- #1
ladymiresa
- 4
- 0
Homework Statement
Two masses are connected by massless and frictionless pulleys and string. The coefficients of friction are µs = 0.35 and µk = 0.25 between mass m1 and the table. The masses are m1 = 8.0 kg and m2 = 8.0 kg.
Find the acceleration of each mass and the tension in the string. (Note: Because of the pulley, if m1 moves a distance L, then m2 moves half that amount, a distance L/2. Think about how this affects the relative acceleration of the two blocks.)
Homework Equations
a1=-1/2a2
fk=ukn=-ukm1g
T-ukm1g=m1a1
T-m2g=m2a2
The Attempt at a Solution
I think the acceleration of block 2 will be negative since it is falling and block 1 will have a positive acceleration since it is moving towards the right.
Ok, I hope I am right in assuming that the accelerations are related as I've written above.
I substituted the a2 into into the first T equation to get T-ukg=-(1/2)m1a2.To cancel the T out, I subtracted the equations to get: (m2-ukm1)g=-1/2 (m2+m1)a2
Then punching in my variables I got a2=-7.35 m/s^2 which I was pleased to see is negative. But then if I use my relationship as a1=-1/2 a2 then I get a1=3.7m/s^2, which is at least positive. But I don't think it makes sense that the acceleration of block 2 would be faster than block 1?
I can't decide where I went wrong? I think it might be my relationship between the two accelerations, but today I asked my professor and she said it looked OK. So now I think I messed something up with the friction... I'm using kinetic but the problem also gave static... do I need to use both? Or does fk not equal ukmg?
I'd appreciate any suggestions. Thanks.
Last edited: