Archives: Solution Manual

PROBLEM 11.188 A golfer hits a ball with an initial velocity of magnitude 0 v at an angle  with the horizontal. Knowing that the ball must clear the tops of two trees and land as close as possible to […]

PROBLEM 11.181* Determine the direction of the binormal of the path described by the particle of Problem 11.96 when (a) 0,t (b) /2 s.t   SOLUTION Given:   2 (cos) 1 (sin) A tt At Bttri jk ft, […]

PROBLEM 11.173 A particle moves along the spiral shown. Determine the magnitude of the velocity of the particle in terms of b, , and .    SOLUTION Given: 2 1 2 rbe   Take time derivative 2 […]

PROBLEM 11.166 The pin at B is free to slide along the circular slot DE and along the rotating rod OC. Assuming that the rod OC rotates at a constant rate  , (a) show that the acceleration of pin […]

PROBLEM 11.158 A satellite will travel indefinitely in a circular orbit around the earth if the normal component of its acceleration is equal to  2 / g Rr, where 2 9.81 m/sg, R = radius of the earth = […]

PROBLEM 11.149 A child throws a ball from point A with an initial velocity v0 at an angle of 3 with the horizontal. Knowing that the ball hits a wall at point B, determine (a) the magnitude of the initial […]

PROBLEM 11.140 A motorist starts from rest at Point A on a circular entrance ramp when t  0, increases the speed of her automobile at a constant rate and enters the highway at Point B. Knowing that her speed […]

PROBLEM 11.131 (Continued) Therefore 520 sin (40 ) sin (130 )      or sin 130 cos cos 130 sin 4(sin 40 cos cos 40 sin )       or sin 130 4 […]

PROBLEM 11.124 Knowing that at the instant shown block A has a velocity of 8 in./s and an acceleration of 6 in./s 2 both directed down the incline, determine (a) the velocity of block B, (b) the acceleration of block […]

PROBLEM 11.116* (Continued) (b) Angle Check the edge. Since the stream clears the edge. .  max max tan 1.875 21.466 xx   61.93   61.9     2 02 0 tan 2cos gx yy x […]

PROBLEM 11.111 (Continued) Then 2 8 1400 tan 24.5 (1 tan )g    or 2 240.345 tan 1400 tan 248.345 0    Solving 10.3786 and 79.949     Rejecting the second root because it […]

PROBLEM 11.106 At halftime of a football game souvenir balls are thrown to the spectators with a velocity v0. Determine the range of values of v0 if the balls are to land between Points B and C. SOLUTION The motion […]

PROBLEM 11.97 An airplane used to drop water on brushfires is flying horizontally in a straight line at 180 mi/h at an altitude of 300 ft. Determine the distance d at which the pilot should release the water so that […]

PROBLEM 11.91 The motion of a vibrating particle is defined by the position vector (4sin ) (cos2 ) ,tt    rij where r is expressed in inches and t in seconds. (a) Determine the velocity and acceleration when […]

PROBLEM 11.82 (Continued) (a) At 8 s, 32.58 m/stv or 117.3 km/hv  (b) At 20 st 660 mx  Copyright © McGraw-Hill Education. Permission required for reproduction or display. PROBLEM 11.83 A training airplane has a velocity of 126 […]

PROBLEM 11.77 An accelerometer record for the motion of a given part of a mechanism is approximated by an arc of a parabola for 0.2 s and a straight line for the next 0.2 s as shown in the figure. […]

PROBLEM 11.71 In a 400-m race, runner A reaches her maximum velocity A v in 4 s with constant acceleration and maintains that velocity until she reaches the half-way point with a split time of 25 s. Runner B reaches […]

PROBLEM 11.64 (Continued) (b) Reading from the x tcurve max 420 mx  (c) Between 10 s and 22 s 100 m 420 m (area under curve from , to 22 s) mvt t  11 1 100 420 (22 […]

PROBLEM 11.59 (Continued) Solving Eqs. (5) and (6) for C a and D a 2 40 mm/s C a 2 10 mm/s D a Now 0 CC vat At 3 s:t 2 (40 mm/s )(3 s) C v or 120.0 […]

PROBLEM 11.52 (Continued) Then, substituting into Eq. (2) 2 40 2 3 mm/s 0 3 B a     or 2 20 mm/s B a 2 20.0 mm/s Ba  (b) From the diagram, constant DA xx  […]

PROBLEM 11.45 Two rockets are launched at a fireworks display. Rocket A is launched with an initial velocity 0 v  100 m/s and rocket B is launched t 1 seconds later with the same initial velocity. The two rockets […]

PROBLEM 11.36 A group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered portion of the flight and […]

PROBLEM 11.27 Experimental data indicate that in a region downstream of a given louvered supply vent the velocity of the emitted air is defined by 0 0.18 / ,vvx where v and x are expressed in m/s and meters, respectively, […]

PROBLEM 11.19 Based on experimental observations, the acceleration of a particle is defined by the relation (0.1a sin x/b), where a and x are expressed in m/s2 and meters, respectively. Knowing that 0.8 mb and that 1 m/sv  when […]

PROBLEM 11.9 The brakes of a car are applied, causing it to slow down at a rate of 10 ft/s2. Knowing that the car stops in 100 ft, determine (a) how fast the car was traveling immediately before the brakes […]

