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erastovalidia
2 months ago
6

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
Engineering
1 answer:
Kisachek [356]2 months ago
3 0

Answer:

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

Explanation:

a) The uniform dresser can be modeled using specific equilibrium equations:

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

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

Following some algebraic manipulations, the formulated equation 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) Similarly, the man can be represented by a set of equilibrium equations:

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

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

After some algebraic changes, the expression for the coefficient of static friction comes out as:

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

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

\mu_{k} = 0.15

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