Moment and EquilibriumAssignment # 3

1) Three cables are used to tether a balloon as shown. Determine the vertical force P exerted by the balloon at A knowing that the tension in cable AB is 259 N.

Solution

The coordinates of point A is

The coordinates of point B is

The coordinates of point C is

The coordinates of point D is

The forces applied at A are: TAB , TAC, TAD and P where P = Pj

To express the other forces in terms of the unit vectors i, j, k, we write

AB = (B - A) = - (4.20 m) i - (5.60 m) j AB = 7.00 m

AC = (C – A) = (2.40 m) i - (5.60 m) j + (4.20 m) k AC = 7.40 m

AD = (D –A) = - (5.60 m) j - (3.30 m) k AD = 6.50 m

Setting TAB = 259N in (1) and (2), and solving the resulting set of equations gives

TAC = 479.15 N TAD = 535.66 N

P = 1031.29 N↑

2. A crate is supported by three cables as shown determine the maximum weight the maximum weight of the crate knowing that each cable can sustain a maximum tension of 616 lb before it fail

3. Collars A and B are connected by a 25-in. long wire and can slide freely on frictionless rods. If a 60-lb force Q is applied to collar B as shown, determine (a) the tension in the wire when x = 9-in. (b) the corresponding magnitude of the force P required to maintain the equilibrium of the system.

Free Body: Collar B

4. The frame ACD is hinged at A and D and is supported by a cable that passes through a ring at B and is attached to hooks at G and H. Knowing that the tension in the cable is 450 N, determine the moment about the diagonal AD of the force exerted on the frame by portion BH of the cable.

Ny j

Nx i

_ TAB lAB

Q = (60 lb) k

Free Body: Collar A

Ny j

Nz k

TAB lAB

P i