an initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 n. the coefficient of static friction between the box and the floor is 0.35. (a) what should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

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14-10-2022
Physics

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an initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100 n. the coefficient of static friction between the box and the floor is 0.35. (a) what should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand, and (b) what is the weight of the sand and box in that situation?

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charithran8975 charithran8975 · Answer 1 · 2022-10-20T04:21:39-04:00

a) The angle between the cable and the horizontal in order to pull the greatest possible amount of sand is 19°. b) The weight of the sand and box in that situation is 3.3x10³ N.

A similar scenario is depicted with a free-body diagram and in the textbook's illustration, where the unknown angle is represented by the symbol. We employ the same system of coordinates as in that figure.

a) Newton's second law thus results in

x : T cosФ - f = ma

y : T sinФ + Fn-mg = 0

With a = 0 and f = f s, max = s F N, we may solve for the mass of the box-and-sand (as a function of angle) as follows:

m = T/g (sinФm + cosФm/us )

Hence, in order to determine the angle m that corresponds to the greatest mass that may be drawn, we will solve using calculus techniques.

dm/dt = T/g (sinФm + cosФm/us ) = 0

As a result, tan m = s is obtained, and for s = 0.35, m = 19 is obtained.

(b) The result of entering our value for m into the formula we discovered for the mass of the box and sand is m=340 kg. This is equivalent to a weight of mg=3.3x10³ N.

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