Static and Kinetic Friction A 20.0-kg crate is at rest on a floor as shown in the figure below. The coefficient of static friction between the crate and floor is 0.700 and the coefficient of kinetic friction is 0.600. A horizontal force To is applied to the and (d) crate. Find the force of friction if (a) (b) (c) $ = 20.0 N, 7 = 30.0N, 7 = 120.0 N. P = 180.0 N. y 13 ? P 7 Ñ (a) (b) (a) A crate on a horizontal surface is pushed with a force P. (b) The forces on the crate. Here, f may represent either the static or the kinetic frictional force. The free-body diagram of the crate is shown in figure (b) above. We apply Newton's second law in the horizontal and vertical directions, including the friction force in opposition to the direction of motion of the box. Strategy Solution Newton's second law gives P-f= ma, EF= = maz N - w = 0. EFy = may Here we are using the symbol f to represent the frictional force since we have not yet determined whether the crate is subject to station friction or kinetic friction. We do this whenever we are unsure what type of friction is acting. Now the weight of the crate is w = (20.0 kg) (9.80 m/s2) = 196 N, which is also equal to N. The maximum force of static friction is therefore (0.700) (196 N) = 137 N. As long as P is less than 137 N, the force of static friction keeps the crate stationary and f, = P. Thus, (a) fs = 20.0 N, (b) fs = 30.0 N, and (c) f, = 120.0 N. (d) If P = 180.0 N, the applied force is greater than the maximum force of static friction (137 N), so the crate can no longer remain at rest. Once the crate is in motion, kinetic friction acts. Then fx = \N = (0.600) (196 N) = 118 N, and the acceleration is m p - fx 20.0 kg 180.0N -118 N = 3.10 m/s2. Significance This example illustrates how we consider friction in a dynamics problem. Notice that static friction has a value that matches the applied force, until we reach the maximum value of static friction. Also, no motion can occur until the applied force equals the force of static friction, but the force of kinetic friction will then become smaller.