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There are two types of friction Both always oppose motion When you pushed your book across the desk, it experienced a type of friction that acts on moving objects This force is known as kinetic friction, and it is exerted on one surface by another when the two surfaces rub against each other because one or both of them are moving To understand the other kind of friction, imagine trying to push a heavy couch across the floor You give it a push, but it does not move Because it does not move, Newton s laws tell you that there must be a second horizontal force acting on the couch, one that opposes your force and is equal in size This force is static friction, which is the force exerted on one surface by another when there is no motion between the two surfaces You might push harder and harder, as shown in Figures 5-8a and 5-8b, but if the couch still does not move, the force of friction must be getting larger This is because the static friction force acts in response to other forces Finally, when you push hard enough, as shown in Figure 5-8c, the couch will begin to move Evidently, there is a limit to how large the static friction force can be Once your force is greater than this maximum static friction, the couch begins moving and kinetic friction begins to act on it instead of static friction A model for friction forces On what does a frictional force depend The materials that the surfaces are made of play a role For example, there is more friction between skis and concrete than there is between skis and snow It may seem reasonable to think that the force of friction also might depend on either the surface area in contact or the speed of the motion, but experiments have shown that this is not true The normal force between the two objects does matter, however The harder one object is pushed against the other, the greater the force of friction that results.

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Figure 5-8 There is a limit to the ability of the static friction force to match the applied force

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If you pull a block along a surface at a constant velocity, according to Newton s laws, the frictional force must be equal and opposite to the force with which you pull You can pull a block of known mass along a table at a constant velocity and use a spring scale, as shown in Figure 5-9, to measure the force that you exert You can then stack additional blocks on the block to increase the normal force and repeat the measurement Plotting the data will yield a graph like the one in Figure 5-10 There is a direct proportion between the kinetic friction force and the normal force The different lines correspond to dragging the block along different surfaces Note that the line corresponding to the sandpaper surface has a steeper slope than the line for the highly polished table You would expect it to be much harder to pull the block along sandpaper than along a polished table, so the slope must be related to the magnitude of the resulting frictional force The slope of this line, designated k, is called the coefficient of kinetic friction between the two surfaces and relates the frictional force to the normal force, as shown below Kinetic Friction Force Ff, kinetic

The kinetic friction force is equal to the product of the coefficient of the kinetic friction and the normal force

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The maximum static friction force is related to the normal force in a similar way as the kinetic friction force Remember that the static friction force acts in response to a force trying to cause a stationary object to start moving If there is no such force acting on an object, the static friction force is zero If there is a force trying to cause motion, the static friction force will increase up to a maximum value before it is overcome and motion starts Static Friction Force Ff, static

The static friction force is less than or equal to the product of the coefficient of the static friction and the normal force

In the equation for the maximum static friction force, s is the coefficient of static friction between the two surfaces, and sFN is the maximum static friction force that must be overcome before motion can begin In Figure 5-8c, the static friction force is balanced the instant before the couch begins to move

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