Question

To transport a series of bundles of shingles A to a roof, a contractor uses a motor-driven lift consisting of a horizontal platform BC which rides on rails attached to the sides of a ladder. The lift starts from rest and initially moves with a constant acceleration ay as shown. The lift then decelerates at a constant rate a2 and comes to rest at D, near the top of the ladder. Knowing that 0 = 61° and that the coefficient of static friction between a bundle of shingles and the horizontal platform is 0.30, determine the largest allowable acceleration ay and the largest allowable deceleration az if the bundle is not to slide on the platform. (Round the final answers to two decimal places.)

Answer 1

Non inertial frame motion can be treated as inertial frame motion by applying a pseudo force over the frame . We are applying a pseudo force on the block to treat it as inertial frame motion . Now drawing FBD we get the normal forces in both conditions . For maximum accelration the block should not move ie. The component of force must be balanced by friction.
SOM: F.B.D 4.4m 40-610 A А B 0.8m mg In Non-inertial frame, applying a pseudo forre. given 0 - 61 A. to f = friction fore = UN mg ma, mgt + ma, sino ma, coso masing ma, Coso = MN magino +mg ma, C6361°30-31mg +ma, sin 6lº) al cos 61'- 0:3 Sin 6o) *50.3x8 a, 0.3xg Cos61 -0.3 $inbi I 13.23 m/s2 Value of a mop = 13-23 m/s² s

For decebration part ma mg masino maz F.BD ma coso f mg friction f = UN' Here N' = mg - masinot fa ma Cosolo 013 1 mg - mg sin61") 2 ma, ces 61° < 0.39 Cos6l+ 0.3x Single A₂ = 3.93 a 2 mop = 3.93 m 182