Calculating Acceleration and Tension in a Pulley System with Inclined Planes

[komarxian]

Homework Statement

Block A has a mass of 75 kg and is initially at rest on a frictionless inclined plane tilted at a 37 ° above the horizon. Block A is attached to a massless rope that is connected to the top of Block B by way of a massless frictionless pulley. Block B also has a mass of 75 kg and hangs vertically. Find the acceleration of the blocks. Also find the Tension, T, in the rope.

Homework Equations

The Attempt at a Solution

When I solved it I found that a = 4 m/s^2, but I think I got it wrong. I used a=(mg-Fparallel)/B, but I may/most likely screwed up here. Any help would be greatly appreciated ;D. I also think that the acceleration might be 0, because it says that it is initially at rest, but that answer also doesn't feel right.
Thank you!

 

[Dr. Courtney]

Draw a picture. Include free body diagrams.

Express Newton's second law for each object.

Solve for a.

 

[haruspex]

I used a=(mg-Fparallel)/B,

You appear to think that adequately explains to others what you did. I assure you it doesn't. E.g. what do you mean by F_parallel? How did you calculate it? What does B represent in the equation - the mass of block B? What about m?
Please post all your steps and define your variables.

 

[komarxian]

Okay, I tried this.

 

[komarxian]

Okay, I tried this. View attachment 94072

Mass A is M and mass B is m

 

[haruspex]

Mass A is M and mass B is m

That looks fine. You are also asked for the tension.

 

[komarxian]

That looks fine. You are also asked for the tension.

So do you know if my answer is correct? Thank you for the help!

 

[haruspex]

So do you know if my answer is correct? Thank you for the help!

Yes, I agree with your answer.

 

[komarxian]

Okay thanks! Will start on the tension now.

 

[komarxian]

Okay, now that I have the acceleration, I was wondering If what I did to get tension was correct? My teacher recomended using the equation that I used in the second image.

 

[WrongMan]

Im sorry but I am pretty sure a is -1.99 ms^-2. i'l put some pics up in a sec

 

[haruspex]

Im sorry but I am pretty sure a is -1.99 ms^-2. i'l put some pics up in a sec

You're right, I didn't notice komarxian had sin and cos mixed up.

 

[komarxian]

Oh darn, I'll take a look at that. @wrongedMan some pics would help a ton! Thank you for the help @haruspex as well

 

[WrongMan]

well without wanting to give it all away :p ... start with that (img), you should try and solve it without inputing any values just find an expression for a then put values in, repeat for T (bit more tricky for T). I'll still be around for a couple of hours to help you out if you get stuck :)edit1: BTW, important bit: sin(37) is NOT 4/5 maybe that was your mistake
edit2: yep that was your mistake

edit 3: ah @haruspex i see that's what you meant, i thought you meant he actually wrote cos instead of sin not that he got the values mixed up

 

[komarxian]

! Thank you! I misread my formula sheet (again) omo.