posted by sophie on .
A large 63.0kg board is propped at a 44 degree angle against the edge of a barn door that is 2.5 m wide.
How great a horizontal force must a person behind the door exert (at the edge) in order to open it? Assume that the coefficient of friction between the board and the door is 0.44, and that the board is firmly set against the ground.
Is the 44 degrees measured with respect to the ground or the door?
This is very similar to a problem asked yesterday, except that there is friction between board and door this time.
M2 = F•L•sinα,
M3 = F(fr) •L•cosα = μ•F•L• cosα,
M2 = M1 +M3,
F•L•sinα = m•g•L•cosα/2 + μ•F•L• cosα,
F•sinα - μ•F•cosα = m•g•cosα/2,
F = m•g•cosα/2•( sinα - μ•cosα) =
=63•9.8•cos44º/2•(sin44º - 0.44•cos44º) = 588 N.
If you have the answer for this problem write it.