Q.
Q1.
A. What is an inertial reference?
B. A rubber bend of length .7m is stretched to connect to points A and B. A tension force of 40 N is thereby developed in the band. A 20-N weight is then attached to the band at C. Find the distance a that point C moves downward if the 20-N weight is constrained to move vertically downward along a frictionless rod.
[Hint If you consider part of the band, the “spring constant” for it will be greater than that of the whole band]
(Ref. See page no. 440, Fig. No P.10.48)
Q2.
A. A light plain is coming in for a landing at a speed of 100 km/hr. The wheels have zero rotation just before touching the runway. If 1/10 the weight of the plane is maintained by the upward force of the runway for the first second, what is the approximate length of the skid mark left by the wheel on the runway? The wheels each weigh 100 N and have a radius of gyration of 180mm and a diameter of 450 mm. The plane weighs with load 8,000 N. The coefficient of friction between the tire and runway is .3.
B. Determine the supporting forces at A, C, D, G, F, and H for the structure. C, D, H and G are ball joint connections.
(Ref. See page no. 208, Fig. No P.5.104)
Q3.
A. A car is traveling at a speed of 55 mi/hr along a banked highway having a radius of curvature of 500 ft. At what angle should the road be banked in order that a zero friction force is needed for the car to go around this curve?
B. A vehicle on a monorail has a speed S = 10 m/s and an acceleration S=4m/s2 relative to the ground reference XYZ when it reaches point A. Inside the vehicle, a 3 kg mass slides along a rod which at the time of interest is parallel to the X axis. This rod rotates about a vertical axis with w=1 rad /s and w=2 rad/s2 relative to the vehicle at the time of interest. Also at this time, the radial distance d of the mass is .2 m and its radial velocity v = .4 m/s inward. What is the dynamic force on the mass at this instant?
(Ref. See page no. 785, Fig. No P.15.143)
Q4.
A. A Bowler releases his ball at a speed of 3m/sec. If the ball has a diameter of 250 mm, what spin w should be put on the ball so there is no slipping? If he puts on only half of this spin w, keeping the same speed of 3 m/sec., what is the speed after .3 sec.? The ball has a mass of 1.8 kg and a dynamic coefficient of friction with the floor of .1. Neglect wind resistance and rolling resistance (as discussed in Section 7.1).
B. A mountain climber of weight W hangs freely suspended by one rope that is fastened at one end to his waist, wrapped one half turn about a rock with x = .2 and held at the other end in his hand. What minimum force in terms of W must he pull the rope into himself with to gain altitude?
Q5.
A. What is meant by the associative law of addicting?
B. Two solid semi cylinders are glued together. Body A has a uniform mass density of 6.54 kN/m3, while body B has a uniform mass density of 10 kN/m3. Determine:
a. Center Volume
b. Center of Mass
c. Center of Gravity
(Ref. See page no. 352, Fig. No P.8.39)
Q6.
A. A space station is in a circular parking orbit around the earth at a distance of 5,000 mi from the center. A projectile is fired ahead in a direction tangential to the trajectory of the space station with a speed of 5,000 mi/hr relative to the space station. What is the maximum distance from earth reached by the projectile?
B. A magnetic field is developed such that the body force on the rectangular parallelepiped of metal is given as
F=(.01x+1/8)k oz/lbm
If the mass density of the metal is 450 lbm/ft3, what is the simplest resultant body force from such a field? Note at the earth’s surface the number of pounds mass equals the number of pounds force of weight.
