1) The horizontal bar represented in figure is acted upon by the four vertical forces f1,f2,f3, and f4, whose location and characteristics are shown. Calculate the horizontal distance from point O at the base of F4 and horizontal line to the line of action of the resultant of the given forces.
F1=400lbs, F2=3500lbs, F3=4500lbs , F4=3000lbs
Between F1 and F2 is 6ft,between F2 and F3 is 6 ft, Between F3 and F4 is 8ft
F1 F2 F3 F4
2) A railroad car that weighs 20,000 lb is traveling eastward with a velocity whose magnitude is 5fps. A second car, on the same track, that weighs 40,000 lbs also traveling in an easterly direction with a velocity of 7.8fps. When the cars collided, they became coupled together and then both cars moved with the same velocity. If friction between the cars and the rails is neglected, what were the magnitude and the direction of the velocity of the car after the collision?
3) A cylinder tank is 20ft in diameter and contains fresh water to a dept of 60 feet.
a) What is the unit pressure, in pounds per square inch, at a depth of 30 ft below the water surface?
b) What is the unit pressure, in pounds per square foot, at a depth of 40ft.
c) What is the total pressure, in pounds, on the bottom of the tank ?
4) Water is flowing uniformly through a pipe with a diameter of 14 inches if the mean velocity of the water is 4.12, what is the rate of discharge in gallons per minute.
5) A canal dug in the ground has a trapezoidal cross section. The width at the bottom is 16.00 feet, and the rate of slope of each inclined side is 1.5 ft horizontal to 1 ft vertical. When the depth of water is 6 ft, what is the hydraulic radius.
Mechanics of Materials
6) A group of rivets ¾ inch in diameter are to connect steel plates 5/16in. thick, and they are to be in single shear. If the allowable unit stresses are 15,000 psi in shear and 48,500 psi in bearing,how many rivets are needed to transmit a total load of 52,000 lb?
7) A simple beam supports a concentrated load at midspan. Describe and show by means of a rough sketch, how the shear varies from the left end to the right end of the beam. (Neglect the weight of the beam.)
8) A simple beam supports two equal concentrated loads placed symmetrically on the beam. Describe and show by means of a rough sketch, how the bending moment varies from the left end to the right end of the beam. (Neglect the weight of the beam.)
9) In the figure, the magnitude of either force P is 160 lb and the arm p is 25 in . Also the arm p' is 30 in.
P P should be at top
a) What is the torque in the cylinder?
b) What is the magnitude of either force P' ?
Technical Math II
10) A) Find the following values .
1) sin 79 degrees 23 min. 30 seconds
2) Cos 22 degrees 43 min.
11) Express each of the following functions as the same function of a positive acute angle.
Example: cos 165d egrees = -cos 15 degrees
(a) sin 175 degrees
(b) cos 215 degrees
12) The three sides of a triangle ABC are a=16, b=32, and c= 40 meters.
Use the law of cosines to find angle B to the nearest second.
13) Name four factors that contribute to frictional loss during a uniform liquid flow inside a constant diameter pipe?