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Engineering Mechanics Dynamics 14th Global Edition Hibbeler - Solutions
R13–2.The motor M pulls in its attached rope with an acceleration ap = 6 m>s 2 . Determine the towing force exerted by M on the rope in order to move the 50-kg crate up the inclined plane. The coefficient of kinetic friction between the crate and the plane is mk = 0.3. Neglect the mass of the
R13–1. The van is traveling at 20 km>h when the coupling of the trailer at A fails. If the trailer has a mass of 250 kg and coasts 45 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop. 20 km/h Prob. R13-1
R13–8. The spool, which has a mass of 4 kg, slides along the rotating rod. At the instant shown, the angular rate of rotation of the rod is u#= 6 rad>s and this rotation is increasing at u$= 2 rad>s2. At this same instant, the spool has a velocity of 3 m>s and an acceleration of 1
R13–7. The 5-kg suitcase slides down the curved ramp for which the coefficient of kinetic friction is mk = 0.2. If at the instant it reaches point A it has a speed of 2 m>s, determine the normal force on the suitcase and the rate of increase of its speed. y = 1 -3 m- Prob. R13-7 -x
R13–6. The bottle rests at a distance of 1.5 m from the center of the horizontal platform. If the coefficient of static friction between the bottle and the platform is ms = 0.3, determine the maximum speed that the bottle can attain before slipping. Assume the angular motion of the platform is
R13–5. The ball has a mass of 30 kg and a speed v = 4 m>s at the instant it is at its lowest point, u = 0. Determine the tension in the cord and the rate at which the ball’s speed is decreasing at the instant u = 20. Neglect the size of the ball. 4 m Prob. R13-5
R13–4. If the motor draws in the cable at a rate of v = (0.05s3>2) m>s, where s is in meters, determine the tension developed in the cable when s = 10 m. The crate has a mass of 20 kg, and the coefficient of kinetic friction between the crate and the ground is mk = 0.2. Prob. R13-4 M
R13–3. Block B rests on a smooth surface. If the coefficients of friction between A and B are ms = 0.4 and mk = 0.3, determine the acceleration of each block if F = 250 N. B A 10 kg Prob. R13-3 25 kg F
The motor M pulls in its attached rope with an acceleration ap = 6 m>s2. Determine the towing force exerted by M on the rope in order to move the 50-kg crate up the inclined plane. The coefficient of kinetic friction between the crate and the plane is mk = 0.3. Neglect the mass of the pulleys
The van is traveling at 20 km>h when the coupling of the trailer at A fails. If the trailer has a mass of 250 kg and coasts 45 m before coming to rest, determine the constant horizontal force F created by rolling friction which causes the trailer to stop. 20 km/h Prob. R13-1
C13–4. Each car is pin connected at its ends to the rim of the wheel which turns at a constant speed. Using numerical values, show how to determine the resultant force the seat exerts on the passenger located in the top car A. The passengers are seated toward the center of the wheel. Also, list
C13–3. Determine the smallest speed of each car A and B so that the passengers do not lose contact with the seat while the arms turn at a constant rate. What is the largest normal force of the seat on each passenger? Use numerical values to explain your answer. Prob. C13-3 B
The tugboat has a known mass and its propeller provides a known maximum thrust. When the tug is fully powered you observe the time it takes for the tug to reach a speed of known value starting from rest. Show how you could determine the mass of the barge. Neglect the drag force of the water on the
If the box is released from rest at A, use numerical values to show how you would estimate the time for it to arrive at B. Also, list the assumptions for your analysis. A B Prob. C13-1
*13–132. The rocket is traveling around the earth in free flight along the elliptical orbit AC. Determine its change in speed when it reaches A so that it travels along the elliptical orbit AB. C B 8 Mm- 8 Mm Probs. 13-131/132 10 Mm-
