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HW Problem

1.) What is the acceleration of the hanging mass? (Indicate the direction with the sign of your answer.)

2.) Determine the tension in the cord. (Indicate the direction with the sign of your answer.)

Seems like the simplest problem but I cant seem to get the right answer. Here's my approach:


$n $ = normal force on $m_1 $

$f_s $ = friction force on $m_1 $

$T $ = tension in the cord

$\mu_k $ = coefficient of kinetic friction


Problem 1.)

$(1)\quad n = m_1 g = (40kg)(9.8m/s^2)$

$(2)\quad n = 392 N$

$(3)\quad f_s = \mu_k n = (0.22)(392N)$

$(4)\quad f_s = 86.24N$

$(5)\quad T = m_2 g - f_s$

$(6)\quad T = (13.4kg)(9.8m/s^2) - 86.24N$

$(7)\quad T = 131.32N - 86.24N = 45.08N$

$(8)\quad m_2 a_{m_2} = m_2 g - T$

$(9)\quad (13.4kg) a_{m_2} = 131.32N - 45.08N$

$(10)\quad (13.4kg) a_{m_2} = 86.24N$

$(11)\quad a_{m_2} = 86.24N/13.4kg = 6.44m/s^2$

$6.44m/s^2$ is wrong, though. Could someone point me in the right direction? Any feedback is welcome, and thanks in advance

SOLUTION:

Equation (5) should be $T-f_s = m_1 a$

$T-f_s = m_1 a$

becomes (after rearranging)

$T-(40kg)a = 86.24N$

and

$m_2 a = m_2 g - T$

becomes (after rearranging)

$T + (13.4kg)a = 131.32N$.

Then we throw those two equations into a matrix:

\begin{bmatrix} 1 & -40 & 86.24 \\ 1 & 13.4 & 131.32 \end{bmatrix}

Solve, and our answers will be:

$a = 0.84m/s^2$

$T = 120.01N$

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closed as off-topic by jinawee, Brandon Enright, Kyle Kanos, user10851, DavePhD Jun 8 '14 at 22:24

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Ok the 5 equation is completely wrong. It should be T-fs=m1a. Also acceleration of m1 = acceleration of m2 since rope is inextesible

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  • $\begingroup$ @user49147 You can see that friction is not acting on m1 but on m2 $\endgroup$ – DSinghvi Jun 8 '14 at 17:14
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    $\begingroup$ In equation (5) I changed $m_1 $ to $m_2 $ and carried out the rest of the problem with the same equations, and ended up with $-13.02m/s^2 $, which is still incorrect. Is there anything else with my work I should change? $\endgroup$ – Garmenarnar Jun 8 '14 at 17:16
  • $\begingroup$ Ok the 5 equation is completely wrong. It should be T-fs=m1a. Also acceleration of m1 = acceleration of m2 since rope is inextesible @user49147 $\endgroup$ – DSinghvi Jun 8 '14 at 17:24
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    $\begingroup$ Okay, I messed around with that equation for a bit, but keep running into problems. How would you find T? Because otherwise, there are two unknown variables in that equation $\endgroup$ – Garmenarnar Jun 8 '14 at 17:38
  • $\begingroup$ You have 2 variables T and a and 2 equations 5 and 8.It would be better to chat in chat room rather than increasing comments here. If you want .Also after getting your answer please accept my solution. $\endgroup$ – DSinghvi Jun 8 '14 at 17:40

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