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Answer :
The minimum coefficient of static friction (\mu_s) needed to prevent slipping is found by analyzing the forces on the man and the cart, balancing the static friction with the components of the man's weight along and perpendicular to the incline's surface.
The question asks to determine the minimum coefficient of static friction (denoted by \\mu_s\\) required to prevent slipping for a 208-pound man pulling a cart up an incline. To solve this, we need to analyze the forces acting on the man and the cart and use the concepts of static friction and normal force.
The force of static friction can be calculated using the equation \\Fs = \mu_s * N\\, where \\Fs\\ is the force of static friction and \\N\\ is the normal force, which is the force exerted by the surface that is perpendicular to the surface. The man's weight and the incline angle will determine \\N\\, and given that the man is pulling the cart with a steady speed, it implies that the frictional force is strong enough to prevent his feet from slipping.
To find the minimum \\mu_s\\, the normal force \\N\\ must be equal to the component of the man's weight perpendicular to the slope, and the static friction force must balance the component of his weight parallel to the slope. Without the actual incline angle or additional details, we can't compute a numeric answer, but the method of solving such problems requires balancing the forces parallel and perpendicular to the incline.
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