The rocket is traveling around the earth in free flight along an elliptical orbit AC. If the rocket has the orbit shown, determine the rocket’s velocity when it is at point A. C B 8 Mm- 8 Mm Probs. 13-131/132 10 Mm-
13–130. If the rocket is to land on the surface of the planet, determine the required free-flight speed it must have at Aso that the landing occurs at B. How long does it take for the rocket to land, going from A to B? The planet has no atmosphere, and its mass is 0.6 times that of the earth. A'
13–129. The rocket is traveling in a free flight along an elliptical trajectory AA. The planet has no atmosphere, and its mass is 0.60 times that of the earth. If the rocket has the orbit shown, determine the rocket’s velocity when it is at point A. A' r=6 Mm 100 Mm Probs. 13-129/130 B A -70 Mm-
*13–128. A rocket is in free-flight elliptical orbit around the planet Venus. Knowing that the periapsis and apoapsis of the orbit are 8 Mm and 26 Mm, respectively, determine(a) the speed of the rocket at point A, (b) the required speed it must attain at A just after braking so that it undergoes
13–127. An elliptical path of a satellite has an eccentricity e = 0.130. If it has a speed of 15 Mm>h when it is at perigee, P, determine its speed when it arrives at apogee, A. Also, how far is it from the earth’s surface when it is at A? Prob. 13-127 P
13–126. The rocket is traveling around the earth in free flight along the elliptical orbit. If the rocket has the orbit shown, determine the speed of the rocket when it is at A and at B. B 30 Mm Prob. 13-126 20 Mm- A
13–125. A rocket is in a free-flight elliptical orbit about the earth such that the eccentricity of its orbit is e and its perigee is r0. Determine the minimum increment of speed it should have in order to escape the earth’s gravitational field when it is at this point along its orbit.
*13–124. The rocket is in free-flight circular orbit around the earth. Determine the time needed for the rocket to travel from the inner orbit at A to the outer orbit at A. 8 Mm -19 Mm- A' Probs. 13-123/124
13–123. The rocket is initially in free-flight circular orbit around the earth. Determine the speed of the rocket at A.What change in the speed at A is required so that it can move in an elliptical orbit to reach point A? 8 Mm -19 Mm- A' Probs. 13-123/124
13–122. The Viking Explorer approaches the planet Mars on a parabolic trajectory as shown. When it reaches point A its velocity is 10 Mm>h. Determine r0 and the required change in velocity at A so that it can then maintain a circular orbit as shown. The mass of Mars is 0.1074 times the mass of
13–121. The rocket is in free flight along an elliptical trajectory AA. The planet has no atmosphere, and its mass is 0.70 times that of the earth. If the rocket has an apoapsis and periapsis as shown in the figure, determine the speed of the rocket when it is at point A. A -6 Mm B r=3 Mm Prob.
*13–120. Determine the constant speed of satellite S so that it circles the earth with an orbit of radius r = 15 Mm. Prob. 13-120 = 15 Mm
13–119. The rocket is traveling in free flight along the elliptical orbit. The planet has no atmosphere, and its mass is 0.60 times that of the earth. If the rocket has the orbit shown, determine the rocket’s speed when it is at A and at B. B -18.3 Mm Prob. 13-119 7.60 Mm A
13–118. The satellite is moving in an elliptical orbit with an eccentricity e = 0.25. Determine its speed when it is at its maximum distance A and minimum distance B from the earth. Prob. 13-118 2 Mm B
*13–116. The rocket is in circular orbit about the earth at an altitude of 20 Mm. Determine the minimum increment in speed it must have in order to escape the earth’s gravitational field. 20 Mm Prob. 13-116
13–115. The speed of a satellite launched into a circular orbit about the earth is given by Eq. 13–24. Determine the speed of a satellite launched parallel to the surface of the earth so that it travels in a circular orbit 800 km from the earth’s surface.
