(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In figure P4.52 (below), the coefficient of kinetic friction between two blocks shown is 0.30. The surface of the table and the pulleys are frictionless. (a) Draw a free-body diagram for each block. (b) Determine the acceleration of each block. (c) Find the tension in the strings.

2. Relevant equations

Since all accelerations are equal:

-a_{2}= a_{3}= -a_{10}

Also, a = F/m

And for gravity: F_{g}=m (in kg)*9.8

3. The attempt at a solution

For the force diagram I know that the 2kg block will have T_{1}pulling it to the left and friction pulling it to the right. The 3kg block will have T_{2}pulling it to the right and friction and T_{1}pulling to the left. And the 10kg ball, sphere, whatever, has T_{2}pulling upward and gravity pulling downward.

F_{k}is 5.88N since F_{n}is 19.6N (0.3*19.6).

And F_{g}is 98N.

- (5.88N - TGot rid of my fractions, LCD of 30..._{1}) / 2kg = (T_{2}- T_{1}- 5.88N) / 3kg = - (T_{2}- 98N) / 10kg

15TUsed the first two equations to solve for T_{1}- 88.2N = 10T_{2}- 10T_{1}-58.8N = 294N - 3T_{2}_{2}

2.5TPlugged in to the last 2 equations and ended up getting..._{1}- 2.94N = T_{2}

25T_{1}- 29.4N - 10T_{1}- 58.8N = 294N - 7.5T_{1}+ 88.2N

T_{1}= 20.906N

The correct answer for T_{1}is 17N. I've looked over my work and couldn't find a mistake in my math, though I'm sure there is. I need help figuring out where I messed up.

I hope this isn't just some dumb mistake because I've spent so long on this single problem.

Thanks in advance.

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# Finding Acceleration and Tension, With Friction

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