ENGR0135 - Statics and Mechanics of Materials 1 (2141)Homework #1

Due: 9/4(daytime sections) or 9/3(evening section)

1. Two spherical bodies weigh 500 lb and 1500 lb at the Earth’s surface. Determine thegravitational force of attraction between the spheres if the distance from center tocenter is 5 ft.

2. Determine the mass m, in SI units, for a 150 lb aluminum engine block under standardconditions (sea level at a latitude of 45 degrees).

3. An important parameter in fluid flow problems is the Reynolds number (Re), whichcan be expressed in equation form as

Re =ρvL

µ=vL

ν,

where ρ is the density of the fluid, v is the velocity, L is a characteristic length forthe flow, µ is the dynamic viscosity of the fluid, and ν is the kinematic viscosity ofthe fluid. If the Reynolds number is dimensionless, what are the dimensions of thedynamic viscosity µ and of the kinematic viscosity ν?

4. Round off the following numbers to three significant figures. Find the percentagedifference between each rounded-off number and the original number by using theoriginal number as the reference.

(a) 0.00164893

(b) 5.99511

(c) 2,367,001

5. Using the law of sines and the law of cosines, determine the resultant of the three forcesshown in the figure below. Locate the resultant with respect to the x-axis shown.

30◦5 kN

7 kN

10 kNx

y

6. Two cables are used to support weight as shown below. The resultant R of the cableforces F1 and F2 has a magnitude of 400 lb and its line of action is vertical. Use thelaw of sines and the law of cosines, in conjunction with a sketch of the force triangle,to determine the magnitudes of the forces F1 and F2.

35◦45◦

F1 F2

R

7. A force is applied to a post as shown below. Determine

(a) The x- and y-components of the force.

(b) The x′- and y′-components of the force.

x

y

30◦

45◦

F = 950Nx′

y′

8. The hot-air balloon shown below is tethered with three mooring cables. The force TB

in cable DB has a magnitude of 2230 N.

(a) Express TB in Cartesian vector form.

(b) Determine the magnitude of the rectangular component of the force TB alongDA.

(c) Determine the angle α between the cables DA and DB.

A (10, 5, 0)m

B (5,−5, 0)m

C (−7,−2, 0)m

D (0, 0, 8)m

x

y

z

TB

9. Three forces are applied to an eye bolt as shown below. Using rectangular components,determine the resultant R of the three forces and the angle θx between the line of actionof the resultant and the x-axis.

30◦5 kN

7 kN

10 kNx

y

10. Determine the magnitude R of the resultant of the three forces shown below. Alsodetermine the angle θx, θy, and θz between the line of action of the resultant and thepositive coordinate axes.

x

y

z

60◦45◦

40◦35◦

30◦

40◦F1 = 300 lb

F2 = 450 lb

F3 = 600 lb