13–114. A communications satellite is in a circular orbit above the earth such that it always remains directly over a point on the earth’s surface. As a result, the period of the satellite must equal the rotation of the earth, which is approximately 24 hours. Determine the satellite’s
13–113. The earth has an orbit with eccentricity 0.0167 around the sun. Knowing that the earth’s minimum distance from the sun is 146(106) km, find the speed at which the earth travels when it is at this distance. Determine the equation in polar coordinates which describes the earth’s orbit
*13–112. The ball has a mass of 2 kg and a negligible size. It is originally traveling around the horizontal circular path of radius r0 = 0.5 m such that the angular rate of rotation is u .0 = 1 rad>s. If the attached cord ABC is drawn down through the hole at a constant speed of 0.2 m>s,
13–111. A 0.2-kg spool slides down along a smooth rod.If the rod has a constant angular rate of rotation u #= 2 rad>s in the vertical plane, show that the equations of motion for the spool are r$- 4r - 9.81 sin u = 0 and 0.8r # + Ns - 1.962 cos u = 0, where Ns is the magnitude of the normal
13–110. Solve Prob. 13–109 if the arm has an angular acceleration of u$= 3 rad>s2 when u#= 2 rad>s at u = 30. A = 2 rad/s -0- 0.5 m Probs. 13-109/110
13–109. The particle has a mass of 0.5 kg and is confined to move along the smooth horizontal slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when u = 30. The rod is rotating with a constant angular velocity
*13–108. The pilot of an airplane executes a vertical loop which in part follows the path of a “four-leaved rose,”r = (-180 cos 2u) m, where u is in radians. If his speed at A is a constant vp = 24 m>s, determine the vertical reaction the seat of the plane exerts on the pilot when the
13–107. The pilot of the airplane executes a vertical loop which in part follows the path of a cardioid, r = 200(1 + cos u) m, where u is in radians. If his speed at A is a constant vp = 85 m>s, determine the vertical reaction the seat of the plane exerts on the pilot when the plane is at A.
13–106. The collar has a mass of 2 kg and travels along the smooth horizontal rod defined by the equiangular spiral r = (eu) m, where u is in radians. Determine the tangential force F and the normal force N acting on the collar when u = 45, if the force F maintains a constant angular motion u = 2
13–105. The smooth surface of the vertical cam is defined in part by the curve r = (0.2 cos u + 0.3) m. The forked rod is rotating with an angular acceleration of u$= 2 rad>s2, and when u = 45 the angular velocity is u.= 6 rad>s.Determine the force the cam and the rod exert on the 2-kg
13–103. Rod OA rotates counterclockwise at a constant angular rate u.= 4 rad>s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r = (1.6 cos u) m. If both collars have a
13–102. The ball of mass m is guided along the vertical circular path r = 2rc cos u using the arm OA. If the arm has a constant angular velocity u.0, determine the angle u … 45at which the ball starts to leave the surface of the semicylinder. Neglect friction and the size of the ball. Probs.
13–101. The 0.5-kg ball is guided along the vertical circular path r = 2rc cos u using the arm OA. If the arm has an angular velocity u.= 0.4 rad>s and an angular acceleration u$= 0.8 rad>s2 at the instant u = 30, determine the force of the arm on the ball. Neglect friction and the size of
*13–100. Determine the normal and frictional driving forces that the partial spiral track exerts on the 200-kg motorcycle at the instant u = 53 p rad, u#= 0.4 rad>s, u$= 0.8 rad>s2. Neglect the size of the motorcycle. r = (50) m Prob. 13-100
13–99. The spring-held follower AB has a mass of 0.5 kg and moves back and forth as its end rolls on the contoured surface of the cam, where r = 0.15 m and z = (0.02 cos 2u) m.If the cam is rotating at a constant rate of 30 rad>s, determine the maximum and minimum force components Fz the
13–98. The spring-held follower AB has a mass of 0.5 kg and moves back and forth as its end rolls on the contoured surface of the cam, where r = 0.15 m and z = (0.02 cos 2u) m.If the cam is rotating at a constant rate of 30 rad>s, determine the force component Fz at the end A of the follower
13–97. A smooth can C, having a mass of 3 kg, is lifted from a feed at A to a ramp at B by a rotating rod. If the rod maintains a constant angular velocity of u#= 0.5 rad>s, determine the force which the rod exerts on the can at the instant u = 30. Neglect the effects of friction in the
