Solution Solving for Jx gives 1x = w COS 25" fi mg cos 25"" fx Substituting known values on the right-hand side of the equation, Significance 45.0 N Hk = =0.082. (62 kg) (9.80 m/s2) (0.906) This result is a little smaller than the coefficient listed in the previous section for waxed wood on snow, but it is still reasonable since values of the coefficients of friction can vary greatly. In situations like this, where an object of mass m slides down a slope that makes an angle 0 with the horizontal, friction is given by fx= #xmg cos 8. All objects slide down a slope with constant acceleration under these circumstances. We have discussed that when an object rests on a horizontal surface, the normal force supporting it is equal in magnitude to its weight. Furthermore, simple friction is always proportional to the normal force. When an object is not on a horizontal surface, as with the inclined plane, we must find the force acting on the object that is directed perpendicular to the surface; it is a component of the weight. We now derive a useful relationship for calculating coefficient of friction on an inclined plane. Notice that the result applies only for situations in which the object slides at constant speed down the ramp. An object slides down an inclined plane at a constant velocity if the net force on the object is zero. We can use this fact to measure the coefficient of kinetic friction between two objects. As shown above, the kinetic friction on a slope is f = Limg cos 0. The component of the weight down the slope is equal to mg sin 0 (see the free-body diagram in the figure above). These forces act in opposite directions, so when they have equal magnitude, the acceleration is zero. Writing these out, Hymg cos 8 = mg sin 8. Solving for Jx, we find that Hx mg cos 0 mg sin 0 = tan 0. Put a coin on a book and tilt it until the coin slides at a constant velocity down the book. You might need to tap the book lightly to get the coin to move. Measure the angle of tilt relative to the horizontal and find J4k . Note that the coin does not start to slide at all until an angle greater than 0 is attained, since the coefficient of static friction is larger than the coefficient of kinetic friction. Think about how this may affect the value for /4x and its uncertainty.