Question

The uniform dresser has a weight of 90 lb and rests on a tile floor for which the coefficient of static friction is 0.25. If the man pushes on it in the horizontal direction, thetatheta= 0o, determine the smallest magnitude of force F needed to move the dresser. Also, if the man has a weight of 150 lb, determine the smallest coefficient of static friction between his shoes and the floor so that he does not sli

Answer 1

Answer:

a) $F = 736.065\,lbf$, b) $\mu_{k} = 0.15$

Explanation:

a) The uniform dresser is modelled by using the following equations of equilibrium:

$\Sigma F_{x} = F - \mu_{k}\cdot N = 0$

$\Sigma F_{y} = N-m\cdot g=0$

After some algebraic manipulation, the following formula is derived:

$F = \mu_{k}\cdot m \cdot g$

$F = (0.25)\cdot (90\,lbm)\cdot (32.714\,\frac{ft}{s^{2}} )$

$F = 22.5\,lbf$

b) The man is described by the following equations of equilibrium:

$\Sigma F_{x} = -F + \mu_{k}\cdot N = 0$

$\Sigma F_{y} = N-m\cdot g=0$

After some algebraic manipulation, the following formula for the static coefficient of friction is:

$\mu_{k} = \frac{F}{m\cdot g}$

$\mu_{k} = \frac{22.5\,lbf}{150\,lbf}$

$\mu_{k} = 0.15$