Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and 2.3

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2 7 Resolve the force F1 into components acting along the u and v axes and determine the magnitudes of the components.

1 Statics Chapter II Fall 2018 Exercises Corresponding to Sections 2.1, 2.2, and Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured counterclockwise from the positive x axis. 2 7 Resolve the force F1 into components acting along the u and v axes and determine the magnitudes of the components. 2 8 Resolve the force F2 into components acting along the u and v axes and determine the magnitudes of the components Determine the design angle ϕ ( 0 o ϕ 90 o ) between struts AB and AC so that the 400-lb horizontal force has a component of 600 lb which acts up to the left, in the same direction as from B towards A. Take θ = If the resultant force of the two tugboats is required to be directed towards the positive x axis, and F B is to be a minimum, determine the magnitude of F R and F B and the angle θ.

2 Statics Chapter II Fall 2018 Exercises Corresponding to Section 2.4 F2 11 If the magnitude of the resultant force acting on the bracket is to be 80 lb directed along the u axis, determine the magnitude of F and its direction θ If the resultant force acting on the bracket is required to be a minimum, determine the magnitudes of F1 and the resultant force. Set = 30. Exercises Corresponding to Sections 2.5 and Specify the magnitude and coordinate direction angles α, β, and γ of F 1 so that the resultant of the three forces acting on the bracket is F R = { 350 k} lb. Note that F 3 lies in the x y plane.

3 Statics Chapter II Fall Determine the magnitude and coordinate direction angles of the resultant force, and sketch this vector on the coordinate system. Exercises Corresponding to Sections 2.7 and Express each of the forces in Cartesian vector form and determine the magnitude and coordinate direction angles of the resultant force The force F has a magnitude of 80 lb and acts at the midpoint C of the thin rod. Express the force as a Cartesian vector (13 th Ed.) Determine the lengths of wires AD, BD, and CD. The ring at D is midway between A and B.

4 Statics Chapter II Fall 2018 Exercises Corresponding to Section Determine the angles θ and φ made between the axes OA of the flag pole and AB and AC, respectively, of each cable Determine the magnitude of the projected component of the 100-lb force acting along the axis BC of the pipe and perpendicular to it Determine the angle θ between the cables AB and AC Determine the magnitude of the projected component of the force F = {400i 200j + 500k} N acting along the cable CA and perpendicular to it.

Statics Chapter III Fall 2018 Exercises Corresponding to Sections 3.1, 3.2, 3.3, 8.1, and 8.2 3 7 The man attempts to pull down the tree using the cable and small pulley arrangement shown.

3 22 The springs BA and BC each have a stiffness of 500 N/m and an unstretched length of 3 m.

5 Statics Chapter III Fall 2018 Exercises Corresponding to Sections 3.1, 3.2, 3.3, 8.1, and The man attempts to pull down the tree using the cable and small pulley arrangement shown. If the tension in AB is 60 lb, determine the tension in cable CAD and the angle θ which the cable makes at the pulley The springs BA and BC each have a stiffness of 500 N/m and an unstretched length of 3 m. Determine the horizontal force F applied to the cord which is attached to the small ring B that the displacement of the ring from the wall is d = 1.5 m Two blocks A and B have a weight of 10 lb and 6 lb, respectively. They are resting on the incline for which the coefficients of static friction are μa = 0.15 and μb = 0,25. Determine the angle θ which will cause motion of one of the blocks. What is the friction force under each of the blocks when this occurs? The spring has a stiffness of k = 2 lb/ft and is originally unstretched.

Statics Chapter III Fall 2018 8 39 (13 th Ed.) Determine the smallest force the man must exert on the rope in order to move the 80-kg crate.

8 47 Crates A and B weight 200 lb and 150 lb, respectively. They are connected together with a cable and placed on the inclined plane.

