Solving a Physics Problem: FBD and Newton's 2nd Law

[c0der]

Homework Statement

Attached

Homework Equations

Attached

The Attempt at a Solution

2ac + 3 = 0 => ac = 1.5m/s^2 upwards

For FBD of C, Newton's 2nd law

2T - 200g = 200*1.5 => T = 1131N

For FBD of the beam,

Take moments about A, and assume beam is rigid (CCW positive):

2.5T - 3T - 300*6*9.81*3 + Rb*6 = 0

RB = 8.92kN upwards

Ra + Rb + T - T - 300*9.81*6 = 0 => RA = 8.73kN

Is this correct? I don't see why the solution is posting the velocity when asking for a reaction

 

[BvU]

Maybe your copy should have been two-sided and the solutions manual continues on the next page?

I draw your attention to the guidelines

4.Do not simply post images of the problem statement or your work.
While posting images may be convenient for you, it's actually one of the most effective ways of getting your request for help ignored. Images are often too big, too small, rotated, upside down, out of focus, dimly lit, or of otherwise poor quality, and your handwriting probably isn't as easy to read as you think it is. Images are a hindrance to the helpers as portions of the problem statement or your work can't easily be quoted. Using images also doesn't qualify as filling out the homework template, so your post may be deleted.

However, as I appreciate you at least show some of your work, I will go through part 3.

2ac + 3 = 0 => ac = 1.5m/s^2 upwards

Looks identical to what's in the middle picture, so I suppose that IS your work... Anyway, it's OK. Even though I can't find what c is. a is the acceleration, I guess, but even that isn't mentioned under 1.) problem statement, all variables and given/known data .

2T - 200g = 200*1.5 => T = 1131N

Bravo.

At his point I am missing something. I see 2 T from the pulley in the crate FBD, but I see only one T pulling down on the beam. My mistake or yours ?

And there is something extra I can't explain: who is trying to pull the motor up with force T ? A little bird ? I sure hope the motor is well bolted on the beam, then!

 

[BvU]

Just for the fun of it, and to hone your physics intuition: If the crate is off-center to the left, would you expect Ra < Rb ?

 

[BvU]

And another one: the crate requires a bit more than 2 kN. The beam requires ... If you find Ra+Rb > 17 kN, do you hear alarm bells ring ?

 

[c0der]

It's not the motor that's being pulled up, if you take a free body of the motor, a normal force is exerted by the beam onto it, plus a tension force is pulling it down. So T is the normal force, otherwise it would fall through the beam. I accidentally used 300kg/m as the self-weight of the beam (it's actually 30kg/m in the problem), you have to include this, which will also contribute to the reaction, it's not only the crate.

Yes, Ra should be greater than Rb by intuition, trying to figure out why this is not the case.

 

[BvU]

if you take a free body of the motor, a normal force is exerted by the beam onto it

Agree, but we were drawing a free body diagram of the beam!

Physics intuition again: if you were standing on the beam pulling in Keira Knightley using a rope, would the force ON the beam be (you and her)*g up or down ?

 

[c0der]

Yes, you are correct, my mistake, don't know what I was thinking. By Newton's 3rd law, the normal force on the beam should be pointing down.

 

[BvU]

I knew Keira might inspire some good physics!

 

[c0der]

haha yes, couldn't find an answer to check against though. For people who have done this problem, I get Ra = 2108.15N and Rb = 1919.65N, hope you get the same answer