2_3_f

Determine the magnitude and coordinate direction angles of F3 so that the resultant of the three forces is zero

2_3_e

Determine the angle  between the edges of the sheet-metal bracket.

2_3_d

A force of F = {-40k} lb acts at the end of the pipe. Determine the magnitudes of the components F1 and F2 which are directed along the pipe’s axis and perpendicular to it.

2_3_c

Determine the angle  between the two cords

2_3_b

Determine the magnitude of the projected component of r1 along r2, and the projection of r2 along r1.

2_3_a

Cable BC exerts a force of F = 28 N on the top of the flagpole. Determine the projection of this force along the z-axis of the pole.

2_2_c

 Determine the position (x, y, 0) for fixing cable BA so that the resultant of the forces exerted on the pole is directed along its axis, from B toward O and has a magnitude of 1 kN. Also, what is the magnitude of force F3?

2_2_b2

Determine the lengths of cords ACB and CO. The knot at C is located midway between A and B.

2_2_a

Determine the length of the connecting rod AB by first formulating a Cartesian position vector from A to B and then determining its magnitude

2: 2-1

Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive x-axis

3_3_e

The pipe assembly is subjected to the 80-N force. Determine the moment of this force about point A.

3_3_d

Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has a radius of 5 ft, to fail at the support of C. This requires a moment of M = 80 lbft to be developed at C.

3_3_b

The curved rod lies in the x-y plane and has a radius of 3 m. If a force of F = 80 N acts at its end as shown, determine the moment of this force about point B.

3_2_h

If it takes a force of F = 125 lb to pull the nail out, determine the smallest vertical force P that must be applied to the handle of the crowbar. Hint: this requires the moment of F about point A to be equal to the moment of P about A. Why?

3_2_e

The Snorkel Co. produces the articulating boom platform that can support a weight of 550 lb. If the boom is in the position shown, determine the moment of this force about points A, B, and C.

3_1_k

If the bucket and its contents have a total weight of 20 lb, determine the force in the supporting cables DA, DB, and DC

3_1_c

The gusset plate is subjected to the forces of four members. Determine the force in member B and its proper orientation  for equilibrium. The forces are concurrent at point O. Take F = 12 kN.

3_1_b

Determine the magnitude and angle  of F so that the particle is in equilibrium

4: 4-47

Problem: Determine the magnitude of the moment of each of the three forces about the axis AB. Solve the problem (a) using a Cartesian vector approach and (b) using a scalar approach

Variable Solution:

Givens: 
F1 = 60 [N]
F2 = 85 [N]
F3 = 45 [N] 
a = 1.5 [m]
b = 2 [m]

Numerical Solution:
M_AB(F1) (scalar) = b⋅F1⋅sin(tan^-1(a/b))
→(2 [m])(60 [N])⋅sin(tan^-1((1.5 [m])/(2 [m])))
M_AB(F1) = 72 [N⋅m] 

M_AB(F1) (vector) = ab⋅f1⋅(a²+b²)^-1/2
→(1.5 [m])(2 [m])(60 [N])⋅((1.5 [m])²+(2 [m])²)^-1/2
M_AB(F1) = 72 [N⋅m] 

M_AB(F2) (scalar) = 0
M_AB(F2) (vector) = 0

M_AB(F3) (scalar) = 0
M_AB(F3) (vector) = 0

4: 4-21

Problem: In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 500 lb * in about point A. Determine the required magnitude of force F.

Variable Solution:

Givens: 
a = 18 [in]
b = 5 [in]
α = 30
M_A = 500 [lb⋅in] CW
**notice that M_A is clockwise so it will be negative in our numerical solution, because it goes into the page

Numerical Solution:
F = -M_A/(bsinα+acosα)
→-(-500 [lb⋅in]) / ((5 [in])sin(30)+(18 [in])cos(30))
F = 27.64 [lb]