A 2.50 kg wood block is pressed against a vertical wood wall by a force applied 34.9° to the horizontal. If the block is initially at rest, and μs=0.493, what force would you need to apply to begin moving the box up the wall?

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Answer 1 · 2017-07-25T08:38:58

$"F"_min=-25.0901 " N"$

negative sign denotes force in opposite direction
pulling instead of pushing at the same angle

$"m"=2.5kg$
$theta=34.9°$
$mu_s=0.493$

enter image source here
[P in image is the applied force]

$"N"="F"costheta$

$"ma"=f_s+"m"g+"F"sintheta=0$
[to start motion, no motion yet: $"a"=0$ ]

$mu_s"N"+"m"g+"F"sintheta$

$mu_s"N"+"F"sintheta=-"m"g$

$mu_s"F"costheta+"F"sintheta=-"m"g$

$"F"(mu_scostheta+sintheta)=-"m"g$

$"F"=-("m"g)/(mu_scostheta+sintheta)$

Substitute the values

$"F"=-((2.5)(9.8))/(0.493cos34.9°+sin34.9°)$

$"F"_min=-25.0901 " N"$