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A crate in the form of a 1.12-m cube contains a piece of machinery whose design is such that the center of gravity of the crate and its contents is located 0.28 m above its geometrical center. The crate rests on a ramp that makes an angle θ with the horizontal. As θ is increased from zero, an angle will be reached at which the crate will either start to slide down the ramp or tip over. Which event will occur if the coefficient of static friction is (a) 0.60? (b) 0.70? In each case give the angle at which the event occurs.

A crate in the form of a 1.12-m cube contains a piece of machinery whose design is such that the center of gravity of the crate and its contents is located 0.28 m above its geometrical center. The crate rests on a ramp that makes an angle θ with the horizontal.  As θ is increased from zero, an angle will be reached  at which the crate will either start to slide down the ramp or tip over. Which event  will occur if the coefficient  of static friction is (a) 0.60? (b) 0.70? In each case give the angle at which the event occurs.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
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Therefore, the crate will tip when the angle of inclination is 33.6° .
It is important to note that the angle θt is independent of coefficient of static friction between the crate and the surface of inclined plane. Therefore, one can use the same value in other parts without repeating the calculations.

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