*13–96. The particle has a mass of 0.5 kg and is confined to move along the smooth vertical slot due to the rotation of the arm OA. Determine the force of the rod on the particle and the normal force of the slot on the particle when u = 30. The rod is rotating with a constant angular velocity u
13–95. A car of a roller coaster travels along a track which for a short distance is defined by a conical spiral, r = 34 z, u = -1.5z, where r and z are in meters and u in radians. If the angular motion u#= 1 rad>s is always maintained, determine the r, u, z components of reaction exerted on
13–94. Using a forked rod, a smooth cylinder P, having a mass of 0.4 kg, is forced to move along the vertical slotted path r = (0.6u) m, where u is in radians. If the cylinder has a constant speed of vC = 2 m>s, determine the force of the rod and the normal force of the slot on the cylinder at
13–93. The girl has a mass of 50 kg. She is seated on the horse of the merry-go-round which undergoes constant rotational motion u#= 1.5 rad>s. If the path of the horse is defined by r = 4 m, z = (0.5 sin u) m, determine the maximum and minimum force Fz the horse exerts on her during the
*13–92. The tube rotates in the horizontal plane at a constant rate of u#= 4 rad>s. If a 0.2-kg ball B starts at the origin O with an initial radial velocity r#= 1.5 m>s and moves outward through the tube, determine the radial and transverse components of the ball’s velocity at the
13–91. The 40-kg boy is sliding down the smooth spiral slide such that z = -2 m>s and his speed is 2 m>s. Determine the r, u, z components of force the slide exerts on him at this instant. Neglect the size of the boy. Prob. 13-91 2. r = 1.5 m
13–90. The boy of mass 40 kg is sliding down the spiral slide at a constant speed such that his position, measured from the top of the chute, has components r = 1.5 m, u = (0.7t) rad, and z = (-0.5t) m, where t is in seconds. Determine the components of force Fr, Fu, and Fz which the slide exerts
13–89. The arm is rotating at a rate of u#= 4 rad>s when u$= 3 rad>s2 and u = 180. Determine the force it must exert on the 0.5-kg smooth cylinder if it is confined to move along the slotted path. Motion occurs in the horizontal plane. 6 = 4 rad/s, 0 = 3 rad/s/ 0 180 Prob. 13-89 = () m
*13–88. Using a forked rod, a 0.5-kg smooth peg P is forced to move along the vertical slotted path r = (0.5 u) m, where u is in radians. If the angular position of the arm is u = (p8 t2) rad, where t is in seconds, determine the force of the rod on the peg and the normal force of the slot on the
13–87. The 0.75-kg smooth can is guided along the circular path using the arm guide. If the arm has an angular velocity u #= 2 rad>s and an angular acceleration u$= 0.4 rad>s2 at the instant u = 30, determine the force of the guide on the can. Motion occurs in the horizontal plane. 0.5 m
13–85. Using air pressure, the 0.5-kg ball is forced to move through the tube lying in the horizontal plane and having the shape of a logarithmic spiral. If the tangential force exerted on the ball due to the air is 6 N, determine the rate of increase in the ball’s speed at the instant u =
F13–16. The 0.2-kg pin P is constrained to move in the smooth curved slot, which is defined by the lemniscate r = (0.6 cos 2u) m. Its motion is controlled by the rotation of the slotted arm OA, which has a constant clockwise angular velocity of u#= -3 rad>s. Determine the force arm OA exerts
F13–15. The 2-Mg car is traveling along the curved road described by r = (50e2u) m, where u is in radians. If a camera is located at A and it rotates with an angular velocity of u#= 0.05 rad>s and an angular acceleration of u $= 0.01 rad>s2 at the instant u = p6 rad, determine the resultant
F13–14. The 0.2-kg ball is blown through the smooth vertical circular tube whose shape is defined by r = (0.6 sin u) m, where u is in radians. If u = (p t2) rad, where t is in seconds, determine the magnitude of force F exerted by the blower on the ball when t = 0.5 s. 0.3 m Prob. F13-14
F13–13. Determine the constant angular velocity u#of the vertical shaft of the amusement ride if f = 45. Neglect the mass of the cables and the size of the passengers. 8 m 1.5 m Prob. F13-13
*13–84. The ball has a mass m and is attached to the cord of length l. The cord is tied at the top to a swivel and the ball is given a velocity v0. Show that the angle u which the cord makes with the vertical as the ball travels around the circular path must satisfy the equation tan u sin u =
13–83. The airplane, traveling at a constant speed of 50 m>s, is executing a horizontal turn. If the plane is banked at u = 15, when the pilot experiences only a normal force on the seat of the plane, determine the radius of curvature r of the turn. Also, what is the normal force of the seat