6 Statics Chapter III Fall (13 th Ed.) Determine the smallest force the man must exert on the rope in order to move the 80-kg crate. Also, what is the angle θ at this moment? The coefficient of static friction between the crate and the floor is μs = Crates A and B weight 200 lb and 150 lb, respectively. They are connected together with a cable and placed on the inclined plane. If the angle is gradually increased. Determine when the crates begin to slide. The coefficients of static friction between the crates and the plane are µa = 0.25 and µb = 0.35.

7 Statics Chapter III Fall 2018 Exercises Corresponding to Section If the bucket and its contents have a total weight of 20 lb, determine the force in the supporting cables DA, DB, and DC The crate has a mass of 130 kg. Determine the tension developed in each cable for equilibrium Determine the tension developed in cables AB, AC, and AD required for equilibrium of the 300-lb crate.

Statics Chapter IV Fall 2018 Exercises Corresponding to Section 4.1 4 5 Determine the moment about point B of each of the three forces acting on the beam.

8 Statics Chapter IV Fall 2018 Exercises Corresponding to Section Determine the moment about point B of each of the three forces acting on the beam The towline exerts a force of P = 6 kn at the end of the 8-m-long crane boom. If θ = 30 o, determine the placement x of the hook at B so that this force creates a maximum moment about point O. What is this moment? 4 12 The towline exerts a force of P = 6 kn at the end of the 8-m-long crane boom. If x = 10 m, determine the position θ of the boom so that this force creates a maximum moment about point O. What is this moment? Exercises Corresponding to Sections 4.2, 4.3, and The pipe assembly is subjected to the force of F = {600i + 800j 500k} N. Determine the moment of this force about point B.

9 Statics Chapter IV Fall Determine the smallest force F that must be applied along the rope in order to cause the curved rod, which has a radius of 4 m, to fail at the support A. This requires a moment of M = 1500 N m to be developed at A Force F acts perpendicular to the inclined plane. Determine the moment produced by F about point A. Express the result as a Cartesian vector. Exercises Corresponding to Section Determine the moment of the force F about an axis extending between A and C. Express the result as a Cartesian vector.

Statics Chapter IV Fall 2018 4 63 Determine the magnitude of the moment of the force F = {50i - 20j - 80k} N about the base line CA of the

Determine the moment of this force about the y axis when the frame is in the position shown. Exercises Corresponding to Section 4.

10 Statics Chapter IV Fall Determine the magnitude of the moment of the force F = {50i - 20j - 80k} N about the base line CA of the tripod The A-frame is being hoisted into an upright position by the vertical force of F = 80 lb. Determine the moment of this force about the y axis when the frame is in the position shown. Exercises Corresponding to Section Two couples act on the beam. Determine the magnitude of F so that the resultant couple moment is 450 lb ft, counterclockwise. Where on the beam does the resultant couple moment act?

Statics Chapter IV Fall 2018 4 72 Determine the magnitude of the couple force F so that the resultant couple moment on the crank is zero.

11 Statics Chapter IV Fall Determine the magnitude of the couple force F so that the resultant couple moment on the crank is zero If the couple moment acting on the pipe has a magnitude of 300 N m determine the magnitude F of the forces applied to the wrenches (13 th Ed.) Determine the distance d between A and B so that the resultant couple moment has a magnitude of MR = 20 N m.

12 Statics Chapter IV Fall 2018 Exercises Corresponding to Section (13 th Ed.) Replace the force system acting on the frame by a resultant force and couple moment at point A Replace the force system by an equivalent resultant force and couple moment at point O. Take F3 = {-200i + 500j - 300k} N.

Statics Chapter V Fall 2018 Exercises Corresponding to Section 9.1 9 17 Locate the centroid (x, y) of the area.

13 Statics Chapter V Fall 2018 Exercises Corresponding to Section Locate the centroid (x, y) of the area (13 th Ed.) Locate the centroid (x, y) of the area. 9 5 Determine the distance x, y to the center of gravity of the homogeneous rod.

Statics Chapter V Fall 2018 9 40 Locate the y centroid of the paraboloid.

