CP? A 25.0-kg box of textbooks rests on a loading ramp that makes an angle ? with the horizontal. The coefficient of kinetic friction is 0.25, and the coefficient of static friction is 0.35. (a) As ? is increased, find the minimum angle at which the box starts to slip. (b) At this angle, find the acceleration once the box has begun to move. (c) At this angle, how fast will the box be moving after it has slid 5.0 m along the loading ramp?

Solution 36E Step 1: Given Mass of the box (m) = 25 kg The coefficient of kinetic friction k = 0.25 The coefficient of static friction s = 0.35 Problem (a) Step 1: To find the minimum angle at which the box is about to slip When the body is about to slip, we should consider the static friction, Hence F x = wsin f s = 0 f = .n s s wsin = .ns---- (1) Step 2: F = n wcos = 0 y n = wcos ----- (2) Step 3: Substituting (2) in (1) wsin= .wcos s = tan s Step 4: = tan ( ) = tan (0.35)1 s = 19.30° Problem (b) To find the cceleration on the box once it starts moving Step 1: a x = g(sin cok) a x = 9.8(sin(19.30°) 0.25 co*(19.30°)) a x = 9.8 * (0.33 - 0.25*0.94) a x = 0.931 m/s 2 Problem (c ) Step 1: To find the speed of the box to travel along the ramp of length 5m Length of the ramp L = 5m v = 2aL