111.2mtantan33.7 .22(0.90m)hθ−−===°AAsis increased from zero the crate slides before it tips. (b) It starts to slide when = 31º. (c) The crate begins to slide when = tan–1μs= tan–10.70 = 35.0º and begins to tip when = 33.7º. Thus, it tips first as the angle is increased. (d) Tipping begins at = 33.7°≈34°.39. The force diagram shown below depicts the situation just before the crate tips, when the normal force acts at the front edge. However, it may also be used to calculate the angle for which the crate begins to slide. Wis the force of gravity on the crate,NFis the normal force of the plane on the crate, and fis the force of friction. We take the xaxis to be down the plane and the yaxis to be in the direction of the normal force. We assume the acceleration is zero but the crate is on the verge of sliding.(a) The xand ycomponents of Newton’s second law are sin0 andcos0NWfFWθθ−=−=respectively. The yequation gives FN= Wcos . Since the crate is about to slidef= sFN= sWcos ,wheresis the coefficient of static friction. We substitute into the
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