Concurrent and non-concurrent forces:

1) Drag force at a given speed on a prototype sailboat hull. A model is placed in a test channel and three cables are used to align its bow on the channel centerline. For a given speed, the tension is 40 N in cable AB and 60 N in cable AE. Determine the drag force exerted on the hull and the tension in cable AC.

Figure.1 Free body diagram

2) In the design of the robot to insert the small cylindrical part in to a close-fitting circular hole, the robot arm must exert a 90 N force P on the part parallel to the axis of the hole as shown. Determine the components of the force which the part exerts on the robot along axes:

a) Parallel and perpendicular to the arm AB, andb) Parallel and perpendicular to the arm BC.

3) A force of 200N is applied to the end of the wrench to tighten a flange bolt which holds the wheel to the axle. Determine the moment M produced by this force about the center O of the wheel for the position of the wrench shown.

4) Two integral pulleys are subjected to the belt tensions shown. If the resultant R of these forces passes through the center O, determine T and the magnitude of R and the counterclockwise angle θ it makes with the x-axis.

5) What horizontal force P must a worker exert on the rope to position the 500N crate directly over the trailer?

6) The system of parallel forces acts on the top of the warrant truss. Determine the equivalent resultant forces of the system and specify its location measured from point A.

7) The bricks on top of the beam and the supports at the bottom create the distributed loading shown in the second figure. Determine the required intensity w and dimension d of the right support so that the resultant force and couple moment about point A of the system are zero.

8) The truss is supported by a pin at point A and a roller at B. Determine the support reactions.

9) Determine the horizontal and vertical components of reaction at the pin A and the tension developed in cable BC used to support the steel frame.

10) As an airplane’s brakes are applied, the nose wheel exerts two forces on the end of the landing gear as shown. Determine the horizontal and vertical components of reaction at the pin C and the force in the strut AB.

11) The wooden plank resting between the buildings deflects slightly when it supports the 500N boy. This deflection causes a triangular distribution of load at its ends, having maximum intensities of wA and wB, each measured in N/m, when the boy is standing 3m from one end as shown. Neglect the mass of plank.

12) Determine the horizontal and vertical components of force at the pin A and the reaction at the rocker B of the curved beam.

13) Determine the largest mass m of the suspended block so that the force in any member does not exceed 30kN (T) or 25kN (C).

14) A ball is thrown horizontally from the top of a 50m cliff at A with a speed of 15m/s and a land at point C. because of a strong horizontal wind, the ball has a constant acceleration in the negative x-direction. Determine the radius of curvature ρ of the path of the ball at B where its trajectory makes an angle of 450 with the horizontal. Neglect any effect of air resistance in the vertical direction.

15) A fixed horizontal guide carries a slider and pin P whose motion is conrolled by the rotating

slotted arm OA. If the arm is revolving about O at the constant rate = 2 rad/s for an interval of its designed motion, determine the magnitudes of the velocity and accelaration of the slider in the slot for the instant when θ=600. Also find the r-components of the velocity and accelaration.

16) A drop of water falls with no initial speed from point A of a highway overpass. After dropping 6m, it strikes the windshield at point B of a car which is traveling at a speed of 100 km/h on the horizontal road. If the windshield is inclined 500from the vertical as shown, determine the angle θ relative to the normal n to the windshield at which the water drop strikes.

17) For a given value of y, determine the upward velocity of A in terms of the downward velocity of B. neglect the diameters of the pulleys.

18) A departmental-store escalator handles a steady load of 30 peoples per minute in elevating them from the first to the second floor through a vertical rise of 7m. the average person has a mass of 65kg. if the motor which drives the unit delivers 3kW, calculate the mechanical efficiency e of the system.

19) The 45.9 gm. golf ball is struck by the five-iron and acquires the velocity shown in a time period of 0.001s. Determine the magnitude R of the average force exerted by the club on the ball. What acceleration magnitude a does this force cause, and what is the distance d over which the launch velocity is achieved, assuming constant acceleration?

20) Calculate the y-coordinate of the centroid of the shaded area.

21) The figure shows a jam cleat designed for a sailboat where the large friction forces developed by the cams prevent the rope from slipping. Determine the force R supported by each cam bearing for the 900N rope tension. The co-efficient of static friction between the rope and the cams is 0.8.

22) The plane figure is symmetrical with respect to the 450 line and has an area of 1600mm2. Its polar moment of inertia about its centroid C is 40x104 mm2. Compute:

a. The polar radius of gyration about O andb. The radius of gyration about the X0-axis.

PART-B

1) If, in order to reduce weight whilst keeping the external diameter constant, the bar is bored axially to produce a cylinder of uniform thickness, what is the maximum diameter of bore possible given that the maximum allowable stress is 240MN/m2? The load can be assumed to remain constant at 100 kN.

2) The coupling shown in Fig. below is constructed from steel of rectangular cross-section and is designed to transmit a tensile force of 50 kN. If the bolt is of 15 mm diameter calculate:

a. the shear stress in the bolt;b. the direct stress in the plate;c. The direct stress in the forked end of the coupling.

3) A compound bar is constructed from three bars 50 mm wide by 12 mm thick fastened together to form a bar 50 mm wide by 36 mm thick. The middle bar is of aluminum alloy for which E = 70 GN/m2 and the outside bars are of brass with E = 100 GN/m2. If the bars are initially fastened at

18°C and the temperature of the whole assembly is then raised to 5WC, determine the stresses set up in the brass and the aluminum.ᾳB = 18 x per 0C and ᾳA = 22 x per 0C and,

What will be the changes in these stresses if an external compressive load of 15 kN is applied to the compound bar at the higher temperature?