A rope inclined at angle 37° to the horizontal is used to drag a 50kg block along a level floor with an acceleration of 1m/s^2 .The coefficient of friction between the block and the floor is 0.2. What is the tension in the rope?


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Question Number 74522 by necxxx last updated on 25/Nov/19

$A r o p e i n c l i n e d a t a n g l e 37 ° t o t h e$ $h o r i z o n t a l i s u s e d t o d r a g a 50 k g b l o c k$ $a l o n g a l e v e l f l o o r w i t h a n a c c e l e r a t i o n$ $o f 1 m / s^{2} . T h e c o e f f i c i e n t o f f r i c t i o n$ $b e t w e e n t h e b l o c k a n d t h e f l o o r i s 0.2 .$ $W h a t i s t h e t e n s i o n i n t h e r o p e ?$
Commented by Rio Michael last updated on 25/Nov/19

Commented by Rio Michael last updated on 25/Nov/19

$f r o m t h e a b o v e d i a g r a m,$ $T c o s 37 ° - F_{f} = m a$ $T c o s 37 ° - F_{N} μ = m a$ $b u t F_{N} = W = m g$ $∴ T c o s 37 - m g μ = m a$ $\Rightarrow T = \frac{m (a + g μ)}{c o s 37 °}$ $T = \frac{50 (1 + 10 (0.2))}{c o s 37} = 187.8 N$
Commented by necxxx last updated on 25/Nov/19

$T h a n k y o u s i r b u t t h e b o o k s a y s t h a t t h e$ $a n s w e r i s 161 N$
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