In a laboratory experiment on friction, a 135-N block resting on a rough horizontal table is pulled by a horizontal wire. The pull gradually increases until the block begins to move and continues to increase thereafter. ?Figure E5.26 shows a graph of the friction force on this block as a function of the pull. (a) Identify the regions of the graph where static friction and kinetic friction occur. (b) Find the coefficients of static friction and kinetic friction between the block and the table. (c) Why does the graph slant upward at first but then level out? (d) What would the graph look like if a 135-N brick were placed on the block, and what would the coefficients of friction be?
ANSWER: The weight of the block is, N = mg = 135 N . Where N is the normal reaction and also defined as weight. a) In the graph at the point (75,75) static friction occurs and at the point (75,50) kinetic friction takes place. b) We know that, the static friction is, F max= S N= S = S 135. As the graph shows that, when the frictional force reaches 75 N, the pull remains constant and the frictional force decreases too. 75 N = ×S135 =S75/135 = 0.555 The kinetic friction also obeys same type of equation, which is, F = K N = KN = K 135 According to the graph, the pull remains same while the frictional force decreases to 50 N. so, this is the frictional force which we are going to use in the above equation. = 50/135 = 0.370. K c) When the pull is applied the first, the friction was zero, then it increases gradually. We know that friction acts in the opposite direction of motion. So when the pull increases, the frictional force increases. So, the graph slants upwards at first. Then the static friction it overcomes and starts moving. Then it overcomes the kinetic friction, so the graph got this level.