13–82. The 2-kg pendulum bob moves in the vertical plane with a velocity of 6 m>s when u = 0. Determine the angle u where the tension in the cord becomes zero. -2m- Probs. 13-81/82
13–81. The 2-kg pendulum bob moves in the vertical plane with a velocity of 8 m>s when u = 0. Determine the initial tension in the cord and also at the instant the bob reaches u = 30. Neglect the size of the bob. -2m- Probs. 13-81/82
*13–80. The 8-kg sack slides down the smooth ramp. If it has a speed of 1.5 m>s when y = 0.2 m, determine the normal reaction the ramp exerts on the sack and the rate of increase in the speed of sack at this instant. Prob. 13-80 0.2ex x
13–79. A collar having a mass 0.75 kg and negligible size slides over the surface of a horizontal circular rod for which the coefficient of kinetic friction is mk = 0.3. If the collar is given a speed of 4 m>s and then released at u = 0, determine how far, s, it slides on the rod before coming
13–78. Determine the maximum constant speed at which the 2-Mg car can travel over the crest of the hill at A without leaving the surface of the road. Neglect the size of the car in the calculation. y=20 (1 10 000- A 100 m- Prob. 13-78 x
13–77. The box has a mass m and slides down the smooth chute having the shape of a parabola. If it has an initial velocity of v0 at the origin, determine its velocity as a function of x. Also, what is the normal force on the box, and the tangential acceleration as a function of x? Prob. 13-77
*13–76. The 35-kg box has a speed 2 m>s when it is at A on the smooth ramp. If the surface is in the shape of a parabola, determine the normal force on the box at the instant x = 3 m.Also, what is the rate of increase in its speed at this instant? 2 m/s A Prob. 13-76 4. 119 x
13–75. Determine the maximum speed at which the car with mass m can pass over the top point A of the vertical curved road and still maintain contact with the road. If the car maintains this speed, what is the normal reaction the road exerts on the car when it passes the lowest point B on the
13–74. The block B, having a mass of 0.2 kg, is attached to the vertex A of the right circular cone using a light cord. The cone is rotating at a constant angular rate about the z axis such that the block attains a speed of 0.5 m>s. At this speed, determine the tension in the cord and the
13–73. The 0.8-Mg car travels over the hill having the shape of a parabola. When the car is at point A, it is traveling at 9 m>s and increasing its speed at 3 m>s2. Determine both the resultant normal force and the resultant frictional force that all the wheels of the car exert on the road
*13–72. The 0.8-Mg car travels over the hill having the shape of a parabola. If the driver maintains a constant speed of 9 m>s, determine both the resultant normal force and the resultant frictional force that all the wheels of the car exert on the road at the instant it reaches point A. Neglect
13–71. A ball having a mass 2 kg and negligible size moves within a smooth vertical circular slot. If it is released from rest when u = 10, determine the force of the slot on the ball when the ball arrives at points A and B. 10 0. r = 0.8 m A 10 B Prob. 13-71
13–70. The 800-kg motorbike travels with a constant speed of 80 km>h up the hill. Determine the normal force the surface exerts on its wheels when it reaches point A. Neglect its size. 100 m Prob. 13-70 A 2x -x
13–69. The skier starts from rest at A(10 m, 0) and descends the smooth slope, which may be approximated by a parabola.If she has a mass of 52 kg, determine the normal force the ground exerts on the skier at the instant she arrives at point B. Neglect the size of the skier. 5 m 10 m y = x- 201 5
*13–68. Prove that if the block is released from rest at point B of a smooth path of arbitrary shape, the speed it attains when it reaches point A is equal to the speed it attains when it falls freely through a distance h; i.e., v = 22gh. h B Prob. 13-68
13–67. Bobs A and B of mass mA and mB (mA > mB) are connected to an inextensible light string of length l that passes through the smooth ring at C. If bob B moves as a conical pendulum such that A is suspended a distance of h from C, determine the angle u and the speed of bob B.Neglect the
13–66. Determine the constant speed of the passengers on the amusement-park ride if it is observed that the supporting cables are directed at u = 30 from the vertical. Each chair including its passenger has a mass of 80 kg. Also, what are the components of force in the n, t, and b directions
13–65. The vehicle is designed to combine the feel of a motorcycle with the comfort and safety of an automobile. If the vehicle is traveling at a constant speed of 80 km>h along a circular curved road of radius 100 m, determine the tilt angle u of the vehicle so that only a normal force from