14 Statics Chapter V Fall Locate the y centroid of the paraboloid Locate the centroid of the quarter cone. Exercises Corresponding to Section 9.2 F9 7 Locate the centroid (x, y, z) of the wire bent in the shape shown.

Statics Chapter V Fall 2018 9 65 Determine the location (x, y) of the

15 Statics Chapter V Fall Determine the location (x, y) of the centroid C of the area. Problem the composite Centroids 1. Locate the centroid (x, y) of area Determine the distance z to the centroid of the shape which consists of a cone with a hole of height h = 50 mm bored into its base.

Statics Chapter V Fall 2018 9 81 The assembly is made from a steel hemisphere, ρst = 7.

Determine the center of mass of the assembly if the height of the cylinder is h = 200 mm.

9 F4 37 Determine the resultant force and specify where it acts on the beam measured from A.

16 Statics Chapter V Fall The assembly is made from a steel hemisphere, ρst = 7.80 Mg/m 3, and an aluminum cylinder, ρal = 2.70 Mg/m 3. Determine the center of mass of the assembly if the height of the cylinder is h = 200 mm. Exercises Corresponding to Section 4.9 F4 37 Determine the resultant force and specify where it acts on the beam measured from A The distribution of soil loading on the bottom of a building slab is shown. Replace this loading by an equivalent resultant force and specify its location, measured from point O.

17 Statics Chapter V Fall Replace the distributed loading by an equivalent resultant force and specify where its line of action intersects a vertical line along member BC, measured from C.

18 Statics Chapter VI Fall 2018 Exercises Corresponding to Sections 5.1, 5.2, 5.3, and 5.4 F5 5 The 25 kg bar has its center of mass at G. If it is supported by a smooth peg at C, a roller at A, and a cord AB determine the reaction at these supports Determine the horizontal and vertical components of reaction at the pin A and the reaction of the rocker B on the beam Determine the reactions at the supports.

Statics Chapter VI Fall 2018 5 25 Determine the reactions on the bent rod which is supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the

19 Statics Chapter VI Fall Determine the reactions on the bent rod which is supported by a smooth surface at B and by a collar at A, which is fixed to the rod and is free to slide over the fixed inclined rod Determine the reactions acting on the smooth uniform bar, which has a mass of 20 kg The man uses the hand truck to move material up the step. If the truck and its contents have a mass of 50 kg with center of gravity at G, determine the normal reaction on both wheels and the magnitude and direction of the minimum force required at the grip B needed to lift the load.

Statics Chapter VI Fall 2018 5 36 The beam of negligible weight is supported horizontally by two springs.

8 24 The uniform thin pole has a weight of 30 lb and a length of 26 ft.

20 Statics Chapter VI Fall The beam of negligible weight is supported horizontally by two springs. If the beam is horizontal and the springs are unstretched when the load is removed, determine the angle of tilt of the beam when the load is applied The uniform thin pole has a weight of 30 lb and a length of 26 ft. If it is placed against the smooth wall and on the rough floor in the position d = 10 ft, will it remain in this position when it is released? The coefficient of static friction is μs = Determine the smallest force P that must be applied in order to cause the 150-lb uniform crate to move. The coefficient of static friction between the crate and the floor is μs = 0.5.

Statics Chapter VI Fall 2018 Exercises Corresponding to Sections 5.1, 5.2, 5.3, and 5.4 5 82 The sign has a mass of 100 kg with center of mass at G.

21 Statics Chapter VI Fall 2018 Exercises Corresponding to Sections 5.1, 5.2, 5.3, and The sign has a mass of 100 kg with center of mass at G. Determine the x, y, z components of reaction at the ball-and socket joint A and the tension in wires BC and BD (13 th Ed.) Determine the tensions in the cables and the components of reaction acting on the smooth collar at A necessary to hold the 50-lb sign in equilibrium. The center of gravity for the sign is at G. RB 2. Determine the tensions TAE and TGF in the two supporting cables resulting from the 1.2 kn tension in cable CD. Assume the absence of any resisting moments on the base of the pole at O about the x and y axes, but not about z axis. Use vector approach.