CHAPTER 11 PROBLEM 11.1 A snowboarder starts from rest at the top of a double black diamond hill. As he rides down the slope, GPS coordinates are used to determine his displacement as a function of time: x= 0.5t3 + […]

PROBLEM 10.102 Determine the couple M that must be applied to member DEFG to maintain the equilibrium of the linkage. SOLUTION Assume A y  : 12 1.5 8 CAA yyy   , 1.5 EC A yy y  […]

PROBLEM 10.95 The horizontal bar BEH is connected to three vertical bars. The collar at E can slide freely on bar DF. Determine the range of values of Q for which the equilibrium of the system is stable in the […]

PROBLEM 10.88 Collar A can slide freely on the semicircular rod shown. Knowing that the constant of the spring is k and that the unstretched length of the spring is equal to the radius r, determine the value of  […]

PROBLEM 10.80 A slender rod AB, of weight W, is attached to two blocks A and B that can move freely in the guides shown. Knowing that the spring is unstretched when AB is horizontal, determine three values of  […]

PROBLEM 10.71 Two uniform rods AB and CD, of the same length l, are attached to gears as shown. Knowing that rod AB weighs 3 lb and that rod CD weighs 2 lb, determine the positions of equilibrium of the […]

PROBLEM 10.61 Using the method of Section 10.8, solve Problem 10.31. PROBLEM 10.31 Solve Problem 10.30 assuming that force P is moved to C and acts vertically downward. SOLUTION Spring: 2(2 sin ) 4 sinAE x l l   […]

PROBLEM 10.52 Knowing that the coefficient of static friction between the block attached to rod ACE and the horizontal surface is 0.15, determine the magnitude of the largest and smallest force Q for which equilibrium is maintained when 30 , […]

PROBLEM 10.44 The position of member ABC is controlled by the hydraulic cylinder CD. Determine the angle  knowing that the hydraulic cylinder exerts a 15-kN force on pin C. SOLUTION 222 222 2 (0.8 m)sin 0.8cos 2( )( )cos(90 […]

PROBLEM 10.36 A load W of magnitude 72 lb is applied to the mechanism at C. Neglecting the weight of the mechanism, determine the value of  corresponding to equilibrium. The constant of the spring is 20 lb/in.,k and the […]

PROBLEM 10.26 (Continued) with 24 in., 4 in., 10 lb, and 18 lblaP Q    2 24 in. 18 lb (10 lb) sin cos 4 in.    or 2 sin cos 0.300   Solving numerically […]

PROBLEM 10.20 For the linkage shown, determine the force Q required for equilibrium when 18 in.,l 600 lb in.,M and 70 .   SOLUTION 1 2cos l C    Virtual Work: 0:U   0MQC   […]

PROBLEM 10.10 The slender rod AB is attached to a collar A and rests on a small wheel at C. Neglecting the radius of the wheel and the effect of friction, derive an expression for the magnitude of the force […]

CHAPTER 10 PROBLEM 10.1 Determine the vertical force P that must be applied at C to maintain the equilibrium of the linkage. SOLUTION Assume A y  2 CA yy   DA yy   11 22 EDA yyy […]

PROBLEM B.73* (Continued) Simplifying 33 3 33 3 xy z 0.12533( ) ( ) 0.5( ) 0 0.11705( ) ( ) 0.62695( ) 0     xy z    Adding and solving for 3 () z […]

PROBLEM B.71* (Continued) (b) To determine the direction cosines , , x yz   of each principal axis, use two of the equations of Eqs. (9.54) and Eq. (9.57). Then 1:K Begin with Eqs. (9.54a) and (9.54b). 11 1 […]

PROBLEM B.68 Given a homogeneous body of mass m and of arbitrary shape and three rectangular axes x , y , and z with origin at O , prove that the sum Ix + Iy + Iz of the mass […]

PROBLEM B.61 (Continued) From the solution to Problem 9.147, we have 36.2542 10 lb ft s y I  32 32 32   39.1721 10 lb ft s 30.4184 10 lb ft s I  x z I  […]

PROBLEM B.56 Determine the mass moment of inertia of the steel fixture of Problems 9.145 and 9.149 with respect to the axis through the origin that forms equal angles with the x, y, and z axes. SOLUTION From the solutions […]

PROBLEM B.50 Brass wire with a weight per unit length w is used to form the figure shown. Determine the mass products of inertia I xy , I yz , and I zx of the wire figure. SOLUTION First compute […]

PROBLEM B.45 A section of sheet steel 2 mm thick is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m 3 , determine the mass products of inertia I xy , I […]

PROBLEM B.39 Determine the mass products of inertia I xy , I yz , and I zx of the steel fixture shown. (The density of steel is 7850 kg/m 3 .) SOLUTION First compute the mass of each component. We […]

PROBLEM B.34 Determine the mass moment of inertia of the steel machine element shown with respect to the yaxis. (The density of steel is 3 490 lb/ft .) SOLUTION First compute the mass of each component. We have 2 490 […]

PROBLEM B.29 (Continued)   123 62 2 22 22 2 62 2 1(3325.97 10 lb s /ft)[(2.25) (3.5) ] in 12 2.25 3.5 1 ft          () () () (3325.97 10 […]

PROBLEM B.25 A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3, determine the mass moment of inertia of the component with respect to each […]