Snowboarding Earlier, we analyzed the situation of a downhill skier moving at constant velocity to determine the coefficient of kinetic friction. Now let's do a similar analysis to determine acceleration. The snowboarder glides down a slope that is inclined at 0 = 130 to the horizontal as shown below. The coefficient of kinetic friction between the board and the snow is (x = 0.20. What is the acceleration of the snowboarder? mg cos 13° a mg sin 13° N 13º (a) (b) (a) A snowboarder glides down a slope inclined at 13° to the horizontal. (b) The free-body diagram of the snowboarder. Strategy The forces acting on the snowboarder are her weight and the contact force of the slope, which has a component normal to the incline and a component along the incline (force of kinetic friction). Because she moves along the slope, the most convenient reference frame for analyzing her motion is one with the x-axis along and the y-axis perpendicular to the incline. In this frame, both the normal and the frictional forces lie along coordinate axes, the components of the weight are mg sin 0 along the slope and mg cos @ at right angles into the slope, and the only acceleration is along the x-axis (@y = 0) . Solution We can now apply Newton's second law to the snowboarder: EF, = max EFy = may mg sin 0 - 1N = ma. N - mg cos 0 = m (0). From the second equation, N = mg cos 0. Upon substituting this into the first equation, we find Significance az = g (sin 0 - 14% cos 0) = 9 (sin 13* - 0.20 cos 13°) = 0.29m/s2. Notice from this equation that if 0 is small enough or (4x is large enough, a, is negative, that is, the snowboarder slows down.