Statics Chapter VIII Fall 2018 Exercises Corresponding to Sections 6.1, 6.2, and 6.

6 17 If the maximum force that any member can support is 8 kn in tension and 6 kn in compression, determine the

4 R6 4 Determine the force in members GF and FB, and BC of the Fink truss and state if the members are in tension or

22 Statics Chapter VIII Fall 2018 Exercises Corresponding to Sections 6.1, 6.2, and Determine the force in each member of the truss, and state if the members are in tension or compression If the maximum force that any member can support is 8 kn in tension and 6 kn in compression, determine the maximum force P that can be supported at joint D. Exercises Corresponding to Section 6.4 R6 4 Determine the force in members GF and FB, and BC of the Fink truss and state if the members are in tension or compression (13 th Ed.) Determine the force in members CD and CM of the Baltimore bridge truss and state if the members are in tension or compression. Also, indicate all zero-force members.

Statics Chapter VIII Fall 2018 6 40 Determine the force in members CD, CF,

23 Statics Chapter VIII Fall Determine the force in members CD, CF, and CG and state if these members are in tension or compression. Exercises Corresponding to Section Determine the force P required to hold the 100-lb weight in equilibrium Determine the reactions at supports A and B.

24 Statics Chapter VIII Fall Determine the horizontal and vertical components of force at pins B and C. The suspended cylinder has a mass of 75 kg Determine the resultant force at pins A, B, and C on the three-member frame Determine the horizontal and vertical components of force which the pins at A and B exert on the frame.

Statics Chapter VIII Fall 2018 6 77 The two- member structure is connected at C by a pin, which is fixed to BDE and passes through the smooth slot in member AC.

25 Statics Chapter VIII Fall The two- member structure is connected at C by a pin, which is fixed to BDE and passes through the smooth slot in member AC. Determine the horizontal and vertical components of reaction at the supports The toggle clamp is subjected to a force F at the handle. Determine the vertical clamping force acting at E The two-member frame is pin connected at E. The cable is attached to D, passes over the smooth peg at C, and supports the 500-N load. Determine the horizontal and vertical reactions at each pin.

Statics Chapter VIII Fall 2018 Exercises Corresponding to Section 7.

7 22 Determine the internal normal force, shear force, and moment at points D and E in the overhang beam.

26 Statics Chapter VIII Fall 2018 Exercises Corresponding to Section Determine the internal normal force, shear force, and the moment at points C and D Determine the internal normal force, shear force, and moment at points D and E in the overhang beam. Point D is located just to the left of the roller support at B, where the couple moment acts. Exercises Corresponding to Section Draw the shear and moment diagrams for the beam (a) in terms of the parameters shown; (b) set P = 800 lb, a = 5 ft, L = 12 ft. F7 8 Determine the shear and moment as a function of x, then draw the shear and moment diagrams.

27 Statics Chapter VIII Fall Draw the shear and moment diagrams for the beam Draw the shear and moment diagrams for the beam Draw the shear and moment diagrams for the beam.

Statics Chapter IX Fall 2018 Exercises Corresponding to Sections 10.1 and 10.2 10 21 Determine the moment of inertia for the shaded area about the x axis.

28 Statics Chapter IX Fall 2018 Exercises Corresponding to Sections 10.1 and Determine the moment of inertia for the shaded area about the x axis Determine the moment of inertia for the shaded area about the y axis Determine the moment of inertia for the shaded area about the x axis Determine the moment of inertia for the shaded area about the y axis. Exercises Corresponding to Section Determine the moment of inertia of the composite area about the x axis.

Statics Chapter IX Fall 2018 10 47 Determine the

29 Statics Chapter IX Fall Determine the moment of inertia for the shaded area about the y axis.

Eng Sample Test 4

Eng Sample Test 4 1. An adjustable tow bar connecting the tractor unit H with the landing gear J of a large aircraft is shown in the figure. Adjusting the height of the hook F at the end of the tow bar is accomplished by