 2013 at 12:40pmWith Damon eq. we know that:

ax = d^2x/dt^2 =-L/2 sin T (dT/dt)^2 + L/2 cos T alpha

And I suppose that :

(dT/dt)^2 is omega^2

and

alpha=g*cos T*3/(2*L)

that we get from m*g*L/2*cos T=1/3*m*L^2*alpha

But putting the numbers (with a correct omega) the answer is wrong, please, could anybody tell me where is the mistake?

- physics(URGENT!!!!!) -
**Anoninho**, Monday, December 9, 2013 at 1:01pmOh, I see...

So, you must derive function "sin/cos" and theta, as both change with time.

Then (without l/2, for simplicity)

x = sin(theta);

dx/dt = cos(theta)*d(theta)/dt;

d^2x/dt^2 = a*db/dt + b*da/dt;

a*db/dt = cos(theta)*d^2(theta)/dt

b*da/dt = (d(theta)/dt)^2*-sin(theta)

As d(theta)/dt = wf and d^2(theta)/dt^2 = alpha

ax = -sin(theta)*w^2 + cos(theta)*alpha

Right? Then just put l/2 on them...

So, well, I think i got it then:

y = cos(theta)

vy = -sin(theta)*d(theta)/dt

ay=-sin(theta)*alpha-cos(theta)*w^2

Thank you so much Damon. :D

- physics(URGENT!!!!!) -
**Anoninho**, Monday, December 9, 2013 at 1:23pm@MegaM

Maybe I'm wrong, but I think that your alpha should be:

3*g*SIN(THETA)/(2*L)

Not cos(theta)...

Try to check it out, maybe I'm wrong. (:

- physics(URGENT!!!!!) -
**shashanoid**, Monday, December 9, 2013 at 1:37pmPlease tell f_x and f_y for m=150g and l=20 and theta=30 please help !!

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 2:02pmalpha is my code for d^2T/dt^2, angular acceleration and dT/dt is omega, angular velocity

- physics(URGENT!!!!!) -
**shashanoid**, Monday, December 9, 2013 at 2:23pmhow to calculate alpha ??

- physics(URGENT!!!!!) -
**Damon**, Monday, December 9, 2013 at 2:51pmSee above for calculating alpha = d^2T/dt^2

I assume that if you folks are taking 8.01 that you are MIT freshmen. Come on now and read carefully and stop asking the same question over and over from someone who took the course in 1955.

- physics(URGENT!!!!!) -
**MegaM**, Monday, December 9, 2013 at 4:25pm@Anoninho

Yes! It was SIN T!!!

Thank you very much!!

- physics -
**sid**, Tuesday, December 10, 2013 at 2:55amA stick of length l = 60.0 cm rests against a wall. The coefficient of static friction between stick and the wall and between the stick and the floor are equal. The stick will slip off the wall if placed at an angle greater than θ = 49.0 degrees. What is the coefficient of static friction, μs, between the stick and the wall and floor?

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