Calculate F1,F2,F3 and P Q2. Object B is leaning against a wall while sitting on

Question

Calculate F1,F2,F3 and P

Q2. Object B is leaning against a wall while sitting on a wedge W. The weight of B is 1000 N. If 10° , = 0.3 (for all surfaces) and the weight of the wedge is almost zero when compared to the weight of B, calculate the following: (a) The minimum force, P, required to push the wedge into the gap between B and the ground. (b) The frictional forces, F1, F2 and F3 created by this minimum force P. Hint: Use the Free Body Diagrams provided. 1000 N W e F 2 F1 [Partial Answer: F1 312 N]

Explanation / Answer

given, weight of B, Mbg = 1000 N

theta = 10 deg

k = 0.3 ( for all surfaces)

weight of wedge = W = 0

a. let the force required to push the wedge into the gap be P

then form force balance

P = F1 + F2cos(10)

N1 = N2cos(10) + F2sin(10)

now, F1 = kN1

and

1000 + F2sin(10) + F3 = N2cos(10)

N2sin(10) + F2cos(10) = N3

F3 = kN3

F2 = kN2

so, P = kN1 + kN2cos(10)

N1 = N2*cos(10) + kN2sin(10) = N2(cos(10) + ksin(10))

N2sin(10) + kN2cps(10) = N3 = N2(sin(10) + kcos(10))

1000 + kN2sin(10) + kN3 = N2cos(10)

1000 + kN2sin(10) + k(N2(sin(10) + kcos(10))) = N2cos(10)

1000 = N2[cos(10) - 0.3(sin(10) + 0.3cos(10)) - 0.3sin(10)]

N2 = 1262.648 N

hence

N1 = N2(cos(10) + 0.3sin(10)) = 1309.242 N

so P = 765.8122 N

b. F1 = kN1 = 392.7726 N

F2 = kN2 = 378.7944 N

N3 = N2(sin(10) + 0.3cos(10)) = 592.296 N

F3 = kN3 = 177.688 N

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