Frictional and Tensional Forces on an Inclined Plane

[parabolic]

Let me start by stating that this is not a homework question. If I just wanted the answer, it is in the back of my book. What I do need is some understanding of how the answer was reached.

Problem:
Two blocks attached by a string slide down a 10degree incline. Block 1 has a mass m₁ = 0.80 kg and block 2 has mass m₂ = 0.25 kg. In addition, the kinetic coefficients of friction between the blocks and the incline are 0.30 for block 1 and 0.20 for block 2. Find (a) the magnitude of the acceleration of the blocks, and (b) the tension in the string.

Answers in the back of the book:
(a) 0.96 m/s²
(b) 0.18 N

http://www.mravery.com/images/Physics.jpg


My attempt at a solution:

After drawing free body diagrams for both blocks I have come up with the following:

Block one calculations
Weight force in x direction (W_x)= sin(10) x (.8) x 9.81

F_nety = ma_y
(Normal Force) - cos(10)x (.8) x 9.81 = 0
N = cos(10)x (.8) x 9.81

Friction = .3 x (cos(10)x (.8) x 9.81)

F_netx = W_x + Tension - FrictionAfter I calculate these, I calculate the same for block 2 ( I will spare you the redundant reading), and obviously the tensional force is opposite. Once i do that I get stuck.

I have been racking my brain for a day and a half. Any help would be greatly appreciated!

Thanks

 

[PhanthomJay]

You have it correct. Now just set Fnetx on block 1 = m1a, and fnetx on block 2 =m2a, and solve for T and a , using the 2 equations to solve for the 2 unknowns.

 

[parabolic]

ok so when i do that I get
(a) -.96 m/s²

why do i get a negative? Does the word "magnitude" mean I disregard the direction (sign)?

for (b) i get the correct answer using the negative

 

[PhanthomJay]

Oh, I get the same result, but we shouldn't be getting a negative acceelration. Something has gone afoul in this problem statement or book answer. I believe that neither block ever moves, and that there is no tension in the string, but I have to leave now, and my mind is fuzzy, so let's ponder. Or maybe one of the night owls will help out.

 

[parabolic]

I also thought that the frictional force was greater than the Weight_x on both blocks. Meaning that they wouldn't move. Weird. I have decided to burn my physics book and change my career path from Mechanical Engineering to Arsonist. Thanks for your help.

 

[PhanthomJay]

I also thought that the frictional force was greater than the Weight_x on both blocks. Meaning that they wouldn't move. Weird. I have decided to burn my physics book and change my career path from Mechanical Engineering to Arsonist. Thanks for your help.

Good morning. My bad. The problem clearly states that
(1) the blocks are sliding down the plane, and
(2) it asks for the magnitude of the acceleration.
If the blocks were just placed on the plane, then released, nothing would happen; they'd remain at rest and there would be no tension in the string. But in this problem, they have been set in motion down the plane by some applied force, then that force is released. The blocks then slow down , moving down the plane, and ultimately come to rest. The acceleration is .96 UP the plane (hence the negative sign, the blocks are decelerating), but its magnitude is .96. The tension value is also correct. If the tension value came out negative, then each block would accelerate , or remain at rest, independent of each other (you can't have negative tension). Such is not the case here. Don't change your career yet!