*13–64. The 1.40-Mg helicopter is traveling at a constant speed of 33 m>s along the horizontal curved path having a radius of curvature of r = 300 m. Determine the force the blade exerts on the frame and the bank angle u. P 0 Probs. 13-63/64
13–63. The 1.40-Mg helicopter is traveling at a constant speed of 40 m>s along the horizontal curved path while banking at u = 30°. Determine the force acting normal to the blade, i.e., in the y¿ direction, and the radius of curvature of the path. P 0 Probs. 13-63/64
13–62. The 2-kg spool S fits loosely on the inclined rod for which the coefficient of static friction is ms = 0.2. If the spool is located 0.25 m from A, determine the maximum constant speed the spool can have so that it does not slip up the rod. A 0.25 ms Probs. 13-61/62
13–61. The 2-kg spool S fits loosely on the inclined rod for which the coefficient of static friction is ms = 0.2. If the spool is located 0.25 m from A, determine the minimum constant speed the spool can have so that it does not slip down the rod. A 0.25 ms Probs. 13-61/62
*13–60. Determine the maximum constant speed at which the pilot can travel around the vertical curve having a radius of curvature r = 800 m, so that he experiences a maximum acceleration an = 8g = 78.5 m>s2. If he has a mass of 70 kg, determine the normal force he exerts on the seat of the
13–59. Cartons having a mass of 5 kg are required to move along the assembly line at a constant speed of 8 m>s.Determine the smallest radius of curvature, r, for the conveyor so the cartons do not slip. The coefficients of static and kinetic friction between a carton and the conveyor are ms =
13–58. The 2-kg block B and 15-kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block travels along a circular path of radius r = 1.5m, determine the speed of the block. Probs. 13-57/58 B
13–57. The 2-kg block B and 15-kg cylinder A are connected to a light cord that passes through a hole in the center of the smooth table. If the block is given a speed of v = 10 m>s, determine the radius r of the circular path along which it travels.
*13–56. A 5-Mg airplane is flying at a constant speed of 350 km>h along a horizontal circular path. If the banking angle u = 15°, determine the uplift force L acting on the airplane and the radius r of the circular path. Neglect the size of the airplane. Probs. 13-55/56
13–55. A 5-Mg airplane is flying at a constant speed of 350 km>h along a horizontal circular path of radius r = 3000 m. Determine the uplift force L acting on the airplane and the banking angle u. Neglect the size of the airplane.
13–54. The collar A, having a mass of 0.75 kg, is attached to a spring having a stiffness of k = 200 N>m. When rod BC rotates about the vertical axis, the collar slides outward along the smooth rod DE. If the spring is unstretched when s = 0, determine the constant speed of the collar in order
13–53. A girl, having a mass of 15 kg, sits motionless relative to the surface of a horizontal platform at a distance of r = 5 m from the platform’s center. If the angular motion of the platform is slowly increased so that the girl’s tangential component of acceleration can be neglected,
*13–52. A girl having a mass of 25 kg sits at the edge of the merry-go-round so her center of mass G is at a distance of 1.5 m from the axis of rotation. If the angular motion of the platform is slowly increased so that the girl’s tangential component of acceleration can be neglected, determine
F13–12. The motorcycle has a mass of 0.5 Mg and a negligible size. It passes point A traveling with a speed of 15 m>s, which is increasing at a constant rate of 1.5 m>s2.Determine the resultant frictional force exerted by the road on the tires at this instant. PA = 200 m Prob. F13-12
F13–11. If the 10-kg ball has a velocity of 3 m>s when it is at the position A, along the vertical path, determine the tension in the cord and the increase in the speed of the ball at this position. 2 m 0 = 45 Prob. F13-11 A 3 m/s
F13–10. The sports car is traveling along a 30 banked road having a radius of curvature of r = 150 m. If the coefficient of static friction between the tires and the road is ms = 0.2, determine the maximum safe speed so no slipping occurs. Neglect the size of the car. p 150 m- Prob. F13-10 0 = 30
F13–9. A pilot weighs 70 kg and is traveling at a constant speed of 36 m>s. Determine the normal force he exerts on the seat of the plane when he is upside down at A. The loop has a radius of curvature of 120 m. 120 m |A Prob. F13-9
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