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# C_6 - Chapter 6 Friction If a body rests on an incline...

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Chapter 6 Friction If a body rests on an incline plane, the friction force exerted on it by the surface prevents it from sliding down the incline. The question is, what is the steepest incline on which the body can rest? A body is placed on a horizontal surface. The body is pushed with a small hori- zontal force F . If the force F is sufficiently small, the body does not move. F W N body F f , Fig. 6.1 Free-body diagram of the body Figure 6.1 shows the free-body diagram of the body, where the force W is the weight force of the body, and N is the normal force exerted by the surface on the body. The force F is the horizontal force, and F f is the friction force exerted by the surface. Friction force arises in part from the interactions of the roughness, or asperities, of the contacting surfaces. The body is in equilibrium and F f = F . The force F is slowly increased. As long as the body remains in equilibrium, the friction force F f must increase correspondingly, since it equals the force F . The body slips on the surface. The friction force, after reaching the maximum value, cannot maintain the body in equilibrium. The force applied to keep the body moving on the surface is smaller than the force required to cause it to slip. Why more force is required to start the body sliding on a surface than to keep it sliding is explained in 1

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2 6 Friction part by the necessity to break the asperities of the contacting surfaces before sliding can begin. The theory of dry friction, or Coulomb friction , predicts: the maximum friction forces that can be exerted by dry, contacting surfaces that are stationary relative to each other; the friction forces exerted by the surfaces when they are in relative motion, or sliding. Static Coefficient of Friction The magnitude of the maximum friction force, F f , that can be exerted between two plane dry surfaces in contact is F f = μ s N , (6.1) where μ s is a constant, the static coefficient of friction , and N is the normal compo- nent of the contact force between the surfaces. The value of the static coefficient of friction, μ s , depends on: the materials of the contacting surfaces; the conditions of the contacting surfaces namely smoothness and degree of con- tamination. Typical values of μ s for various materials are shown in Table 6.1. Table 6.1. Typical values of the static coefficient of friction. Materials μ s metal on metal 0.15 - 0.20 metal on wood 0.20 - 0.60 metal on masonry 0.30 - 0.70 wood on wood 0.25 - 0.50 masonry on masonry 0.60 - 0.70 rubber on concrete 0.50 - 0.90 Equation (6.1) gives the maximum friction force that the two surfaces can exert without causing it to slip. If the static coefficient of friction μ s between the body and the surface is known, the largest value of F one can apply to the body without causing it to slip is F = F f = μ s N . Equation (6.1) determines the magnitude of the maximum friction force but not its direction. The friction force resists the impend- ing motion.
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C_6 - Chapter 6 Friction If a body rests on an incline...

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