ENGR0135 - Statics and Mechanics of Materials 1 Homework #2

1. Four forces act on a particle as shown below. Determine the magnitudes of forces F1

and F2 so that the particle is in equilibrium.

F1

F2

800N

1000N

x

y

37◦ 45◦

60◦

2. The block shown below weighs 100 lb and rests on a smooth (frictionless) surface.

(a) Draw a free-body diagram for the block.

(b) Determine the force exerted on the block by the smooth surface and the magnitudeof the force P that is required to prevent motion of the block.

20◦ 30◦P

3. The air balloon shown below is tethered by three mooring cables AD, BD, and CD.If the net lift of the balloon is 10 kN, determine the forces exerted on the balloon byeach of the three mooring cables.

A (10, 5, 0)m

B (5,−5, 0)m

C (−7,−2, 0)m

D (0, 0, 8)m

x

y

z

4. A 500 kg mass is supported by steel cables A and B, as shown below. Determine theminimum diameters required for the two cables if the allowable normal stress in thecables is 150 MPa.

A

B

45◦

500 kg

5. A system of three steel pipes, AB, BC, and CD, is loaded and supported as shownbelow. The loads are applied to the rigid plates that connect the pipes at B, C, andD. If the normal stress in each pipe must not exceed 24 ksi, determine the minimumcross-sectional areas required for each of the pipe sections.

14 in 16 in 20 in

A BC

D

30 kip 5 kip 15 kip

6. A 0.75 in diameter solid aluminum rod is press fit into an aluminum pipe, whose innerdiameter is 0.75 in and outer diameter is 1 in, as shown below. Determine the averageshearing stress at the interface between the rod and pipe, if the depth of the press fitL is 0.75 in and the applied axial load P is 100 lb.

PP

L

7. A steel bar, with a rectangular cross section, has a butt-welded joint, as shown below,and will be used to carry an axial tensile load of 750 kN. If the normal and shearstresses on the plane of the weld must be limited to 80 MPa and 50 MPa, respectively,determine the minimum thickness t required for the bar.

60◦ 750 kN750 kN 125mm

8. A wooden tension member with a 2-× 3-in rectangular cross section will be fabricatedwith an inclined glued joint (45◦ ≤ φ ≤ 90◦) at its midsection, as shown below. If theallowable stresses for the glue are 50 psi in tension and 35 psi in shear, determine

(a) The optimum angle φ for the joint.

(b) The maximum safe load P for the member, using the optimum angle for the joint.

P

P

φ